論文 / 著書情報
Article / Book Information
題目(和文)
Title(English)

MODELLING ESTABLISHMENT OF TEMPORARY LOGISTICS HUB
FOR HUMANITARIAN RELIEF OPERATIONS

著者(和文)

MAHARJANRajali

Author(English)

Rajali Maharjan

出典(和文)

学位:博士(学術),学位授与機関:東京工業大学,
報告番号:甲第11002号,
授与年月日:2018年9月20日,
学位の種別:課程博士,
審査員:花岡 伸也,髙田 潤一,髙木 泰士,朝倉 康夫,福田 大輔

Citation(English)

Degree:Doctor (Academic),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第11002号,
Conferred date:2018/9/20,
Degree Type:Course doctor,
Examiner:,,,,

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Science Tokyo Research Repository)

MODELLING ESTABLISHMENT OF TEMPORARY LOGISTICS HUB
FOR HUMANITARIAN RELIEF OPERATIONSA Dissertation
Submitted to the Department of International Development Engineering
In Partial Fulfillment of the Requirements of the Degree ofDoctor of Philosophy

Rajali Maharjan
2018

Graduate School of Science and Engineering
Tokyo Institute of Engineering© 2018 Rajali Maharjan

ACKNOWLEDGEMENT
I would like to thank a number of people without whom this thesis would not have beenpossible.
Firstly, I would like to express my sincere gratitude to my supervisor Professor Shinya Hanaoka
for the continuous support during my PhD study and other extracurricular activities, for hispatience, freedom, motivation, time, effort, and immense knowledge. His guidance has helped
me to be the person I am today. I could not have imagined a better supervisor for my PhD study.
I would also like to gratefully thank Transport Studies Unit Professor Yasuo Asakura, Professor
Tetsuo Yai, Associate Professor Daisuke Fukuda, and Associate Professor Yasunori
Muromachi for the insightful comments and constructive criticisms which helped me togradually better my thesis.
Besides my supervisor, I would like to thank the rest of my thesis committee: Professor Yasuo
Asakura, Associate Professor Daisuke Fukuda, Professor Junichi Takada, and Associate
Professor Hiroshi Takagi for their insightful comments and suggestions, but also for the hardquestions which incented me to widen my research from various perspectives.
I thank my fellow lab mates for the stimulating discussions, all the cherishable moments,
support, and motivation. Their support and motivation helped me to overcome setbacks andstay focused on my graduate study. I greatly value their friendship and I deeply appreciate theirbelief in me.
Above all, I would like to thank my family and specially my husband for the love, patience,and support throughout my doctoral journey. I dedicate this thesis to the memory of my father
whose dreams I am living with the completion of this thesis.
In loving memory of my father Ramesh Maharjan (1961-2011).

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ABSTRACTDisaster response operations are inherently complicated. Despite the complexities,
uncertainties, and lack of sufficient information about the extent of the damages, disaster
response facilities must be set up quickly after the occurrence of the disaster. Disaster response
facility like temporary logistics hub plays a momentous role in increasing the efficiency andeffectiveness of humanitarian relief operations. Establishment of temporary logistics hubs
(TLH) requires multitude of decisions be made within a very short span of time while also
taking account of multiple objectives, multiple actors, need for evaluation of both qualitativeand quantitative attributes, and consideration of uncertain and time-varying nature ofparameters. Moreover, the decision on whether to open, how many to open, where to locate,when to open, how to allocate open facilities to demand points, and determining the order of
establishment of TLHs is based purely on the amount and the quality of information available
during the decision-making time. This necessitates involvement of range of decision-makers
with diverse background to be involved in the decision making process so as to enable
synthesizing more and better information.
This study deals with the establishment of TLHs. The study developed mathematical models,decision-making approach involving multiple decision-makers, and has amalgamatedmathematical models with decision-making approach to enable comprehensive TLH
establishment decision-making. Firstly, a multi-period multi-objective model with multisourcing is developed to determine the location of the TLHs. A fuzzy factor rating system(FFRS) under the group decision-making (GDM) condition is then proposed to determine theweights of the objectives when multiple objective and multiple decision-makers exist. Second,a possibilistic multi-objective location-allocation model for relief supply and distribution
considering uncertain and time-varying nature of demand, costs, and available quantities ofrelief, time-varying coverage is developed while also accommodating qualitative attributes
necessary to determine when and where to establish (TLH) along with their numbers in eachworking period. Finally, a decision support system that considers multiple decision-makers andsubjective attributes, while also addressing the impreciseness inherent in post-disaster
decision-making is developed for ordering the establishment of TLHs. To do so, an
optimization model was combined with a fuzzy multi-attribute group decision-making
approach.

iv

Numerical illustrations were performed for the three models using data from the April 2015
Nepal earthquake. The methodology developed herein offers managerial insights for postdisaster decision-making within a short span of time when resources are limited and theireffective utilization is vital. The optimization results provide useful managerial insights for
decision-makers by considering the trade-off between two non-commensurable objectives;
determining the optimal number along with where, when, and in what order to establish TLHs.
The interview with decision-makers shows the heterogeneity of decision opinions, thus
substantiating the importance of group decision-making. The results also highlight theimportance of considering the opinions of multiple actors/decision-makers to enable
coordination and avoid complication between the growing numbers of humanitarian responders
during disaster response.

v

Table of content
ACKNOWLEDGEMENT ....................................................................................................... iii
ABSTRACT .............................................................................................................................. iv
LIST OF FIGURES .................................................................................................................. ix
LIST OF TABLES ..................................................................................................................... x
CHAPTER 1 Introduction.......................................................................................................... 1
1.1 Background ...................................................................................................................... 1
1.2 Research motivation ......................................................................................................... 6
1.3 Temporary logistics hub (TLH) ....................................................................................... 8
1.4 Aims and objectives ....................................................................................................... 12
1.5 Scope and limitations of the study ................................................................................. 13
1.6 Outlines and approach of the study ................................................................................ 14
1.7 Contributions of the study .............................................................................................. 16
CHAPTER 2 Literature review ................................................................................................ 17
2.1 Chapter overview ........................................................................................................... 17
2.2 Disaster and disaster management ................................................................................. 17
2.3 Humanitarian logistics.................................................................................................... 19
2.4 Facility location in humanitarian operations .................................................................. 20
2.4.1 Based on length of operational horizon ................................................................... 21
2.4.2 Based on state of facilities ....................................................................................... 21
2.4.3 Based on number of objective ................................................................................. 21
2.4.4 Based on the nature of parameters ........................................................................... 22
2.4.5 Based on the role/purpose of facilities .................................................................... 22
2.5 Single objective FLP ...................................................................................................... 22
2.6 Multi-objective facility location problem ...................................................................... 27
2.6.1 A priori method ....................................................................................................... 27
2.6.2 A posteriori method ................................................................................................. 27
2.7 Temporary facility location problem during disaster response ...................................... 28
2.8 Multi-criteria FLP .......................................................................................................... 29
2.9 Decision making during disaster response ..................................................................... 31
2.10 Group decision making (GDM) ................................................................................... 32
2.11 Uncertainty in humanitarian operations ....................................................................... 32
2.11.1 Stochastic optimization.......................................................................................... 33
2.11.2 Robust optimization ............................................................................................... 33

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2.11.3 Fuzzy programming ............................................................................................... 33
2.12 Positioning in the current literature .............................................................................. 38
2.13 Chapter summary ......................................................................................................... 39
CHAPTER 3 A multi-actor multi-objective optimization approach for locating temporary
logistics hubs during disaster response .................................................................................... 41
3.1 Introduction .................................................................................................................... 41
3.2 Fuzzy factor rating system under group decision making.............................................. 42
3.3 Problem description........................................................................................................ 43
3.4 Methodology .................................................................................................................. 44
3.4.1 Mathematical model formulation ............................................................................ 44
3.4.1.1 Model assumptions ........................................................................................... 45
3.4.1.2 Nomenclature .................................................................................................... 46
3.4.1.3 Formulation ....................................................................................................... 47
3.4.2 Solution strategy for the multi-objective TLH location model ............................... 48
3.4.3 Fundamentals of fuzzy set theory ............................................................................ 50
3.4.4 Algorithm of an FFRS under the GDM condition ................................................... 53
3.5 Model discussion ............................................................................................................ 54
3.6 Numerical illustration and analysis ................................................................................ 55
3.6.1 April 2015 Nepal earthquake ................................................................................... 55
3.6.2 Nature of the data .................................................................................................... 56
3.6.3 Results ..................................................................................................................... 58
3.6.3.1 Calculating the weight of the objectives ........................................................... 58
3.6.3.2 Optimization results .......................................................................................... 59
3.7 Chapter summary ........................................................................................................... 64
CHAPTER 4 A credibility based multi-objective temporary logistics hub location-allocation
model for relief supply and distribution under uncertainty ..................................................... 65
4.1 Introduction .................................................................................................................... 65
4.2 Problem description........................................................................................................ 67
4.3 Mathematical model formulation ................................................................................... 68
4.3.1 Assumptions ............................................................................................................ 68
4.3.2 Nomenclature........................................................................................................... 69
4.3.3 Formulation ............................................................................................................. 70
4.4 Solution strategy............................................................................................................. 72
4.4.1 Determine the values of qualitative attributes ......................................................... 72
4.4.2 Convert the multi-objective possibilistic model to single objective model............. 72vii

4.4.3 Apply fuzzy chance constrained programming approach to the possibilistic modeland obtain its crisp equivalent .......................................................................................... 73
4.5 Numerical illustration and analysis ................................................................................ 77
4.5.1 Relief chain configuration ....................................................................................... 77
4.5.3 Results ..................................................................................................................... 79
4.5 Chapter summary ........................................................................................................... 87
CHAPTER 5 Fuzzy multi-attribute group decision-making for ordering the establishment of
temporary logistics hubs .......................................................................................................... 89
5.1 Introduction .................................................................................................................... 89
5.2 Fuzzy multi-attribute group decision-making ................................................................ 90
5.3 Model formulation.......................................................................................................... 91
5.3.1 Selection of location alternatives for TLHs ............................................................. 92
5.3.2 Determining the importance weight of attributes .................................................... 94
5.3.3 Identifying the order of establishment of TLHs ...................................................... 97
5.4 Numerical illustration and analysis ................................................................................ 99
5.4.1 Optimal number and the spatial location of TLHs .................................................. 99
5.4.2. Determining the importance weight of attributes ................................................. 100
5.4.3 Order of establishment of TLHs ............................................................................ 102
5.5 Chapter summary ......................................................................................................... 107
CHAPTER 6 Summary and Conclusion ................................................................................ 109
6.1 Facility location in perspective .................................................................................... 109
6.2 Summary and Conclusion ............................................................................................ 109
6.3 Comparison of results................................................................................................... 112
6.4 Practical implication and applicability ......................................................................... 113
6.5 Recommendation for future establishment of TLHs .................................................... 114
6.6 Scope of future work .................................................................................................... 117
REFERENCES ...................................................................................................................... 119
APPENDIX ............................................................................................................................ 127

viii

LIST OF FIGURES
Figure 1.1: Regional logistics hubs established during Nepal earthquake 2015 ....................... 3
Figure 1.2: Regional logistics hubs during Ecuador earthquake 2016 ...................................... 4
Figure 1.3: Use of storage services in Dhulikhel hub ................................................................ 7
Figure 1.4: Structure of humanitarian relief chain ..................................................................... 9
Figure 1.5: Mobile storage units .............................................................................................. 10
Figure 1.6: Details of MSU used by WFP ............................................................................... 11
Figure 1.7: Setup of mobile storage units ................................................................................ 12
Figure 1.8: Forklift used for handling relief materials in mobile storage units ....................... 12
Figure 1.9: Organization of the dissertation ............................................................................ 15
Figure 2.1: Disaster management cycle ................................................................................... 18
Figure 3.1: A trapezoidal fuzzy number .................................................................................. 51
Figure 3.2: Location of supply points, candidate TLHs, and demand points .......................... 57
Figure 3.3: Spatial location of the optimal TLHs .................................................................... 60
Figure 3.4: Change in the cost attributes and unsatisfied demand with a changing number of
TLHs ........................................................................................................................................ 61
Figure 3.5: Change in location choices with changing number of TLHs ................................ 62
Figure 3.6: Comparison of single-sourcing with multi-sourcing ............................................. 63
Figure 4.1: Illustration of concept of time-varying coverage .................................................. 68
Figure 4.2: Spatial location of supply points, candidate TLHs, and PODs ............................. 78
Figure 4.3: Optimal location of TLHs considering multiple objectives with uncertainty inparameters when minimizing total cost ................................................................................... 80
Figure 4.4: Optimal location of TLHs considering multiple objectives with deterministic
parameters when minimizing total cost ................................................................................... 83
Figure 4.5: Sensitivity analysis on confidence level (α) .......................................................... 86
Figure 4.6: Sensitivity analysis for spread of symmetric triangular fuzzy number ................. 86
Figure 5.1: Spatial location of temporary logistics hubs ....................................................... 100
Figure 5.2: Performance of TLHs over all attributes ............................................................. 106
Figure 6.1: Facility location problem in perspective ............................................................. 109ix

LIST OF TABLES
Table 2.1: List of single objective optimization based studies on FLP ................................... 24
Table 2.2: List of multi-objective optimization based studies on FLP .................................... 25
Table 2.3: List of studies focusing on temporary FLP............................................................. 26
Table 2.4: List of multi-criteria FLP studies ............................................................................ 30
Table 2.5: List of studies taking account of uncertainty for modeling location problem ........ 36
Table 3.1: Linguistic variables and fuzzy numbers ................................................................ 52
Table 3.2: Importance ratings of the objectives ....................................................................... 58
Table 3.3: Aggregated fuzzy ratings of the objectives ............................................................ 59
Table 3.4: Defuzzified values of the aggregated fuzzy rating and normalized weights of theobjectives ................................................................................................................................. 59
Table 3.5: Sensitivity of the available quantity of relief materials in the TLHs ...................... 62
Table 4.1: Nature of input parameters ..................................................................................... 79
Table 4.2: Allocation of relief supplies from supply points to TLHs (in 10,000 kg) .............. 81
Table 4.3: Allocation of relief supplies from TLHs to POD (in 10,000 kg)............................ 82
Table 4.4: Comparison of the results of multi-objective model with uncertainty in parametersand deterministic parameters ................................................................................................... 84
Table 4.5: Sensitivity analysis on the number of TLHs ........................................................... 85
Table 5.1: Linguistic variables and fuzzy numbers for ratings ................................................ 96
Table 5.2: Description of the attributes.................................................................................. 101
Table 5.3: The importance weight of attributes ..................................................................... 102
Table 5.4: Decision-makers’ evaluation and fuzzy rating matrix .......................................... 103
Table 5.5: Fuzzy rating matrix ............................................................................................... 104
Table 5.6: Aggregated fuzzy number, defuzzified total score, and order of establishment .. 105
Table 5.7: Comparison of single and multiple actor scenarios .............................................. 107
Table 6.1: Details of storage hubs during Nepal earthquake 2015 ........................................ 115
Table 6.2: Summary of the TLH selection............................................................................. 116

xCHAPTER 1 Introduction

1.1 BackgroundIn the recent years, the world has witnessed several devastating disasters and a significant
growth in human life losses, economic losses, and material damages caused by natural disasters
such as earthquakes, flood, tsunami, and storm. Disaster management entails all the activities
taken before, during, and after the disaster with the aim of getting back to normalcy while
minimizing its impacts. Although knowing what to do, how to do it, and having the resourcesto actually do it helps to increase the chance of survival and limits damages, given the disaster’s
unpredictability of the occurrence and its corresponding impacts, preparedness and mitigation
activities often tend to be very costly to implement. Therefore, effective disaster response
becomes critical to ensure success of disaster management activities.
Effective disaster salvage requires implementing different disaster response facilities
immediately after a disaster has occurred. The location of facilities, particularly distribution
centers, warehouses, medical centers, and shelters, plays a significant role in ensuring the
success of emergency humanitarian relief operations. From a logistics point of view, aneffective response to a crisis demands setting up logistics hubs and/or distribution centers inappropriate locations. In the pre-disaster stage, facility location planning includes finding
locations for warehouses, distribution centers, and evacuation centers based on assumed
scenarios, while in the post-disaster stage, such planning includes locating emergency shelters,
medical centers, relief distribution centers, and logistics hubs for a particular disaster-affectedarea.
Of the numerous types of facilities prevalent in humanitarian operations, this study focuses on
those intended for relief distribution. These facilities can be categorized as permanent or
temporary based on the length of their operational horizon. Permanent facilities operate before
the disaster and have long or even infinite operational horizon, whereas temporary response
facilities only operate once the location of the disaster is known and have a short operational
horizon. While determining the location for a permanent facility is a strategic decision, doing
so for temporary facility is a tactical/operational decision with which decision-makers are faced
after a disaster.

1

In the ideal situation, vulnerable countries should prepare designated spaces for these facilities
along with safety stockpiles in advance of any disaster occurring, however, the situation inreality is often different. Although no specific correlation between investment in disaster
preparedness and a country’s GDP has been established, developed countries are typically
better prepared to tackle the consequences of disasters compared with developing nations. If
we examine the earthquakes that have recently impacted developed countries such as New
Zealand and Japan, namely the earthquake in Christchurch in 2011 and the Great East Japan
earthquake in 2011, respectively, although they caused widespread damage, the resulting
fatality rate was relatively modest (Lubkowski, 2014). By contrast, even relatively moderate
earthquakes in developing nations still lead to large losses of life. The earthquakes in Haiti in2010 and Nepal in 2015 are prime examples (Lubkowski, 2014).
The lack of advance preparedness in emerging countries suggests the need for an appropriate,
effective, and efficient response. Moreover, the unpredictability of disasters prevents
authorities from determining an exact location for emergency facilities beforehand and giventhat permanent facilities alone may be insufficient, emergency temporary facilities become
especially important in developing countries where disaster preparedness falls short. One
important feature of these facilities is their short operational horizon (i.e., they are removed
soon after the response stage is over) (WFP, 2016). Temporary facilities have been deployed
in recent emergency humanitarian response operations such as the April 2015 Nepal earthquake(Figure 1.1) and April 2016 Ecuador earthquake (Figure 1.2). In figure 1.1, rectangular shapeshows the location of staging areas and circles shows the location of regional logistics hubs. It
can be observed that Kathmandu and Bharatpur operates as staging area with much bigger
capacity than the logistics hubs. The different size of the circles represents difference in thecapacity of the logistics hubs: a bigger circle represents a higher capacity and vice versa.
Regional logistics hubs in Dhulikhel, Deurali, Chautara, Chariokot, Bidur, and Dhadingbesi
have capacities in descending order.

2

Figure 1.1: Regional logistics hubs established during Nepal earthquake 2015
Source: Logistics Cluster, Nepal 2015
The appropriateness of a logistics hub’s location can determine the success or failure of ahumanitarian relief operation. However, the unpredictability of disasters makes it difficult toascertain the precise location of logistics hubs beforehand. Moreover, high inventory holding
costs, as well as limited funds and operating resources often restrict the number of permanent
facilities. Therefore, the temporary nature of such facilities is an indispensable part ofhumanitarian relief operations (Maharjan and Hanaoka, 2018). A typical location problem
includes ascertaining the number, spatial location, and the allocation of demand to open
facilities. On the other hand, locating TLHs during disaster response also requires determining
the timing and the order of establishment of the facilities when resources are limited. The
disaster response operation in most emerging countries is resource constrained and requires theeffective allocation of resources to ensure their effective utilization. During the initial response
stage of the 2015 Nepal earthquake, the number of mobile storage units available in-country
was limited, which resulted in several hindrances faced during establishment of regional

3

logistics hubs—including delay in establishment and mobile storage units having insufficient
capacity.

Figure 1.2: Regional logistics hubs during Ecuador earthquake 2016
Source: Logistics Cluster, Ecuador 2016
Selecting where, when, and in what order to locate temporary facilities for emergency
operations is an important task. On the contrary, response operations are inherently
complicated. This is often complicated by time-varying and uncertain nature of the disaster
impact, the growing number of humanitarian actors, prevalence of multiple and often
conflicting objectives, need to evaluate non-quantitative attributes, and inherent complexity
and uncertainty of the situation. These factors can significantly affect the overall performanceof the relief chain network.
Time-varying nature may arise due to a number of reasons. These reasons include aftershock
damages, people returning to greater self-sufficiency, beneficiaries moving between different
areas in hopes of finding greater relief, or unexpected challenges such as outbreak of disease
epidemics, issues with availability of relief, and the market dynamics induced by the disaster.
Due to the chaotic situation in the critical period, the information is always incomplete,inaccurate and changing over time.

4Uncertainty may arise due to randomness or/and fuzziness (Pishvaee and Torabi, 2010,
Pishvaee et al. 2012, and Tofighi et al. 2016). Randomness stems from the random nature ofdata for which, discrete or continuous probability distributions are estimated based on available
but sufficient objective/historical data. Fuzziness arises due to the impreciseness in predicting
the parameter value either due to lack of knowledge regarding their exact values i.e., facingwith epistemic uncertainty about these data (Kabak and Ulengin, 2011, Pishvaee and Torabi,2010) or due to information asymmetry. In the context of disaster response operations,
uncertainty arising due to random nature of disaster can be avoided since the location of disasterand demand can be obtained soon after the occurrence of disaster. However, the uncertainty
arising due to fuzziness may persist long after its occurrence. This type of uncertainty includes
those data such as demand of relief items, costs, and relief availability. Factors like inefficiency
in needs assessment, information asymmetry, lack of information, and lack of coordination
between the responding entities are the major sources of this kind of uncertainty. Moreover,depending on the location of disaster occurrence, the districts in need may be situated in remoteareas, and the disaster site might be in a state of chaos making a complete overview impossible
to achieve (Thomas and Kopczak, 2005).
The inclusion of multiple actors is important to build a sense of ownership of the establishedfacilities, a lack of which was identified to be one of the bottlenecks in the successful operationof regional logistics hubs during the April 2015 Nepal earthquake (WFP, 2016). While thehumanitarian code of conduct prioritizes minimizing victims’ suffering, the budgetary
limitations and organizational and environmental constraints creates a trade-off situation. In
reality, relief organizations commonly plan and execute logistics activities within the confinesof a limited budget (Cook and Lodree, 2012) highlighting the importance of minimizing
operational costs where a balance is always sought between the humanitarian and cost based
objectives.
In location decision-making, traditional network models take into account quantitative factors
and aim to minimize the total cost or to maximize profitability or coverage. Non-quantitative
criteria—such as, manpower qualifications, geographical characteristics, and road networks—
are also important in deciding location. While optimization approaches can be used forevaluating quantitative factors, this evaluation of qualitative factors is often accompanied by
ambiguity and vagueness (Önüt et al. 2010). This is particularly true in the aftermath of adisaster, when the environment is chaotic, and there is limited information and time. In the5aftermath of a disaster the decision-making process typically involves multiple decisionmakers with varying interests and opinions. Indeed, the growing complexity and uncertainty ofdecision situations make it less and less possible for a decision-maker to consider all relevant
aspects of a problem, thereby necessitating the participation of multiple experts in the decisionmaking process (Ben-Arieh and Z. Chen, 2006). As such, achieving a proper balance among
them is a significant challenge.
Essentially, disaster managers have to make myriad of reactive operational decisions to solve
complex dilemmas with little to no information under immensely stressful conditions as they
respond to emergencies. Moreover, current guidance suggests that within the humanitarian
coordination architecture, decisions should be made by a group rather than by individuals(IASC, 2009, 2015). As the number of actors involved in disaster response operations has
continued to grow, a complex network that often struggles to efficiently coordinate efforts has
emerged (Balcik et al., 2010; Bharosa et al., 2010; Bealt et al., 2016). This highlights the needfor a simple and inclusive methodology. Under these circumstances, an appropriate decisionmaking strategy would require that the resolutions and opinions of a group of decision-makers
be taken into account when evaluating the subjective and objective attributes in the TLH
selection process.
Indeed, Ortuno et al. (2013) concluded the need to use a decision support system incorporating
optimization tools to enhance applicability in real life. However, existing studies that focus on
temporary facilities (Afshar and Haghani, 2012; Lin et al., 2012; Khayal et al., 2015; Stauffer
et al., 2016; Cavdur et al., 2016) formulate their problems as single objective optimization
problems without concerning for uncertainty arising due to impreciseness. Moreover, theamalgamation of optimization models and decision-making approaches with group decision
theories to determine the location of temporary facilities for emergency operations is alsolacking in the literature.
1.2 Research motivation
With the advent of a disaster, one can only attempt to minimize its impact and corresponding
damages and suffering caused. Irrespective of the level of preparedness, the inherently
unpredictable nature of disasters prevent determining the precise location of the response
facilities beforehand. Moreover, the level of disaster preparedness is non uniform in the
different parts of the world. The developing and underdeveloped countries lag far behind their6

developed counterparts. In situations like this, temporary response facilities plays a very
important role in enhancing the disaster response operations.
Recent humanitarian disaster response operations have seen growing utilization of temporary
nature of response facilities for example during the disaster response in Nepal earthquake 2015
(Figure 1.1) and Ecuador earthquake 2016 (Figure 1.2). This dissertation gains its motivationfrom the April 2015 Nepal earthquake. Having closely observed disaster response operations
performed by government, national and international humanitarian organizations, community
organizations religious groups during Nepal earthquake 2015, one thing was for sure that thetemporary nature of response facilities are very important to facilitate relief distribution toaffected people/communities. Traditionally, key decisions to make regarding temporary
response facilities are (1) how many facilities to establish; (2) where to establish; (3) how toallocated demand to open facilities. However, due to the dynamics of the situation additional
aspects regarding (4) how to accommodate multiple decision-makers who may have same orvarying preferences; (5) how to account for uncertainty arising due to impreciseness; (6) how
to effectively utilize limited resources etc.

Figure 1.3: Use of storage services in Dhulikhel hub(a) Storage per sector in % of total m3 stored(b) Top 10 users in terms of m3 stored
Source: Logistics Cluster, 2015
Nepal’s disaster response operations involved establishment of nine hubs in different parts ofthe country and 117 organizations have used the storage service, a total of 37,227 m3 was stored
in the hubs until the end of September. Number of organizations using the hubs range between
four in Dhunche to 86 in Kathmandu. Figure 1.3 shows the usage of storage service in7

Dhulikhel hub where multiple relief items and multiple organization’s involvement can beobserved from (a) and (b). However, one of the main shortcoming of the entire operational
strategy was the time it took to identify the location and set up hubs. The earliest identificationof the hub location took as long as two weeks (Logistics cluster, 2016). Further, the operationof established hubs faced ownership issues because organizations were willing to use but notwilling to take responsibility of its operation.
This dissertation aims to address the shortcomings faced during Nepal earthquake and buildon the existing literature in humanitarian logistics by developing comprehensive models andmethodologies for making establishment decisions.
1.3 Temporary logistics hub (TLH)
Temporary logistic hub is a place designated for short term storing, sorting, consolidating,deconsolidating, and distributing emergency relief materials to the final distribution centers. It
acts as an intermediator between the central warehouse or point of entry and the points of
distribution (POD). Figure 1.4 shows the positioning of the TLH in the humanitarian relief
chain. It is established in the response phase of the disaster (especially appropriate in thedeveloping countries where the level of disaster preparedness is low). Often mobile storage
units (MSUs) or movable warehouses (also referred to as WiikHalls or RubbHalls) are used as
TLHs where hard structures are unavailable or inadequate. Features of temporary logistic hub:

Its operational horizon is short, which essentially depends on the scale of disaster,
severity of its impact, population size, and economic situation of affected areas,
accessibility issues, and market functionality.



TLHs are time-varying in nature which can be opened, closed, and relocated within theoperational horizon.



TLH uses storage units that can be assembled, dissembled, and transported within ashort period of time without much hassle.

8

Figure 1.4: Structure of humanitarian relief chain
MSUs can be easily assembled, disassembled, and transported. These mobile storage units arefire retardant, waterproof, rot proof, and UV stabilized and are usually costly. MSUs are mostoften used in sizes 10×20 meters to 10×32 meters. Most systems can be erected in 4 meter
lengths, allowing for customization between these sizes. They are steel or aluminum frame(aluminum being much lighter and therefore cheaper for shipment) with heavy polyester cover.
MSUs should be erected on flat hard earth, on raised elevation to protect against flooding.
When planning locations, care should be taken that trucks have sufficient access. Pallets should
be used to raise stored goods off the ground. It is possible to install MSUs with local labor –WFP will often provide technical oversight if requested. WFP contractors, and other privatecompanies are also options for support in erecting the MSUs. Key features of MSUs can besummarized as:Fast set up with three to four personnel without use of lifting equipment or working onheights. Figure 1.7 shows schematic of MSU setup.

Made of durable aluminum box profiles and hot-dipped galvanized hardware, withcovers of durable fire retardant and UV resistant translucent PVC fabric and fully HF
welded for long life.

Designed to withstand high winds up to 31 m/s (<110 km/h) and can be used in both
hot and cold climates.

9

Figure 1.5: Mobile storage units
MSU transport crates are too large for commercial airlines, so transportation will be via sea orlarge cargo planes. For planning the size of warehouse needed, WFP estimates a-

10x24m MSU can store 350-500 metric tons of food goods;-

10x32m will hold 500-750 metric tons.

In this study, we use a 10m x 32m MSU. Different humanitarian organizations have different
sizing, features and preferences for the type of MSUs they use, figure 1.5 and figure 1.6 shows
examples of MSUs used by different organizations. Figure 1.6 shows the details of MSU used
by WFP with dimension and materials. The modularity of MSUs enables ease in capacity
expansion and reduction since the length of the MSUs can be endlessly extended with additionof extra modules. The application of this modularity can be observed from figure 1.1, where
logistics hubs of different sizes and capacities were established in different locations. In
addition to having proper vehicle accessibility to the TLHs, it is also important to ensure that
forklifts (shown in figure 1.8) are available to handle relief goods within the established MSUs.

10

Dimensions
Standard size
Total living area
Main floor

6.5 m x 8 m
52 m2
52 m2

Centre height
Width
Ridge height

3.90 m6.50 m8.00 mSide wall height

2.50 mTotal size

2.90 m x 3.00 m

Modular frame

Aluminium box profiles 2.70 m – 3.50 m: Hot dipped galvanized steel
apex base plates and other steel components

Materials
Outer tent
Ventilators
Doors
Modularity

Roof, wall, gable covers: 700 gsm PVC coated polyester, white, UV
protected
The gable ends are fitted with high placed large ventilators withremovable mosquito netting and adjustable rain flap.
Both gable ends are fitted with lace up doors, 290X300 cm.
The length of the shelter can be endlessly extended with modules of
6.5 x 3 m or 6.5 x4 m
Figure 1.6: Details of MSU used by WFP

11

Figure 1.7: Setup of mobile storage units

Figure 1.8: Forklift used for handling relief materials in mobile storage units
1.4 Aims and objectives
The aim of this dissertation is to introduce the concept of temporary logistics hubs for effective
disaster response and answer the questions of where, when, in what order should TLHs beestablished and how to allocate demand to open facilities in the disaster response period. In
12doing so, the study aims to develop models that take account of the trade-off relationshipbetween different objectives, qualitative attributes, multiple decision-makers, challenges facedby the decision-makers during the chaotic and often ambiguous disaster response period.
To achieve this aim, the following specific objectives are drawn:
1. To develop a multi-actor multi-objective optimization approach for determining thelocation of TLHs during disaster response and identify if the multi-actor existing indisaster management/response will have different preference for different objectives.
2. To develop a multi-objective optimization model that determines the location andallocation of TLHs under epistemic uncertainty in parameters.
3. To determine the order of establishment of TLHs taking account of quantitative andqualitative attributes to ease TLH setting up process post disaster.
1.5 Scope and limitations of the study
The study focuses on model development for distribution network design on
strategic/tactical level decision-making from humanitarian organization’s perspective. The aimof this dissertation is to enable TLH establishment decision-making. Whilst it is important toaccount for operational decision-making like last mile distribution, there has been plenty ofstudies already focusing on that. The choice of objectives for model building represent theinterest and intention from the relief provider’s side (humanitarian organizations) and thehumanitarian objective. Limitations regarding assumptions are explained in each chapters
before the model development.
This study does not take account of time necessary to reach affected people when
deciding on the TLH establishment decision.

This study considers a single package of relief which weighs 10 kilogram and consists
up of food, basic medical supplies, and a blanket that is enough to sustain an individual
for a week. Therefore, prioritization of goods are not considered within the scope of
this study.

The decision-makers are assumed to be homogeneous and therefore have equal
importance, which might not hold true in real-world disaster operations. Developing amethod to determine the relative importance of decision makers and incorporating into
the model is thus a possible extension.

13The nature of uncertainty presented in this study accounts only for impreciseness in the
data.



This study does not take account of equity issues.

1.6 Outlines and approach of the study
The thesis comprises of six chapters, Figure 1.9 shows the organization, flow, and therelationship between chapters of the dissertation. Chapter one introduces the background, theconcept of TLH, the scope and limitation, and the organization of the dissertation and finallyhighlights the contribution of this study.
Chapter two reviews the extant of literature on facility location problem (FLP) in humanitarian
logistics with special focus on (1) single objective FLP, (2) multi-objective FLP, (3) temporary
FLP, (4) uncertainty based FLP, and (5) multi-criteria FLP aimed for both pre and post-disaster
operations with special focus on post-disaster operations. We also review decision-making
approaches and the nature and sources of uncertainty prevalent in humanitarian operations.
Chapter three answers the question of where to locate TLHs. To do so, we develop a multiactor multi-objective optimization approach for locating TLHs during disaster response. The
model accounts for the time dependent nature of parameters. The preference of multiple
actors/decision-makers is identified. A fuzzy factor rating system (FFRS) under groupdecision-making (GDM) condition is proposed to determine the weight of the objectives in a
multi-objective optimization problem while taking account of multiple decision-makers.
Chapter four answers the question of where and when to locate the TLHs and how to allocate
the demand to the open TLHs. In doing so, we develop a credibility based multi-objective
optimization model that determines the location and allocation of TLHs under epistemic
uncertainty and time-varying nature of parameters. Pertaining to the time-varying and uncertain
nature of parameter values, the corresponding impact on the location of TLH is analyzed inthis chapter.
Chapter five answers the question of where and in what order TLHs should be established. An
optimization model with the objective of minimizing total unsatisfied demand is amalgamatedwith a fuzzy multi-attribute group decision-making (FMAGDM) approach that takes accountof multiple decision-makers’ decision-opinion when evaluating the set of alternatives versus
selected attributes is proposed to determine the order of establishment of TLHs under resource
14

constrained situation. The impact of heterogeneity of decision-makers is also explored. Though
we have used a single objective optimization approach for generating the optimal TLH number
and their spatial location alternatives in this chapter, the multi-objective optimization models
both the deterministic one and the possibilistic models in chapter 3 and chapter 4 can also be
used to generate alternatives. Depending on the actual need of the situation, appropriate
mathematical model can be used in the first phase.
Chapter six summarizes the findings and concludes what has been achieved through thisdissertation. Potential implications for real life location decision-making is also illustrated.
CHAPTER 1
Introduction

CHAPTER 2
Literature review

CHAPTER 3: WHERE?

CHAPTER 3: WHERE & WHEN?

A multi-actor multi-objective
optimization approach for locating
temporary logistics hubs during disaster
response location problem

A credibility based multi-objective
temporary logistics hub locationallocation model for relief supply anddistribution under uncertainty

CHAPTER 5: WHERE & WHICH ORDER?
Fuzzy multi-attribute group decision-making for ordering
the establishment of temporary logistics hubs

CHAPTER 6
Summary and Conclusion

Figure 1.9: Organization of the dissertation
15

1.7 Contributions of the study
The contribution of this study is manifold. First, the contribution lays on the exploration ofdifferent dimensions of TLH location problem. This study answers the question of where, when,
what order TLHs should be established along with the allocation of the demand to the open
TLHs. Ordering the establishment of TLHs is a new concept that we have introduced in thisstudy. This allows for effective utilization of TLHs under resource constrained situation. Prior
studies have only focused on where to locate them.
Second, this study develops deterministic and possibilistic mathematical models that can takeaccount of humanitarian and cost based objectives, time-varying and uncertain nature ofparameter values, and TLH’s short operational horizon.
Third, the concept of multi-sourcing is introduced. The mathematical model developed in thisstudy investigates the impact of single sourcing versus multi-sourcing strategy and therefore
highlighting its significance.
Fourth, the study uses a FFRS under GDM to calculate the weight of objectives in a multiobjective optimization problem. The difficulty in calculating the weight of objectives is one of
the major challenges preventing the use of the weighted sum method; thus, the application of
the FFRS under GDM is a novel feature of this study among those focusing on humanitarian
operations.
Fifth, this study develops approach based on fuzzy set theory and fuzzy linguistic variables
which enables dealing with the vagueness and imprecision inherent in evaluating subjective
and objective attributes in post-disaster decision-making scenarios which involves multiple
decision-makers.
Finally, this study shows that amalgamating an optimization model with multi attributedecision-making approach enables the evaluation of both subjective and objective attributes,
and has enhanced applicability to real life scenarios.

16CHAPTER 2 Literature review

2.1 Chapter overview
As the entirety of this study revolves around locating ‘temporary’ facilities in the postdisaster phase, this chapter provides an overview of the published literature relating to theresearch topic which has been outlined from the broad view of the disaster management andhumanitarian logistics before moving on to the specific topic. Even though the temporary
nature of facilities brings in further dynamics to the location problem, fundamentally we are
dealing with FLP, therefore the literature review has explored research concepts and methods
that are used for locating facilities in humanitarian logistics. In doing so different types andaspects of facility location modeling are also explored.
The second section starts with the general and a brief introduction to disaster and disastermanagement where we explore the significance of disaster response period in humanitarian
operations. The third section briefs on the role of logistics in ensuring successful humanitarianassistance and also brings into perspective the role of facilities within the humanitarian context.
In the fourth section we review the extant of literature on facility location in humanitariancontext. In the following three sections we review decision making approaches, the nature, andsource of uncertainty in humanitarian operations. In section eight we explain the positioningof this dissertation in the current literature. The final section summarizes all the sections.
2.2 Disaster and disaster management
A disaster is a sudden, calamitous event that seriously disrupts the functioning of acommunity or society and causes human, material, and economic or environmental losses thatexceed the community’s or society’s ability to cope using its own resources. The advent of thedisaster prompts for coordinated actions among people and organizations to protect life,
property, reduce human loss and damage. The field of disaster management deals with thesekinds of issues. The Red Cross and Red Crescent Society defines disaster management as theorganization and management of resources and responsibilities for dealing with all
humanitarian aspects of emergencies, in particular preparedness, response and recovery inorder to lessen the impact of disasters. A disaster management life cycle consists of fourphases: mitigation, preparedness, response, and recovery. Mitigation involves all the17preventive activities performed beforehand to comprehend and reduce the risks associated withdisaster. Examples of mitigation activities includes building codes and zoning, vulnerability
analyses, and public education. Preparedness focuses on activities as emergency planning,
construction of emergency operation centers, and prepositioning of emergency supplies in
anticipation of disasters. Response phase involves coordinated actions like activation of
emergency plan, search, rescue and evacuation of people, medical care, relief distribution,
fatality management and all other activities taken during and shortly after the disaster. The
recovery phase includes all the activities performed to repatriate and restore the systems, people,
and communities to acceptable level of operation which will eventually bring self-sustainability
to affected communities. The following figure shows the schematic of the disaster management
cycle.

Preparedness

Mitigation

Response

RecoveryFigure 2.1: Disaster management cycle

Irrespective of the type of disaster, most of the sudden onset disasters are unpredictable in termsof the time of occurrence, their location, number of people dead, injured or affected. In suchcases, depending on the scale of the disaster, preparedness alone may not always be sufficientwhich makes response phase one of the most important and critical components of disastermanagement. Response is defined as the actions taken to save lives and prevent further damage
in a disaster or emergency situation. The aim of disaster response is to provide immediate
assistance to maintain life, improve health, and support the morale of the affected population.
Such assistance may range from providing specific but limited aid, such as assisting affected
people with transport, temporary shelter, and food, to establishing semi-permanent settlementin camps and other locations. The main focus in the response phase is on meeting the basic
needs of the people until more permanent and sustainable solutions can be found. Owing to its
importance, this study aims to enhance response to disaster or emergency situation.
18

2.3 Humanitarian logistics
Humanitarian logistics is defined as the process of planning, implementing and controllingthe efficient, cost-effective flow of and storage of goods and materials as well as related
information, from point of origin to point of consumption for the purpose of alleviating thesuffering of vulnerable people (Thomas and Mizushima, 2005). Humanitarian logistics deals
with logistical issues throughout the disaster management system, including various activities
such as procuring, storing, transporting food, water, medicine, and other supplies as well as
human resources, necessary machinery and equipment, and the injured people before, during,
and after disasters have struck (Nikbakhshand Farahani, 2011). Unpredictability of demand (interms of timing, type, and size), suddenly-occurring demand in very large amounts, short leadtimes for a wide variety of supplies, high stakes associated with adequate and timely delivery,and lack of resources (supply, people, technology, transportation capacity, and money) areamong the few of the factors that distinctly highlights the complexity and unique challenge ofhumanitarian logistics compared to commercial logistics (Balcik and Beamon, 2008).
Logistics is one of the most critical components of successful humanitarian assistance which
can mean the difference between a successful or failed operation (Van Wassenhove, 2006).
Therefore, the effectiveness and efficiency of humanitarian logistics operation plays animportant role in delivering right assistance to the right people at the right time. Thoughhumanitarian response is usually improved with focus on preparative activities that aims at
reducing the procurement and transportation phase in disaster response (Duran et. al. 2007,
Tomasini and Van Wassenhove 2009) one may argue the economic feasibility of holding hugequantities of inventories of food and non-food items in anticipation of unpredictable disasters.
Therefore, an emphasis on humanitarian logistics is often placed in response to disaster(Barbarosoğlu and Arda 2004; Sheu, 2007).
Logistics operations during the disaster response involves assessment and planning,procurement, transport, customs, cold chain, warehousing and inventory management, fleet
management, distribution, monitoring and evaluation, and quality control (Logcluster, 2018).
However, the basic task of humanitarian logistics comprises acquiring and delivering
requested supplies and services at the places and times they are needed, whilst ensuring bestvalue for money (IFRC, 2018). The process of acquiring and delivering emergency relief
supplies and services normally involves movement of emergency relief supplies between
suppliers/port of origin, central warehouse, local warehouse and to the final demand areas. This19

process generally necessitates procurement, transport (which involves a combination ofinternational, national, and local transport), and warehousing and inventory management doneright. Given the uncertain nature of disasters it is almost impossible to determine the locationof the local warehouses beforehand which makes the transportation and/or relief distribution
process a complicated task. A warehouse is simply defined as a planned space for the storage
and handling of goods and material. In general, warehouses are focal points for product andinformation flow between sources of supply and beneficiaries. However, in humanitarian
supply chains, warehouses vary greatly in terms of their role and their characteristics(Logcluster, 2018). Moreover, appropriate location of warehouses plays a detrimental role inthe success and failure of a humanitarian operation.
2.4 Facility location in humanitarian operations
Location decisions arise in a variety of commercial and humanitarian operations. In either
cases, the success or failure of both commercial and humanitarian operations depends in parton the locations chosen for the facilities from where the operations are carried out. As one of
the core problems in humanitarian logistics operations, facility location is receiving burgeoning
attention from both academics and practitioners. Facility location problems deal with selecting
the placement of facilities (often from a list of integer possibilities) to best meet the demanded
constraints. More specifically, facility location problems serve to decide where, how many,
how large, and how should demand for the facilities’ services be allocated to the facilities tooptimally locate them. The answer to these questions depend intimately on the context in which
the location problem is being solved and on the objectives underlying the location problem(Daskin, 2013).
Generally speaking, facility location problems can be modeled using different approaches.
While some studies determine locations based on qualitative and quantitative approaches
together, some use them separately. Moreover, facility location problems can also be modeled
as covering problems, P-median models, and P-center models. Irrespective of the modelingapproach either an exact or a heuristic based solution methodology can be applied. In greater
detail, facility location problems can be classified based on the length of their operational
horizon, dynamicity, number of objectives, modelling approaches, and so on. However, within
the humanitarian context a new classification of facilities can be done based on their role in theoverall humanitarian operation. Below we explain these classifications in detail:20

2.4.1 Based on length of operational horizon
Based on the length of the operational horizon as well as timing of operation, facility
location models intended for humanitarian operations can be categorized as permanent or
temporary. Permanent facilities are established and operate before the disaster in the predisaster phase and are known to have long or even infinite operational horizon, whereas
temporary response facilities only operate once the location of the disaster is known in the postdisaster phase and have a short operational horizon ranging from few weeks to few months.
While determining the location for a permanent facility is a strategic decision, doing so for
temporary facility is a tactical/operational decision with which decision-makers are faced aftera disaster. Examples of permanent facilities are warehouses and pre-designated evacuation
centers where inventories of relief materials are held, whereas temporary facilities exist in theform of logistics hubs, emergency shelters, medical centers, and evacuation centers.
2.4.2 Based on state of facilities
Another popular classification of facility location models can be done based on number of
periods as static location models and dynamic location models. In static location models, theinputs do not depend on time; therefore, it considers only a single period input that is a
representative of set of inputs. The dynamic location models take account of multiple
operational periods where we are concerned not only with the question of where to locate
facilities but also with the question of when to open new facilities or to close existing facilities.
In the static location models facilities sited are normally fixed whereas in the multi-period or
dynamic models, the location of the facilities is time-varying hence can change within theoperational horizon. In other words, in the dynamic models, facilities may be opened, closed
or moved throughout the planning horizon (Ballou, 1968; Wesolowsky and Truscott, 1975).
However, in some models of dynamic facility location problems, once a facility is opened it isassumed to be available for all future periods (Daskin, 2013). Dynamic FLPs can further be
categorized as dynamic deterministic and dynamic uncertain models based on the nature of theparameters under consideration.
2.4.3 Based on number of objective
Based on the number of objectives, facility location models can further be classified as
single objective or multi-objective location models. Facility location problems in humanitarian
operations are inherently multi-objective in nature. While the humanitarian code of conduct
21

emphasizes on minimizing human suffering, the donation based humanitarian operation isoften cost constrained creating a tradeoff situation. Commonly used objectives for facility
location problems in humanitarian context relates to minimizing cost, time or maximizing
demand satisfaction or minimizing unsatisfied demand.
2.4.4 Based on the nature of parameters
Given the unpredictable nature of disasters, humanitarian operations are often tainted withhigh degrees of uncertainties, subsequently the parameters used for modeling location
problems can either be deterministic or uncertain. Different studies have used different
approaches; some studies model the uncertain nature using approaches like stochastic
programming, robust optimization, or possibilistic programming whereas other studies assume
the parameters to be deterministic.
2.4.5 Based on the role/purpose of facilities
Classifying facilities based on their purpose can be unique to humanitarian operations only.
Within this context, facilities can be classified as warehouse, evacuation center, emergency
shelter, and emergency medical center. Warehouse (also logistics hub) serves as a planned
space for the storage and handling of goods and material (Fritz Institute) and acts as a focal
point for the flow of information and relief goods between suppliers and beneficiaries. Bothevacuation center and emergency shelter are planned space for providing temporary shelter tothe affected people. Emergency medical center is a place designated for taking care of injured
people.
2.5 Single objective FLP
As one of the most popular approach to FLP, the highest number of studies (eighteen) haveused this approach to model location problem in humanitarian logistics. Table 2.1 lists thestudies that have used single objective optimization approach to FLP. From Table 2.1 we canobserve that almost all the studies modeled FLP considering facilities to be static and a single
period of operation. Consideration of uncertainty seemed to be popular in this category andstochastic optimization using either exact algorithm or heuristic algorithm is applied. In termsof objective, minimization of expected cost or costs in general was found to be the objective of
choice in most cases with few studies maximizing coverage, or minimizing distance. While
single objective optimization seems to be a preferred approach for FLP targeting pre-disaster22

phase, Doyen et al. (2012), Ahmadi et al. (2015), Pradhananga et al. (2016), Zokaee et al.
(2017), and Yahyei and Bozorgi-Amiri (2018) have accounted for both pre-and post-disaster
phase.

23

Table 2.1: List of single objective optimization based studies on FLP
S.N Author

Year Classification based on
No. of State of Objective Nature ofperiod facilities
parameter

Solution Approachalgorithm

Phase ofdisaster

Objectives

1

Chang et al.

2007 SP

Static

SO

US

H

Qn

Pre

Minimize costs

2
3

Balcik & Beamon
2008 SP
Ukkusuri & Yushimito 2008 SP

StaticStatic

SO
SO

US
D

E
E

Qn
Qn

Pre
Pre

Maximize total expected demand coverage
Minimize costs

4
5

Rawls & Turnquist
Duran et al.

2010 SP
2011 SP

StaticStatic

SO
SO

US
D

H
E

Qn
Qn

Pre
Pre

6

Doyen et al.

2012 SP

Static

SO

US

H

Qn

Minimize expected costs
Minimize the expected average response
time
Pre+Post Minimize total cost

7
8

Rawls & Turnquist
Yushimito et al.

2012 MP2012 SP

StaticStatic

SO
SO

US
D

E
H

Qn
Qn

Pre
Pre

9

Galindo & Batta2013 SP

Static

SO

D

E

Qn

Pre

10

Rennemo et al.

2014 SP

Static

SO

US

E

Qn

Pre+Post Maximizes utility

11

Ahmadi et al.

2015 SP

Static

SO

US

E+H

Qn

Post

Minimize costs

12

Salman and Yucel2015 SP

Static

SO

US

H

Qn

Post

Maximize expected demand coverage

13

Pradhananga et al.

2016 SP

Static

SO

US

E

Qn

Pre+Post Minimize pre and post disaster costs

14

Tofighi et al.

2016 SP

Static

MO

US

E+H

Qn

Pre

15

Zokaee et al.

2016 SP

Static

SO

UR

E

Qn

Pre+Post Minimize total cost

16

Baskaya et al.

2017 SP

Static

SO

D

E

Qn

Pre

Minimizes average distance travelled17
18

Maharjan & Hanaoka
Elci & Noyan2017 SP2018 SP

StaticStatic

SO
SO

D
UC

E
E

Qn
Qn

Pre
Pre

Maximize coverage
Minimize total cost

19

Yahyaei & BozorgiAmiri

2018 SP

Static

SO

UR

E

Qn

Pre+Post Minimize total cost

Minimize the expected costs
Maximize the coverage of affected regions
while minimizing human suffering
Minimize total expected cost

Minimize total cost

SP: Single period; MP: Multi-period; SO: Single objective; D: Deterministic; US: Uncertain stochastic; UR: Uncertain robust; E: Exact
algorithm; H: Heuristic algorithm; Qn: Quantitative approach MO: Multiple objective;
24

Table 2.2: List of multi-objective optimization based studies on FLP
S.N Author

Year Classification based on

Solution

No. of period State offacilities

Objective Nature of algorithm
parameter

Approach Phase of Objectives
disaster1

Tseng et al.

2007

MP

Static

MO

D

E

Qn

Post

2

Doerner et al.

2009

SP

Static

MO

D

E+H

Qn

Pre

3

Salmeron & Apte 2010

SP

Static

MO

US

E

Qn

Pre

4

Bozorgi-amiri et
al.

2013

SP

Static

MO

U

E

Qn

Pre

5

Abounacer et al.

2014

SP

Static

MO

D

E+H

Qn

Pre

6

Barzinpour &2014
Esmaeili
Rezaeo-Malek & 2014
TavakkoliMoghaddam
Wang et al.
2014

SP

Static

MO

D

E

Qn

Pre

SP

Static

MO

UR

E

Qn

Pre

SP

Static

MO

D

H

Qn

Pre

9

Bozorgi-amiri
and Khorsi

2016

MP

Static

MO

US

E

Qn

10

Yilmaz and
Kabak

2016

SP

Static

MO

D

E

Qn

7

8

Minimize total cost
Minimize total travel time
Maximize minimum satisfaction
Minisum facility location criterion andmaximal covering location criterion
Minimization of tsunami risk
Minimization of costs
Minimize expected number of casualties
Minimize expected unmet transfer
population
Minimize sum of expected value andvariance of total cost
Minimize sum of maximum shortage
Minimize the total transportation duration
Minimize the total number of agents
Minimize the non-covered demand
Maximize cumulative coverage
Minimize total cost
Minimize average response time
Minimize total operational cost

Minimization of the maximum vehicle route
travelling time
Minimization of relief distribution cost
Maximization of the minimum route
reliability
Pre+Post Minimizes maximum unsatisfied demand
Minimize total travel time
Minimize pre- and post-disaster cost
Post
Minimizing distance
Minimizing number of facilities

25

Table 2.2 (contd.): List of multi-objective optimization based studies on FLP
S.N

Author11

Haghi et al.

12

Jha et al.

13

Sahebjamnia etal.
Babaei &Shahanaghi

14

15

Vahdani et al.

16

Tavana et al.

Year

Classification based on
Solution Approach Phase of
Objectives
disasterNo. of period State of Objective Nature of algorithm
facilities
parameter
2017
SP
StaticMO
U
E+H
Qn
Pre+Post Maximize response level
Minimizing total cost
2017
SP
StaticMO
US
H
Qn
Pre+Post Minimize total cost
Maximize customer satisfaction
2017
SP
StaticMO
D
Simulation
Qn
Pre
Total cost
Reduce response time
2017
SP
Static
MO
U
E+H
Qn
Pre
Minimize loss or logistic cost
Maximize chance of demand satisfaction
Maximize budget
2018
MP
StaticMO
UR
H
Qn
Pre+Post Minimizing total cost
Minimizing total time
Maximize route reliability
2018
MP
StaticMO
D
H
Qn
Pre+Post Minimize preparedness cost
Minimize total relief operational cost
Minimize total operational relief time

Table 2.3: List of studies focusing on temporary FLP
S.N Author

Year Classification based on
No. of State ofperiod facility

Solution Approach Phase ofdisaster
Objective Nature of algorithm
parameter

Objectives

1
2

Afshar & Haghani 2012
Lin et al.
2012

MP
MP

StaticStatic

SO
SO

D
D

E
H

Qn
Qn

Pre
Post

Minimize total weighted unsatisfied demand
Minimize logistics and penalty costs

3

Khayal et al.

2015

MP

Dynamic

SO

D

E

Qn

Post

Minimize logistics and penalty costs

4

Cavdur et al.

2016

SP

Static

SO

US

E

Qn

Post

5

Stauffer et al.

2016

MP

Static

SO

D

E

Qn

Minimize total distance travelled, unmet demand,and total number of facilities in terms of cost.
Pre+Post Minimizes total vehicular costs over the planning
period.

26

2.6 Multi-objective facility location problem
Despite the popularity of single objective optimization models, many studies have used themulti-objective approach to model different types of problems within humanitarian logistics.
Moreover, multiple objectives are a distinguishing feature of humanitarian logistics operations
unlike in the commercial sector where the minimization of logistics costs is the primary
motivation. Table 2.2 tabulates the studies which have considered more than one objective
when determining the location of logistical facilities. From Table 2.2 we can observe that theobjectives of: (1) minimizing cost; (2) minimizing travel/response time; (3) maximizing
satisfaction; (4) minimizing unsatisfied demand; (4) maximizing coverage are the different
types of objectives considered by different studies. Cost can be observed as the most popular
objective amidst the studies using multi-objective approach to FLP. The objectives of concern
can broadly be categorized into the cost and the humanitarian objectives.
Among a total of sixteen studies adopting multi-objective optimization approach to FLP, mostof the studies (eleven) focus on the pre-disaster stage where the facilities under consideration
are static whereas, Tzeng et al. (2007), Bozorgi-Amiri and Khorsi, (2016), Haghi et al. (2017),
Jha et al. (2017), Vahdani et al. (2018), and Tavana et al. (2018) focuses both on the pre- andpost-disaster stage. While facilities are assumed to be static in almost all the studies, the studies
focusing on pre- and post-disaster stage considers uncertainty in parameter values. In terms ofsolution algorithm studies have adopted both exact and heuristic algorithm. However, thereview of these studies reveal that none of the studies using multi-objective approach hasaddressed the temporary FLP.
Within the genre of multi-objective optimization problem there exists several solution methods.
The solution methods can broadly be classified into:
2.6.1 A priori method
A priori method requires that sufficient preference information is expressed before the solution
process. Well known examples of a priori methods include scalarization, lexicographic method,and goal programming. This method is especially useful when decision-makers are available
and their preference can be elicited. One disadvantage of this method is that it cannot produce
all the Pareto optimal solutions.
2.6.2 A posteriori method
A posteriori methods aim at producing all the Pareto optimal solutions or a representative
subset of the Pareto optimal solutions. Most a posteriori methods fall into either one of the27

following two classes: mathematical programming based a posteriori methods, where analgorithm is repeated and each run of the algorithm produces one Pareto optimal solution, andevolutionary algorithms where one run of the algorithm produces a set of Pareto optimal
solutions. The main advantage of evolutionary algorithms, when applied to solve multiobjective optimization problems, is the fact that they typically generate sets of solutions,allowing computation of an approximation of the entire Pareto front. The main disadvantageof evolutionary algorithms is their lower speed and the Pareto optimality of the solutions cannot
be guaranteed. It is only known that none of the generated solutions dominates the others.
2.7 Temporary facility location problem during disaster response
In this section we review the studies that have used the term ‘temporary facility/hub’ in
their studies to provide a state of the art in temporary FLP. The term temporary came into lightjust recently and has been gaining growing attention. Table 2.3 shows summarized review ofthe studies using the term ‘temporary’ for facility location. In the study conducted by Afshar
and Haghani (2012), temporary facilities receive, arrange, and ship the relief commodities
through a distribution network during the initial response stage for deployment to lower levels.
The authors’ model integrated logistics disaster operations by minimizing total weighted
unsatisfied demand. Their model considers vehicle routing, pickup/delivery schedules, and the
optimal location of temporary facilities. Lin et al. (2012) define temporary depots as anintermediator between the central depot and demand points. They propose a two-phaseheuristic approach to locate temporary depots and allocate covered demand by minimizing
logistics and penalty costs. Khayal (2015) develops a network flow model for the dynamic
selection of temporary distribution facilities and allocation of resources for emergency
response planning by minimizing logistics and penalty costs. In their study, they allow for thetransfer of excess resources between temporary facilities operating in different time periods toreduce deprivation.
In Cavdur et al. (2016), temporary disaster response facilities serve disaster victims until central
disaster response units arrive. The authors develop a two-stage stochastic program forallocating temporary disaster response facilities in short-term disaster operations byminimizing the total distance travelled, unmet demand, and the cost of facilities. Finally, in
Stauffer et al. (2016), a single objective dynamic hub location model with the option for
temporary hubs for managing the vehicle fleet is developed. The model minimizes total
vehicular costs over the planning period to determine the location of temporary hubs for28

vehicles. The temporary hub only opens after a mega disaster and operates as a regional hub
for vehicles if sufficient vehicles are in the disaster location. Nevertheless, it is important thata single temporary facility can provide the minimum services for short-term storing, sorting,and handling that involves consolidating and deconsolidating emergency relief materials.
From the review of the studies focusing on temporary FLP, we can conclude that single
objective optimization using either exact or heuristic algorithm has been a popular research
direction, however these studies do not to take account of important aspects like the short
operational horizon, time-varying nature of temporary facilities, inherent uncertainty indecision making during disaster response situations, uncertainty arising due to impreciseness,and multiple decision-makers prevalent in post-disaster decision-making.
2.8 Multi-criteria FLP
Multi-criteria decision making (MCDM) indicates a discipline of operations research thatconsiders decision problems in the context of a number of decision criteria (Triantaphyllou etal., 1998). Specifically, MCDM includes a series of techniques “aimed at supporting decisionmakers faced with evaluating alternatives taking into account multiple, and often conflictive,
criteria” (Thokala and Duenas, 2012). Multi-criteria FLP is another approach used for
determining the location of facilities in humanitarian logistics. Within the context of MCDM,
multi-attribute decision-making method (MADM) is one popular method used for decisionmaking process which involves evaluation of qualitative and quantitative attributes. Of themany MADM methods reported in the literature (Saaty, 1980, 2000; Hwang and Yoon, 1981,
Chen and Hwang, 1992; Yoon and Hwang 1995; Olson, 1996; Triantaphyllou and Sanchez,
1997; Zanakis et al., 1998; Gal et al., 1999; Triantaphyllou, 2000; Figueira et al., 2005) simple
additive weighing (SAW), Analytic Hierarchy Process (AHP), Technique for Order Preferenceby Similarity to Ideal Solution (TOPSIS), PROMETHE, ELECTRE are among the few
important methods that have been frequently applied in decision-making problems. Table 2.4
lists the studies that uses multi-criteria approach to FLP for determining the location offacilities in the humanitarian context. From Table 2.4 we can elicit that AHP is the most popular
multi-criteria approach used followed by PROMETHE, ELECTRE, TOPSIS, and goal
programming. While most of the studies focus on the pre-disaster stage Vitoriano et al. (2011)
and Turgut et al. (2011) develops model for post-disaster stage. The choice of attributes/criteria
differ based on the context of each study however, cost seems to be common to almost all thestudies. In terms of the number of decision-makers considered, He et al. (2017) and Timperio
29

et al. (2017) are the only two studies that include more than one decision-maker in the decisionmaking process. Nonetheless, these studies neither deal with temporary facility location
problem nor consider attributes pertinent to these facility’s establishment highlighting the needfor further studies on this topic.
Table 2.4: List of multi-criteria FLP studies
S.N.

Author Year Approach MCDM-Method

1

Zhang et al.

2009

Ql

2

Vitoriano et 2011
al.

Ql

3

Turgut et al

2011

Ql

4

Degener et
al.

2013

Ql

5

BozorgiAmiri &Asvadi

2015

Ql

6

Roh et al.

2015

Ql

7

He et al.

2017

Ql

8

Timperio et
al.

2017

Ql

Phase of Decision
Attributes/Criteria
disaster makers
AHP
Pre
N
Safety and reliability
Transportation condition
Situation of disaster affected area
Natural environment
Goal
Post
N
Total costprogramming
Equity(GAMS+CPLEX)
Priority
Reliability
Security
AHP
Post
N
Cost
Transportation
Infrastructure
Geographical location
Suitability of climate
PROMETHEE
Pre
S
Cost
I+II
Delivery time
Spatial distance
Infrastructure
ClimateEconomic aspects
Personnel-related aspects
AHP
Pre
S
Availability
Risk
Technical issues
Cost
Coverage
AHP + Fuzzy
Pre
M
Location
TOPSIS
National stability
Cost
Cooperation
Logistics
ELECTRE-II
PreS
Traffic condition
Capacity
Surrounding environment
Distance
Cost
Fuzzy AHP
Pre
M
Coverage
Access to affected zone Risk
Access to infrastructure
Access to corridor
Congestion
National development plan

N: Not specified; S: Single decision-maker; M: Multiple decision-makers; Ql: Qualitative approach30

2.9 Decision making during disaster response
Simply defined, decision-making is a thought process of selecting a logical choice from theavailable options. Decision-making for/during disaster response is a rather complicated task
faced in the aftermath of a disaster. Numerous decisions ranging from strategic, tactical, andoperational decision are to be made for preparing and responding to humanitarian emergencies.
Strategic decisions are usually long-term decisions which includes determining the location of
permanent warehouses in anticipation of disasters. Tactical decisions are made for an
operational horizon ranging from medium to long-term, this includes deciding the location of
temporary hubs, and evacuation centers. Operational decisions are short term decisions madefor daily or weekly operations, this may include selecting the location of last mile relief
distribution centers of point of distributions.
The complexity in making these range of decisions arises due to the growing number ofhumanitarian actors, prevalence of multiple and often conflicting objectives, need forevaluating several qualitative and quantitative attributes, and inherent complexity anduncertainty of the situation. While prevalence of multiple actors is a distinctive feature ofhumanitarian operations existing studies focusing on facility location problem have not taken
account of it. However, Roh et al. (2015) discusses about prevalence of multiple decisionmakers in their study and Timperio et al (2017) is one such study which has taken account ofmultiple experts for evaluating location alternatives in their study. Vitoriano et al. (2011) notesa lack of attention on development of mathematical models and solution algorithms forstrategic and tactical decisions in the field of humanitarian logistics. Furthermore, our review
of studies on FLP in humanitarian logistics shows that only a small number of studies has taken
account of complexity of decision-making post disaster and the need for including multiple
decision-makers.
Humanitarian operations often receives attention and response from diverse group of
responders coming from different backgrounds. Many a times disaster response sees
involvement of national government, international communities, nonprofit humanitarianorganizations, logistics companies, local communities, and religious groups. This diversity
necessitates studies to take account of both homogeneity and heterogeneity among thedecision-makers. Therefore, nature of the decision-makers and their decision opinions can leadto the generation of four situations:31

(1) When the decision-makers are homogeneous and their decision opinions are also
homogeneous(2) When the decision-makers are homogeneous but their decision opinions are heterogeneous(3) When the decision-makers are heterogeneous but their decision opinions are homogeneous(4) When the decision-makers are heterogeneous and their decision opinions are also
heterogeneous.
2.10 Group decision making (GDM)
Group decision making is the process of making a judgement based on the opinion ofdifferent individuals. A GDM process can be defined as a decision situation where (1) there
are two or more individuals’ different preferences but the same access to information, eachcharacterized by his/her own perceptions, attitude, motivations, and personalities; (2) allrecognize the existence of a common problem; and (3) all attempt to reach a collective decision(Bui, 1987). The inherently multi-actor nature of decision-making during large scale disastercan hugely benefit from GDM. The concept of GDM can be used to incorporate multiple
decision-makers’ decision opinions. While moving from a single decision-maker to a multiple
decision-maker setting plays an important role in successful decision making, it also introduces
a great deal of complexity into the analysis. Fuzzy multi-attribute methods are often coupledwith GDM to address the vagueness and imprecision inherent in location decisions. The GDM
concept can be applied to the popular MADM techniques like SAW, AHP, and TOPSIS (Rao,2007 pp. 38).
2.11 Uncertainty in humanitarian operations
Generally, disasters are characterized by a high degree of uncertainty. Oxford Dictionary
defines uncertainty as the state of being uncertain; Uncertain is defined as not able to be relied
on; not known or definite. Uncertainties can prevail both in pre-disaster planning stage and thepost-disaster response phase. In the pre-disaster stage uncertainties arises due to theunpredictable nature of disasters, while in the post-disaster stage uncertainties arise due to thelack of information, poor quality of information, due to information asymmetry, or due to lackof cooperation and coordination between the involved parties. Existing studies on humanitarian32

operations have considered uncertainties arising in demand, product prices, supply availability,
affected areas, demand location, and transportation network (Liberatore et al. 2013).
Uncertainties may arise due to randomness, fuzziness, fuzzy randomness and greyness. Fromthe viewpoint of optimization theory, there is no difference among the uncertainties such as
randomness, fuzziness, fuzzy randomness and greyness except for the arithmetical operations
on them. Liu (1999) named the optimization theory in uncertain (random, fuzzy, fuzzy random,
grey, etc.) environments the uncertain programming. Based on the extant of literature
uncertainty can be modeled in three different approaches:
2.11.1 Stochastic optimization
In Stochastic Optimization, the uncertain numerical data are assumed to be random. In thesimplest case, these random data obey a known in advance probability distribution, while inmore advanced settings, this distribution is only partially known. Stochastic location models
assumes scenarios of disaster occurrence and its impact and assumes the values of parameters
to follow a probability distribution with each possible scenario. The uncertainty here refers to
the uncertainty associated with the occurrence of disaster and its accompanying impacts interms of affected people, transportation accessibility among other issues. Stochastic location
models are typically applied for preparedness planning.
2.11.2 Robust optimization
Robust optimization is a field of optimization theory that deals with optimization problems inwhich a certain measure of robustness is sought against uncertainty that can be represented asdeterministic variability in the value of the parameters of the problem itself and/or its solution.
Robust optimization works with a deterministic, set-based description of the uncertainty. The
robust optimization approach constructs a solution that is feasible for any realization of theuncertainty in a given set. Unlike stochastic location models, robust location models do notpresume the knowledge of probability distribution of parameters to be preexisting, rather a setof possible scenarios are developed/considered. The concept of uncertainty here is similar to
uncertainty in stochastic location models. Robust location models are also typically applied for
preparedness planning.
2.11.3 Fuzzy programming
Fuzzy programming offers a powerful means of handling optimization problems with fuzzy
parameters. Fuzzy programming can address issues arising due to epistemic uncertainty.
33

Epistemic uncertainty arises due to lack of knowledge of decision-maker about the actual valueof parameters. Unlike both stochastic and robust optimization approach, fuzzy programming
only deals with the impreciseness in the values of the parameters where no presumption
regarding the scenarios of disasters and probability distribution of parameter values is required.
This is especially suitable for post-disaster operations.
Uncertainty in the required data is one of the issues when designing a humanitarian relief chain
via optimization (Tofighi et al. 2016). Randomness and fuzziness are the two main sources of
uncertainties (Pishvaeee and Torabi, 2010; Pishvaee et al. 2012; Tofighi et al. 2016).
Randomness stems from the random nature of data for which, discrete or continuous
probability distributions are estimated based on available but sufficient objective/historical data.
Stochastic or robust programming approaches are often used to take account of the randomness
where the values of the parameters are assumed to follow a probability distribution wheneverrandom distributional information is available for input data. This usually requires events torepeat hence, it is applicable when historical data is available. Whereas fuzziness arises due tothe impreciseness in predicting the parameter value either due to lack of knowledge regarding
their exact values i.e., facing with epistemic uncertainty about these data (Kabak and Ulengin,
2011; Pishvaee and Torabi, 2010) or due to information asymmetry. In this study, we areinterested in accounting for epistemic uncertainty.
Fuzzy decision theories attempt to deal with the vagueness—that is, fuzziness—inherent in thesubjective or imprecise determination of preferences, constraints, and goals (Yager and Filev,
1994). In addition to its abundant application in commercial logistics, fuzzy group decision
making is a popular approach used for facility location problems (cf. Kahraman et al. 2003;
Chou et al. 2008; and Ertuğrul (2011)). However, their application in humanitarian logistics isnominal.
Table 2.5 shows the list of studies that has taken account of uncertainty in different phases ofdisaster for modeling location problem. From the table, we can observe that accounting for
uncertainty in parameters is popular among the studies intended for location selection in predisaster phase. Ahmadi et al. (2015), Salman and Yucel (2015), and Cavdur et al. (2016) are
the only three studies that focuses specifically on post-disaster facility location problem.
Among the two sources of uncertainty, more often studies have addressed uncertainty arising
due to randomness (Table 2.5) and therefore have used stochastic or robust approaches toaccount for it. Tofighi (2016) is one such study that has accounted for uncertainty arising due
34

to impreciseness or fuzziness in the post-disaster phase. Tofighi (2016) developed a two-stage
scenario-based possibilistic-stochastic programming approach to address a two-echelon
humanitarian logistics network design problem in preparation for potential earthquakes. The
study aims to minimize distribution time and cost of unmet demand and considers theuncertainty that may arise in the pre- and post-disaster phase. The study uses stochastic
approach to generate disaster scenarios and a possibilistic approach to account for uncertainty
in parameter values in pre and post-disaster phase. However, the study does not deal with thetemporary facility location problem which comes into operation in the post-disaster phase.
Further review of studies listed in Table 2.5 demonstrates that all the studies adopts a purely
quantitative approach to modeling location problem.

35

Table 2.5: List of studies taking account of uncertainty for modeling location problem
Classification based on

S.N

AuthorSolution
Year No. of
Nature of algorithm
Objective
periodparameter

ApproachPhase ofdisaster

Objectives

1

Chang et al.

2007

SP

SO

US

H

Qn

Pre

Minimize costs

2

Balcik & Beamon

2008

SP

SO

US

E

Qn

Pre

Maximize total expected demand coverage

3

Rawls & Turnquist

2010

SP

SO

US

H

Qn

Pre

4

Salmeron & Apte

2010

SP

MO

US

E

Qn

Pre

Minimize expected costs
Minimize expected number of casualties
Minimize expected unmet transfer population

5

Doyen et al.

2012

SP

SO

US

H

Qn

6

Rawls & Turnquist

2012

MP

SO

US

E

Qn

Pre

Minimize the expected costs

7

Bozorgi-amiri et al.

2013

SP

MO

U

Exact

Qn

Pre

Minimize sum of expected value and variance of
total cost
Minimize sum of maximum shortage

8

Rennemo et al.

2014

SP

SO

US

E

Qn

9

Rezaeo-Malek &TavakkoliMoghaddam

2014

SP

MO

UR

E

Qn

Pre

Minimize average response time
Minimize total operational cost

10

Ahmadi et al.

2015

SP

SO

US

E+H

Qn

Post

Minimize costs

11

Salman and Yucel

2015

SP

SO

US

H

Qn

Post

Maximize expected demand coverage

12

Pradhananga et al.

2016

SP

SO

US

E

Qn

13

Tofighi et al.

2016

SP

MO

US

E+H

Qn

14

Zokaee et al.

2016

SP

SO

UR

E

Qn

Pre+Post Minimize total cost

15

Bozorgi-amiri andKhorsi

2016

MP

MO

US

E

Qn

Minimizes maximum unsatisfied demand
Pre+Post Minimize total travel time
Minimize pre- and post-disaster cost

Pre+Post Minimize total cost

Pre+Post Maximizes utility

Pre+Post Minimize pre and post disaster costs
Pre

Minimize total cost36

Table 2.5 (contd.): List of studies taking account of uncertainty for modeling location problem

S.
N

Classification based on

Solution
Phase of
ApproachdisasterNature of algorithm
Objective
parameter

AuthorYear

16 Cavdur et al.

2016

TS

SO

U

E

Qn

Post

17 Haghi et al.

2017

SP

MO

U

E+H

Qn

Pre+Post

18 Jha et al.

2017

SP

MO

US

H

Qn

19 Babaei & Shahanaghi 2017

SP

MO

U

E+H

Qn

20 Elci & Noyan

2018

SP

SO

UC

E

Qn

2018

SP

SO

UR

E

Qn

Pre+Post Minimize total cost

2018

MP

MO

UR

H

Qn

Minimizing total cost
Pre+Post Minimizing total time
Maximize route reliability

21

Yahyaei & BozorgiAmiri

22 Vahdani et al.

No. ofperiodObjectives

Minimize total distance travelled, unmet demand,and total number of facilities in terms of cost.

Maximize response level
Minimizing total cost
Minimize total cost
Pre+Post
Maximize customer satisfaction
Minimize loss or logistic cost
Pre
Maximize chance of demand satisfaction
Maximize budget
Pre

Minimize total cost37

2.12 Positioning in the current literatureThis dissertation can be positioned in the current literature in temporary facility location
problem with the following contributions:Firstly, this study provides a new dimension to the TLH location problem byincorporating the conflicting objectives, the diverse preferences of multiple decisionmakers, its temporary nature, need for multi-sourcing, uncertainty in parameters,
quantitative and qualitative attributes, and determining the order of establishment of theselected facilities.

In Chapter – 3, we develop a multi-period multi-objective optimization model withmulti-sourcing for the TLH location problem. It uses a FFRS under GDM condition to
calculate the weight of objectives in a multi-objective optimization problem. The
difficulty in calculating the weight of objectives is one of the largest challenges
preventing the use of the weighted sum method; thus, the application of the FFRS under
GDM is a novel feature of this study among those focusing on humanitarian operations.
The fuzzy approach uses fuzzy linguistic variables to illicit the preferences of decisionmakers for different objectives. This approach is suitable for multi-actor GDM
problems given the uncertainty and complexity inherent in decision-making during
disasters.



In Chapter – 4, we develop a multi-objective location-allocation model for relief supply
and distribution under uncertainty. The uncertainty under consideration is the epistemic
uncertainty arising due to the impreciseness in predicting the parameter value. A fuzzy
credibility based chance constrained programming is used to cope with epistemic
uncertainty of imprecise data by using suitable possibility distribution. The model takes
account of the time-varying and uncertain nature of parameters and time-varying natureof TLH location.

In Chapter – 5, we introduce the concept of the order of establishment of TLHs, thisstudy develops and implements a three-stage methodology aimed at the effective
utilization of mobile storage units when their availability is scarce. We show that
amalgamating an optimization model with the multi-attribute decision-making
approach enables the evaluation of both subjective and objective attributes, and hasenhanced applicability to real life scenarios. We illustrate the value of applying fuzzy
linguistic variables to deal with the vagueness and imprecision inherent in evaluating38

subjective attributes in post-disaster decision-making that involves multiple decisionmakers.
To support the developed methodology and contributions, we implement a numericalillustration using data from a real-life disaster—the Nepal earthquake of April 2015.

2.13 Chapter summary
In this chapter we reviewed the existing literature on facility location problem within thecontext of humanitarian logistics. Of the numerous types of facilities prevalent in humanitarian
operations, we limited our review to studies focusing on facilities intended for relief
distribution with special attention to temporary facilities. Our review reveals that most of thestudies focus on the pre-disaster stage highlighting the importance of facilities for enhancing
preparedness. In term of modelling approach, studies have modeled a single period assuming
facilities to be static in nature. Contrary to the humanitarian code of conduct which states thathighest priority should be given to minimizing humanitarian suffering the objective ofminimizing cost has been the most preferred objective among all the studies we have reviewed.
From the methodological perspective, we reviewed literatures using both optimization
approach and MCDM approach to location selection problem and found out that optimization
is more popular as a methodology compared to MCDM. Amid the studies using optimization
approach we further classified studies based on the number of objectives and found out thatboth single objective and multi-objective approaches are almost equally popular. In terms ofsolution algorithm both heuristic and exact methods seem to be popular. While the number ofstudies developing models for facilities without specific mentioning of its state is quite huge,
the number of studies focusing on temporary facilities are quite small. Similarly, the numberof studies adopting multi-criteria approach to FLP is also limited.
From the literature review we can conclude that only a limited number of studies focus onmodeling temporary nature of disaster response facilities. Moreover, none of the studies
focusing on temporary facilities have incorporated multiple objectives for FLP in humanitarian
logistics; decision aid models that involve multiple actors are rarely used to address temporary
FLP; the uncertain nature of parameters has not been taken into account; and the need for
determining their order of establishment when the resources are limited. According to Kovacs
and Spens (2007), the typical actors involved in disaster response operations include aid
agencies, donors, governments, the military, logistics providers, and other non-governmental
39

organizations, which makes the presence of multiple actors another distinctive feature ofhumanitarian logistics operations. From a practical perspective, the many actors involved indisaster management must thus be included in location selection.

40

CHAPTER 3 A multi-actor multi-objective optimization approach forlocating temporary logistics hubs during disaster response

3.1 Introduction
Multiple objectives are a distinguishing feature of humanitarian logistics operations unlikein the commercial sector where the minimization of logistics costs is the primary motivation.
Multi-objective optimization is capable of handling the non-commensurable nature of different
types of objectives through three stages: model building, optimization, and decision-making(preference articulation). The decision-making step (involving either single or multiple actors)
can happen either before the optimization (a priori articulation of preferences) or thereafter (aposteriori articulation of preferences). Multiple actors are another differentiating feature ofdisaster response operations. The typical actors involved in disaster response operations ranges
from large scale aid agencies, donors, governments, the military, logistics providers, other nongovernmental organizations, to very small local community groups.

From a practicalperspective, the many actors involved in disaster management must thus be included in location
selection.
Humans are unsuccessful in making quantitative predictions, whereas they are comparatively
efficient in qualitative forecasting. Further, humans are more prone to interferences frombiasing tendencies if they are forced to provide numerical estimates since the elicitation ofnumerical estimates forces an individual to operate in a mode which requires more mental
effort than that required for less precise verbal statements (Karwowski and Mital, 1986;
Kahraman et al. 2003). Fuzzy linguistic models permit the translation of verbal expressions
into numerical ones, thereby dealing quantitatively with imprecision in the expression of theimportance of each criterion. While decision-making under conditions of risk and uncertainty
have been modeled by probabilistic decision theories and by game theories, fuzzy decision
theories attempt to deal with the vagueness or fuzziness inherent in subjective or imprecise
determination of preferences, constraints and goals (Yager 1982).
The vagueness and ambiguity that surrounds decision-making during emergencies often
increases the complexity of the location selection problem. Hence, different approaches must
be employed. Among the approaches capable of incorporating multiple actors into the decision41

making process, the fuzzy factor rating system (FFRS), which is applicable to both individualand group decision-making (GDM) (Chou et al., 2008), is an effective method for solving
problems in a fuzzy group decision environment (Ou and Chou, 2009). Such a fuzzy approachis suitable for GDM problems under uncertainty because of the vagueness and imprecision
inherent in decision-making during emergencies.
Based on the foregoing, the existing literature on temporary facilities fails to take account ofthe (1) temporary nature, (2) multi-objective nature, or (3) multi-actor nature of disaster
response facilities. Therefore, to address the gaps in the literature, we develop a multi-actor,
multi-period multi-objective optimization model with multi-sourcing and a short operational
horizon to determine the location of temporary logistics hubs (TLHs) in the post-disaster stage.
The objectives are minimizing total costs and minimizing total unsatisfied demand. We use theweighted sum method to solve the multi-objective optimization model and an FFRS under
GDM to determine the weight of the objectives under the a priori articulation of preferences.
The FFRS under the GDM condition enables combining the decision opinions of a multitudeof actors prevalent in disaster relief operations.
3.2 Fuzzy factor rating system under group decision making
The factor rating system, which is also known as a multi-factor rating system or scoring
method, is a popular and easily applied subjective decision-making method under the multiattribute decision-making approach (Heragu, 1997; Chou et al., 2008). The chaotic and often
turbulent nature of disaster management necessitates a simple yet efficient method that includes
decision-makers’ preferences. Although conventional factor rating system approaches havebeen successfully applied for rating different criteria, these approaches are less effective when
dealing with the inherent imprecision of linguistic valuation in the decision-making process(Liang and Wang, 1991; Chen, 2001; Kahraman et al., 2003; Chou et al., 2008). To overcome
the shortcomings of traditional approaches, fuzzy set theory, which allows for vague and/or
imprecise boundaries, provides a mechanism to use fuzziness in the subjective or imprecise
determination of preferences, constraints, goals, and group decisions (Kahraman et al., 2003;
Yager, 1982; Ou and Chou, 2009) is integrated with the factor rating system in this study.
The review of the literature reveals the integration of many concepts and approaches with fuzzy
set theory to enhance its capability of handling multi-attribute decision-making problems withimprecise attributes. While existing studies have used statistical approaches, scaling42

approaches, and multi-attribute approaches, the weights obtained through multi-attributemethods are considered to be more stable than those produced by direct evaluations (Maggino
and Ruviglioni, 2009). Additionally, a fuzzy approach is more suitable for GDM problems
given the uncertainty inherent in disaster management operations. The FFRS is thus aneffective method for solving problems in a fuzzy group decision environment (Ou and Chou,
2009).
3.3 Problem description
The problem under consideration is determining the location of TLHs. Figure 1.4 shows the
structure of a typical humanitarian supply chain and the positioning of TLHs within. The
supplies from permanent warehouses or entry points typically come in larger vehicles, whichmight be unable to access affected areas because of partial or complete damage to roads andbridges. In the absence of logistics hubs, the congestion created by larger vehicles using
vulnerable road networks may cause delivery times to increase significantly. In particular, thetemporary nature of hubs is important in developing countries where infrastructure facilities
are poor and disaster preparedness usually falls short. The major two decisions regarding
temporary hubs are to determine (1) their optimal number and (2) location while considering
the length of their operational horizon.
Determining the location of TLHs in the immediate aftermath of a disaster is a complicatedtask because of the multi-actor and multi-objective nature of the decision-making process. The
two objectives considered in this study are minimizing total costs and minimizing total
unsatisfied demand, which are non-commensurable. The choice of objectives represents anattempt to minimize total unsatisfied demand of affected people within the confines of limited
budget. Our interview with the decision-makers revealed that the humanitarian organization’s
operations are often carried out within the confines of a limited budget therefore requiring costto be minimized for the entire length of operation while also minimizing total unsatisfied
demand. Moreover, cost is a function of distance and transportation cost per vehicle perkilometer and time is a function of distance and vehicular speed. Although we do not explicitly
consider time minimization as the model objective, we are basically minimizing distance toreach affected areas within the current model formulation. Besides, lack of vehicular speed
data during the immediate aftermath of disaster prevents using time as an objective. Under the
given circumstances cost minimization has been used as a proxy for time minimization.

43

Typically, it is impossible for a single organization to meet the demand of all affected people
in need, as such no single organization can be the sole decision-maker. Therefore, involving
multiple humanitarian organizations in the disaster response is crucial for making location
selection decisions. Furthermore, it is also important to consider the time-varying nature of cost
attributes and demand of affected areas. The time-varying nature of demand is a common
feature of humanitarian operations, in which, within the operational horizon, costs, available
resources, and demand may vary (either increase or decrease) in each time period. Several
factors affect the short operational horizons of TLHs such as the number of people affected or
injured, location of the demand points, pattern of relief demand, number of houses damaged or
destroyed, socioeconomic situation of the affected areas, type of disaster, and accessibility
conditions within and outside the affected area. The main goal here is to identify how long it
will take for society to return to normal functioning so that the TLHs can be decommissioned
and made ready for their next disaster response mission.
How to prioritize the demand points in the affected area is another aspect of the location
selection problem that arises because of the nature of disaster impact. Disaster impacts are nonuniform: some areas are highly affected, while other receive only mild effects. This variationnecessitates the allocation of emergency relief materials to affected areas’ demand points basedon the severity of disaster impact. Multi-sourcing ensures that the number of TLHs assigned toserve an affected area depends on the severity of the disaster impact in that area. The higher
the disaster impact, the larger is the number of TLHs assigned. The main decision is todetermine the number of hubs required to supply emergency relief materials, select theirlocations, and allocate demand to open hubs in such a way that the total objective is minimized
without exceeding the capacity of facilities over the entire planning horizon.
3.4 Methodology
3.4.1 Mathematical model formulation
The proposed multi-period multi-objective TLH location model with multi-sourcing and ashort operational horizon allows us to accurately capture the changing levels of relief demandand costs over the planning horizon. Multi-sourcing helps ensure agility while addressing
priority needs, which means that even if one of the hubs fails to meet the demand of affectedareas, another hub will be able to fulfill this demand without distress. Multi-sourcing thus refers

44to the situation where demand in each affected area can be split between open facilities. The
operational horizon refers to the length of time the TLH will be functioning.
We formulate a multi-objective optimization problem that minimizes total costs and total
unsatisfied demand under time-varying demand, costs, and available units of emergency relief.
Each district or demand point has an associated demand for emergency relief materials. Alongthe discrete time horizon, demand from the affected zone changes in a known way related tochanges in the number of affected people and recovery of affected people, as a result of which
demand can either increase or decrease or be stable.
The establishment of logistics hubs is required to meet the demand of affected people over theentire relief time horizon. Each logistics hub has a known threshold of emergency relief
supplies that can be supplied. This threshold depends upon the available units of emergency
relief supplies, which in turn depends on factors such as resource availability, the quality of thedisaster response, and in addition to the capacity of TLHs. The amount of emergency reliefmaterials available in TLHs can be either less than or equal to the capacity of TLHs but cannot
exceed their capacity.
Each demand point can be served from one or more TLHs, a decision determined based on theseverity of the disaster impact and that the demand can exceed supply. The shipment ofemergency relief materials between supply points, TLHs, and demand points incurs a variabletransportation cost proportional to the quantity, distance, capacity of vehicles, and time period.
Further, the establishment of a new facility incurs a fixed opening cost, which represents theinitial investment for the mobile storage units, procurement cost, cost of leasing land, and costof transporting the mobile storage units from the supply sources to the candidate TLHs. Ourmodel is deterministic in that the location of the disaster and affected areas are known before
the decision to open a TLH is made. A single commodity emergency relief package isconsidered for distribution purpose. The model formulation epitomizes situation moreprevalent in developing countries where demand usually exceed supply. The following
subsection provides the mathematical model and its notations, parameters, and variables.
3.4.1.1 Model assumptions


The location of supply points, candidate TLHs, and PODs and the distance between them
are known.

45

Two types of vehicle are used. One for relief transportation and other for relief delivery.

The updated information in terms of disaster-induced damage conditions and casualties
associated with each affected area can be obtained during the crucial rescue period.



The total demand of affected people is assumed to be changing by time in a known way,
and can be split or served by one or more facilities.

All parameters of the model including cost, relief availability, and demand are variable
during the planning horizon.



Relief materials are limited in availability.



TLHs have maximum available units of relief goods at a certain time period.

Multiple decision-makers are considered for determining the weight of objectives only.

3.4.1.2 Nomenclature
The notations used in the mathematical model are as follows:
SetsT

set of time periods

I

set of supply pointsJ

set of temporary logistic hubs (TLHs)

K

set of affected area demand points

Parameters
𝑇𝐶𝑖𝑗𝑡 transportation cost of shipping one unit of the relief package from supply point i to TLH
j in period t [USD per unit]
𝑇𝐶𝑗𝑘𝑡 transportation cost of shipping one unit of relief package from TLH j to the affectedarea’s demand point k in period t [USD per unit]
𝐹𝐶𝑗

Fixed cost of opening a TLH in the candidate location [USD]

𝑄𝑆𝑖𝑡

maximum available quantity of emergency relief materials at supply point i ∈ I in periodt [kg]

𝑄𝐻𝑗𝑡

maximum available quantity of emergency relief materials at TLH j ∈ J in period t [kg]𝑑𝑘𝑡demand of the affected area’s demand point k in period t [kg]46

P

total number of TLHs

𝑛𝑘𝑡number of TLHs allocated for demand point 𝑘 in period t

Ma very large number

Variables
𝑟𝑖𝑗𝑡

amount of emergency relief materials shipped from supply point i ∈ I to TLH j ∈ J inperiod t ∈ T

𝑞𝑗𝑘𝑡

amount of emergency relief materials shipped from TLH j ∈ J to the affected area’s
demand points k ∈ K in period t ∈ T𝑦𝑗binary variable that equals 1 if the facility at j is selected as a TLH and 0 otherwise

𝑧𝑗𝑘𝑡binary variable that equals 1 if TLH 𝑗 serves demand point 𝑘 in period t ∈ T and 0
otherwise

3.4.1.3 Formulation
The multi-objective optimization problem is formulated as follows:
Minimize,
𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 1: O1 = ∑𝑗 𝐹𝐶𝑗 𝑦𝑗 + ∑𝑖 ∑𝑗 ∑𝑡 𝑇𝐶𝑖𝑗𝑡 𝑟𝑖𝑗𝑡 + ∑𝑗 ∑𝑘 ∑𝑡 𝑇𝐶𝑗𝑘𝑡 𝑞𝑗𝑘𝑡

(3.1)

𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 2: O2 = ∑𝑘 ∑𝑡 𝑑𝑘𝑡 − ∑𝑗 ∑𝑘 ∑𝑡 𝑞𝑗𝑘𝑡

(3.2)

Constraints,∑𝑘 𝑞𝑗𝑘𝑡 = ∑𝑖 𝑟𝑖𝑗𝑡∀𝑗 ∈ J, 𝑡 ∈ T(3.3)∑𝑗 𝑟𝑖𝑗𝑡 ≤ 𝑄𝑆𝑖𝑡∀𝑖 ∈ I, 𝑡 ∈ T(3.4)∑𝑖 𝑟𝑖𝑗𝑡 ≤ 𝑄𝐻𝑗𝑡

∀ 𝑗 ∈ J, 𝑡 ∈ T(3.5)∑𝑘 𝑞𝑗𝑘𝑡 ≤ 𝑄𝐻𝑗𝑡

∀𝑗 ∈ J, 𝑡 ∈ T(3.6)∑𝑗 𝑦𝑗 ≤ 𝑃

(3.7)

∑𝑗 𝑞𝑗𝑘𝑡 ≤ 𝑑𝑘𝑡∀𝑘 ∈ K, 𝑡 ∈ T(3.8)

𝑧𝑗𝑘𝑡 ≤ 𝑦𝑗∀𝑗 ∈ J(3.9)
47

∑𝑗 𝑧𝑗𝑘𝑡 ≤ 𝑛𝑘𝑡∀ 𝑘 ∈ K, 𝑡 ∈ T(3.10)

𝑞𝑗𝑘𝑡 ≤ 𝑀𝑧𝑗𝑘𝑡∀𝑗 ∈ J, 𝑡 ∈ T(3.11)

𝑟𝑖𝑗𝑡 ≥ 0∀𝑖 ∈ I, 𝑗 ∈ J, 𝑡 ∈ T(3.12)

𝑞𝑗𝑘𝑡 ≥ 0∀𝑗 ∈ J, 𝑘 ∈ K, 𝑡 ∈ T(3.13)𝑦𝑗 ∈ {0,1}∀𝑗 ∈ J(3.14)

𝑧𝑗𝑘𝑡 ∈ {0,1}∀𝑗 ∈ J, 𝑘 ∈ K, 𝑡 ∈ T(3.15)The objective function (3.1) minimizes total costs, which include the fixed cost of opening a
TLH, transportation cost from the supply point to the TLH, and transportation cost from the
TLH to the affected area’s demand points. Objective function (3.2) minimizes total unsatisfied
demand.
Constraint (3.3) ensures that the flow of emergency relief materials from the supply points to
TLHs should be equal to the flow from the TLHs to the affected area’s demand points.
Constraints (3.4) – (3.6) are the availability constraints. Constraint (3.4) ensures that thequantity of emergency relief materials moved from the supply points to the TLHs should beless than or equal to the maximum available quantity of emergency relief materials in the
supply point in each period. Similarly, constraints (3.5) and (3.6) ensure that the quantity ofemergency relief materials moved from the supply points to the TLHs and from the TLHs tothe affected area’s demand points should be less than or equal to the maximum available
quantity of emergency relief materials in the TLHs in each period. Constraint (3.7) limits thenumber of opened hubs to P. Constraint (3.8) ensures that the quantity of emergency relief
delivered to each demand point does not exceed its demand. Constraint (3.9) ensures that ademand point is served by the TLH only if that TLH is open. Constraint (3.10) enforces multisourcing, ensuring that each demand point is served by a prespecified number of TLHs.
Constraints (3.11) ensures emergency relief distribution only between the assigned TLH andthe demand point. Constraints (3.12) – (3.15) express the nature of the decision variables usedin the model.
3.4.2 Solution strategy for the multi-objective TLH location model48

In our study, we use a priori method for solving multi-objective optimization problem. This
involves priori articulation of preference of the decision-makers using FFRS under GDM
which involves four decision-makers. This solution methodology is especially suitable fordecision-making during the disaster response phase when a decision that is acceptable to all
the parties involved is essential. Often the decision-makers have to make myriad of reactive
decisions in response to the disaster in a very short period of time with little information. Whenthe preference in terms of weight of the objectives can be elicited from all the decision-makers
involved, one Pareto optimal solution can be obtained. This helps in minimizing the overall
decision-making time and building a sense of ownership of the established TLHs.
The weighted sum approach is a frequently used method for combining different objectivefunctions in a multi-objective optimization problem. This approach, also known as thescalarization method, minimizes the positively weighted convex sum of the objectives that
represents a new optimization problem with a unique objective function. The theorem of theweighted sum method states that “if x* is a Pareto-optimal solution of a convex multi-objective
optimization problem, then there exists a non-zero positive weight vector w such that x* is asolution.” This theorem suggests that for a convex multi-objective optimization problem, any
Pareto solution can be found by using the weighted sum method (Miettinen, 1998). The
solutions obtained by using different weight settings represent the points on the Pareto front,
meaning that the solutions are Pareto-optimal. The only requirement is the weight factors wi>=0 and sum of wi=1. Therefore, we use the weighted sum method in this study.
The simplicity of using this method to solve multi-objective optimization problems is often
complicated by the difficulty in determining the weight of the objectives. The weights used
represent decision-makers’ preferences and priorities, while the relative value of the weightreflects the relative importance of the objectives. Typically, infinitely many Pareto-optimal
solutions exist for a multi-objective problem. Thus, it is often necessary to incorporate
decision-makers’ preferences for these objectives to determine a single suitable solution. By
employing methods that incorporate the a priori articulation of such preferences, the user
indicates his or her preferences before running the optimization algorithm and thissubsequently allows the algorithm to determine a single solution. Alternatively, with aposteriori articulation of preferences, one manually selects a single solution from a
representation of the Pareto-optimal set (Marler and Arora, 2010). This study focuses on theuse of the weighted sum method that incorporates the a priori articulation of preferences.

49

Given the multi-actor nature of disaster management, it is necessary that the weight assigned
to the objectives comply with the preference of multiple decision-makers. When decisions
made by more than one person are modeled, two differences from the case of a single decisionmaker can be considered: first, the goals of the individual decision-makers may differ such thateach places a different ordering on the alternatives; second, the individual decision-makers may
have access to different information upon which to base their decision. Theories known as nperson game theories deal with both these considerations, team theories of decision-making
deal only with the second, and group decision theories deal only with the first (Kahraman et al.
2003). This study focuses on GDM to determine the weight of the objectives.
A GDM process can be defined as a decision situation where (1) there are two or moreindividuals’ different preferences but the same access to information, each characterized by
his/her own perceptions, attitude, motivations, and personalities; (2) all recognize the existenceof a common problem; and (3) all attempt to reach a collective decision (Bui, 1987). The
concept of GDM is used to incorporate multiple decision-makers’ decision opinions. Fuzzy
multi-attribute methods are often coupled with GDM to address the vagueness and imprecision
inherent in location decisions. We use the FFRS under the GDM condition to determine theweight of the objectives in the a priori articulation state. This allows us to incorporate multiple
decision-makers’ decision opinions.
3.4.3 Fundamentals of fuzzy set theory
Zadeh (1965) pioneered the use of fuzzy set theory to address problems involving fuzzy
phenomena. Fuzzy set theory uses approximate rather than precise reasoning (Saaty and Tran,
2007) and can process data by using partial set membership functions. Fuzzy logic allows
impersonating ambiguous and uncertain linguistic knowledge and offers a robust framework
for model designers dealing with systems that contain high uncertainty (Aguilar-Lasserre et al.,2009). Triangular, trapezoidal, and Gaussian are among the three simplest and most commonlyused shapes to represent fuzziness. Researchers have proven that triangular and trapezoidal
shapes perform slightly better than the Gaussian shape because of their computational
efficiency and the ease of data acquisition (Zimmerman, 2001). While triangular shapes
represent fuzzy numbers, trapezoidal shapes represent fuzzy intervals. Trapezoidal fuzzy
numbers are therefore the most widely used form of fuzzy numbers because they can behandled arithmetically and interpreted intuitively (Chou et al., 2008). Hence, the linguistic50

terms assessing scarcely quantifiable variables are represented by trapezoidal fuzzy numbersin this study.
A fuzzy set Ã = (a, b, c, d) on R, a ≤ b ≤ c ≤ d, is called a trapezoidal fuzzy number if its
membership function is
(𝑥−𝑎)
(𝑏−𝑎)

1,
𝜇Ã (𝑥)= (𝑥−𝑑),𝑎 ≤ 𝑥 ≤ 𝑏,𝑏 ≤ 𝑥 ≤ 𝑐,

,
(𝑐−𝑑)

{ 0,

𝑐 ≤ 𝑥 ≤ 𝑑,

(3.16)

𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒,

Figure 3.1: A trapezoidal fuzzy number
where 𝑎, 𝑏, 𝑐, 𝑑 are real numbers (Dubois and Prade, 1978; Keufmann and Gupta, 1991). As
shown in Figure 3.1, the trapezoidal fuzzy number can be denoted by (𝑎, 𝑏, 𝑐, 𝑑). The 𝑥 in theinterval [𝑏, 𝑐] gives the maximal grade of 𝜇Ã (𝑥)i.e., 𝜇Ã (𝑥)=1; this is the most probable valueof the evaluation data. The constants c and d are the lower and upper bounds of the available
areas of the evaluation data, respectively. These constants reflect the fuzziness of the evaluation
data (Liang, 1999).
Given two trapezoidal fuzzy numbers, 𝐴̃ = (a, b, c, d) and 𝐵̃ = (e, f, g, h), the four main
operations of these two fuzzy numbers can be expressed as follows (Keufmann and Gupta,
1991; Liang and Wang, 1991; Chen and Hwang, 1992; Chiou et al., 2005):
1. Addition of two trapezoidal fuzzy numbers ⊕51𝐴̃ ⊕ 𝐵̃ = (a+e, b+f, c+g, d+h), a ≥0, e ≥0(3.17)

2. Multiplication of two trapezoidal fuzzy numbers ⊗𝐴̃ ⊗ 𝐵̃ = (ae, bf, cg, dh), a ≥0, e ≥0(3.18)

3. Multiplication of any real number k and a trapezoidal fuzzy number ⊗𝑘 ⊗ 𝐵̃ = (ka, kb, kc, kd), a ≥0, k ≥0

(3.19)

4. Division of two trapezoidal fuzzy numbers /𝐴̃
𝑎 𝑏 𝑐 𝑑=(, , , ), a ≥0, e ≥0̃𝐵
ℎ 𝑔 𝑓 𝑒(3.20)

3.4.3.2 Linguistic variables and fuzzy numbers
In fuzzy set theory, conversion scales are applied to transform linguistic terms into fuzzy
numbers. Determining the number of conversion scales is generally intuitive: while too few
conversion scales reduce analytical discrimination capability, too many conversion scales
make the system overly complex and impractical (Chou et al., 2008). In this study, a scale of
1–5 is used for the importance weight following Liang (1999). Given the fuzzy nature of thisweight selection problem, the importance weights of the individual objectives are used as the
linguistic variables in this study. Table 3.1 lists the linguistic variables and fuzzy numbers used.
Determination of the conversion scale for the linguistic variables is generally assumed to be
intuitive: while too few conversion scales reduce analytical discrimination capability, too many
conversion scales make the system overly complex and impractical. The current study uses a
scale of 1-5 for the importance weight in the manner employed by Liang and Wang (1991),
Liang (1999), Yong (2006) and Chou et al. (2008).
Table 3.1: Linguistic variables and fuzzy numbers
Linguistic variables

Fuzzy numbers

Very Low (VL)

(0,0,0,3)

Low (L)(0,3,3,5)

Medium (M)(2,5,5,8)

High (H)(5,7,7,10)

Very High (VH)

(7,10,10,10)52

3.4.4 Algorithm of an FFRS under the GDM condition
In the following section, we explain the algorithm of the proposed method by using theconcepts of fuzzy set theory and factor rating system under the GDM condition. The decisionmakers are assumed to act in the best interests of the affected people. The proposed method
derives its insights from Chou et al. (2008) and Ou and Chou (2009).
Step 1: Selection of decision-makers
Under the GDM scenario, multiple decision-makers can be chosen. The choice of decisionmaker also varies case-to-case and country by country. However, the effectiveness of GDM isinfluenced by group size. Yetton and Botter (1983) point out that a group of five, and to a lesser
extent, seven, is the most effective. A committee of decision-makers can be formed based on
their overall role in the disaster management activity. The nature of these decision-makers andtheir decision opinions can lead to the generation of four situations: (1) when the decisionmakers are homogeneous and their decision opinions are also homogeneous; (2) when thedecision-makers are homogeneous but their decision opinions are heterogeneous; (3) when thedecision-makers are heterogeneous but their decision opinions are homogeneous; and (4) when
the decision-makers are heterogeneous and their decision opinions are also heterogeneous.
Step 2: Collecting decision opinions and establishing decision matrices
The next step is to collect their decision opinions and determine if decision-makers arehomogeneous or heterogeneous. If the degree of the importance of decision-makers is equal,
then the group of decision-makers is deemed to be a homogeneous group.
In a committee of k decision-makers (Dt, t = 1,2,…, k) responsible for assessing n objectives(Oj, j=1,2,…, n), the degree of the importance of the decision-makers is It, t = 1,2,…, k, where1

It ∈ [0,1] and ∑𝑘𝑡=1 𝐼𝑡 = 1 . If 𝐼1 = 𝐼2 =…= 𝐼𝑘 = 𝑘 , the group of decision-makers is called ahomogeneous group; otherwise the group is called a heterogeneous group.
Step 3: Constructing the aggregated fuzzy rating of the individual objectives
Subsequently, we construct the aggregated fuzzy rating of the individual objectives. Table 3.1
shows the linguistic variables and corresponding fuzzy numbers for the decision-makers tõ𝑗𝑡 = (𝑎𝑗𝑡 , 𝑏𝑗𝑡 , 𝑐𝑗𝑡 , 𝑑𝑗𝑡 ), j = 1, 2, …., n; t = 1, 2,
access the importance of the objectives. Let 𝑊

53

….,k, be the linguistic rating given to objectives 𝑂1 , 𝑂2 ,…., 𝑂𝑛 by decision-maker 𝐷𝑡 . The
̃𝑗 = (𝑎𝑗 , 𝑏𝑗 , 𝑐𝑗 , 𝑑𝑗 ), of objective 𝑂𝑗 assessed by the committee of kaggregated fuzzy rating, 𝑊
decision-makers is defined as
̃𝑗 = (𝐼1 ⊗ 𝑊̃𝑗1 ) ⊕ (𝐼2 ⊗ 𝑊̃𝑗2 ) ⊕ . . . ⊕ (𝐼𝑘 ⊗ 𝑊̃𝑗𝑘 ),
𝑊(3.21)

where 𝑎𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑎𝑗𝑡 , 𝑏𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑏𝑗𝑡 , 𝑐𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑐𝑗𝑡 , 𝑑𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑑𝑗𝑡 .
Step 4: Computing the weight of objectives
To compute the weight of objectives, defuzzify the fuzzy rating of the individual objectives;compute the normalized weights, and construct the weight vector. To defuzzify the rating of̃𝑗 , denoted as
the fuzzy objectives, the signed distance is adopted. The defuzzification of 𝑊
̃𝑗 ) is therefore given byd(𝑊̃𝑗 ) = 1(𝑎𝑗 + 𝑏𝑗 + 𝑐𝑗 + 𝑑𝑗 )d(𝑊𝑘(3.22)

The crisp value of the normalized weight for objectives 𝑂𝑗 , denoted by 𝑊𝑗 , is given by
̃ 𝑗)
𝑑(𝑊
,
̃
𝑗=1 𝑑(𝑊𝑗 )𝑊𝑗 = ∑𝑛(3.23)

where ∑𝑛𝑗=1 𝑊𝑗 = 1. The weight vector W = [𝑊1 , 𝑊2 , . . . , 𝑊𝑛 ] is therefore formed.
This crisp value of the normalized weight of the objectives 𝑂𝑗 can therefore be used as theweight of the objectives in the weighted sum approach.
3.5 Model discussion
The applicability of the methodology developed in section 3.4 in real life problems is discussed
here. The methodology was developed being inspired by a real world humanitarian supply
chain design problem, a mixed integer linear program for a three-echelon, multi-capacitatedhumanitarian supply chain network design is developed. The methodology developed hereintakes account of several significant factors (1) multiple objectives; (2) multiple actors; (3)prioritization of affected areas; (4) short operational horizon for designing the post-disaster
relief distribution network. Our model captures both the fixed opening cost of establishing a
TLH and the variable transportation cost of supplying the emergency relief to TLHs and54

distributing them to the affected area PODs. Scalarization is adopted to solve the multiobjective optimization model. It is a simple yet effective method which guarantees a Pareto
optimal solution. Scalarization involves priori articulation of preferences. A FFRS under GDM
is developed to determine the weight of the objectives.
There are supply sources, TLHs and affected area PODs in the relief network which is a typical
network setting. The methodology developed herein is applicable to any situation which
requires establishment related decision-making involving multiple decision-makers,
prioritization needs, while considering trade-off between non-commensurable objectives. In
particular, the proposed methodology can be applied to establishment decision-making related
to SAR centers, emergency medical centers, general logistics hubs etc. Numerical illustration
and analysis in Section 3.6 further highlights on the applicability of the methodology for a reallife disaster case of Nepal earthquake 2015.
3.6 Numerical illustration and analysis
To support the usefulness of the proposed model as a decision-making tool for selecting
the location of TLHs, we evaluate the performance of the model by using disaster data fromthe April 2015 Nepal earthquake.
3.6.1 April 2015 Nepal earthquake
On 25 April 2015, a 7.8 magnitude earthquake occurred in Barpak in the Gorkha district, which
is approximately 78 km northwest of the capital city, Kathmandu. Aftershocks occurred forweeks after the initial earthquake. The earthquake resulted in roughly 8,790 deaths and 22,300
injuries, while some 773,174 houses were destroyed (501,783) or damaged (271,391) (NPC,
2015). At the height of the emergency, some 188,900 people were temporarily displaced. Of
Nepal’s 75 districts, 39 were affected and 14 of those were declared severely affected. The 14
districts prioritized are located in Kathmandu, Bhaktapur, Lalitpur, Makwanpur, Nuwakot,
Rasuwa, Dhading, Gorkha, Kavrepalanchok, Sindhupalchok, Sindhuli, Dolakha, Ramechhap,
and Okhaldhunga. Approximately 5.4 million people live in these 14 districts, which arelocated in the western and central regions of Nepal. Of these, 2.8 million people were estimatedto need assistance.
The government of Nepal declared a state of emergency in the country on 25 April and called
upon the international humanitarian community for support. More than 450 aid organizations55

responded to the emergency (UNOCHA, 2015) by facilitating rescue, evacuation, relief
distribution, rehabilitation, and recovery. A number of governmental, non-governmental,
national, and international organizations conducted large-scale operations in the 14 mostaffected districts. The humanitarian supply chain during the immediate aftermath of theearthquake faced many challenges such as the lack of vehicles, congestion in the airport, thelack of coordination and cooperation, and operational and location issues related to the use ofregional logistics hubs. Disaster response proved extremely difficult due to the large scale ofthe devastation, huge number of responders, manifold objectives of multiple organizations,infrastructural difficulties in accessing affected zones, and poor weather conditions. Apart fromthe inevitable challenges, many criticized the Nepalese government for its lack of preparedness,
which caused relief supplies to pile up at the airport (The New York Times 2015, Disaster
Recovery Journal 2015).
3.6.2 Nature of the data
In this example, the supply points are the points of entry to Nepal from neighboring
countries via land and air. We did not consider seaports because Nepal is a landlocked country.
We selected seven entry points: The Mechi customs office, Jhapa; Biratnagar customs office,Morang; Bhairawa customs office, Kapilbastu; Kodari customs office, Sindhupalchok;
Nepalgunj customs office, Banke; Birgunj customs office, Parsa; and Tribhuwan international
airport, Kathmandu. We ensured the selected entry points had warehouses in place to handle
the sudden upsurge in emergency relief materials. The amount of emergency relief materials
available in the supply points was assumed to be known. Eleven candidates in Dhading,
Dolakha, Gorkha, Kathmandu, Kavrepalanchok, Makwanpur, Nuwakot, Okhaldhunga,
Ramechhap, Sindhuli, and Sindhupalchok were selected for locating TLHs. The opening of a
TLH incurs a fixed opening cost. The capacity of a candidate TLH is restricted by the available
units of emergency relief materials.

56

Figure 3.2: Location of supply points, candidate TLHs, and demand points
Among the 14 severely affected districts, 13, namely Bhaktapur, Dhading, Dolakha, Gorkha,
Kathmandu, Kavrepalanchok, Lalitpur, Makwanpur, Nuwakot, Okhaldhunga, Ramechhap,
Sindhuli, and Sindhupalchok, were used as the demand points in this study. One district inRasuwa was not considered because of the lack of distance-related data. Figure 3.2 shows thespatial location of the supply points, candidate TLHs, and affected areas’ demand points. The
demand points represent the location of the aggregated demand arising in each district. The
demand points and candidate hubs overlap with each other. Demand was estimated based on
the severity of the disaster impact. According to Salmeron and Apte (2010), the degree ofseverity differentiates the demand in each zone. A larger proportion of the population isassumed to require relief in major crisis-hit areas compared to crisis-hit areas. Rasuwa, Gorkha,
Nuwakot, Dhading, Sindhupalchok, Dolakha, and Ramechhap were identified as major crisishit areas and Kavrepalanchok, Sindhuli, Okhaldhunga, Makwanpur, Lalitpur, Bhaktapur, andKathmandu as crisis-hit areas. Similarly, major crisis-hit districts were allocated two TLHs,
whereas crisis-hit districts were assigned a single TLH. The nature of the demand is assumed
to be increasing initially and then stagnating after a while. This assumption is in reference tothe numerical results of Sheu (2010).

57

As discussed earlier, the operational horizon of TLHs is affected by many factors; as such, theoperational horizon was assumed to be five weeks in this numerical example. We considered asingle package relief delivery system. A single emergency relief package was assumed toweigh 10 kg and include essential items such as meals, a basic medical kit, blankets, baby
supplies, and clothing. We assumed that a single emergency relief package was sufficient tosustain an individual for a week.
3.6.3 Results
In this section, we first calculate the weight of the objectives by using an FFRS under the
GDM condition and then present the results of the optimization model. We ignore the first 72
hours of critical importance, acknowledging the reality of real-life emergency responses.
Assuming that TLHs could be established within 72 hours is unrealistic because of the timeneeded and complexity of finding an appropriate location. Hence, our model is valid for the
response situation after the first 72 hours. The distribution planning is considered for 35 days
divided into five weekly periods.
3.6.3.1 Calculating the weight of the objectives
Step 1: A committee of four decision-makers, D1, D2, D3, and D4, from four humanitarianorganizations active in disaster management in Nepal is formed. Objective O1 represents
minimizing total costs and O2 represents minimizing total unsatisfied demand.
Step 2: Table 3.2 shows homogeneous and heterogeneous decision opinions of the decisionmakers from different humanitarian organizations. From this, two situations can be generated:when the decision-makers are homogeneous and when they are heterogeneous. However, in
this study, we only explore the situation when the decision-makers are homogeneous becauseof the complexity of determining their importance without bias.
Table 3.2: Importance ratings of the objectives
Objectives

Decision-makers (Homogeneous)
D1

D2

D3

D4

O1

H

M

H

M

O2

VH

VH

VH

H

58

Step 3: The importance rating of each objective is assessed by using the linguistic variables
and their respective fuzzy numbers. The aggregated fuzzy rating of the individual objective
when the decision-makers are homogeneous is constructed (see Table 3.3) by using equation(3.21).
Table 3.3: Aggregated fuzzy ratings of the objectives
Objectives

Decision-makers

Aggregated fuzzy
rating

D1

D2

D3

D4

O1

(5, 7, 7, 10)(2, 5, 5, 8)(5, 7, 7, 10)(2, 5, 5, 8)(3.5, 6, 6, 9)

O2(7, 10, 10, 10) (7, 10, 10, 10) (7, 10, 10, 10)(5, 7, 7, 10)(6.5, 9.25, 9.25, 10)

Step 4: The defuzzified values of the aggregated fuzzy rating (Table 3.4) are obtained by using
equation (3.22) and the crisp value of the normalized weight is calculated by using equation(3.23).
Table 3.4: Defuzzified values of the aggregated fuzzy rating and normalized weights of theobjectives
Objectives

O1

O2

Defuzzified value of aggregated fuzzy rating

6.125

8.750

Normalized weight

0.411

0.588

3.6.3.2 Optimization results
The model was coded in Lingo 17.0 Optimization modeling software. All the experiments
were run on a personal computer with an Intel (R) Core (TM) i3-3220 CPU (3.30 GHz) and 8
GB of RAM. All the test problems were computed in under 10 minutes.
To determine the optimal number of TLHs, the model was run without constraint (3.7). The
model results in eight optimal TLHs with locations in Gorkha, Kathmandu, Kavrepalanchok,
Makwanpur, Nuwakot, Ramechhap, Sindhuli, and Sindhupalchok to meet the time-varying
demand over the entire planning horizon. The eight selected TLHs result in the minimum valueof both objectives over the entire planning horizon. Figure 3.3 shows the spatial location of theeight selected TLHs in Nepal.

59

Figure 3.3: Spatial location of the optimal TLHs
Furthermore, calculations were carried out to understand the impact of the number of TLHs on
both the cost and the unsatisfied demand objectives. The results in Figure 3.4 show the change
in cost attributes and total unsatisfied demand with a change in the number of TLHs. Irregularnature of results can be observed from the figure when the number of TLH is 5. This might be
attributed to (1) high transportation cost from TLHs to the PODs; (2) time-varying nature of
the transportation cost; The study considers transportation cost to be time-varying, therefore an
initially increasing, then stagnating and gradual decrease in transportation cost is assumed as
an impact of the disaster. This nature is reflective of the real life situation after Nepal
earthquake 2015; (3) high level of demand satisfaction with minimum number of TLHs as aresult of which both the upstream and the downstream transportation cost from TLHs to PODs
is quite high at this point. High transportation cost at this point may be attributed to high levelof demand satisfaction with minimum number of TLHs. When the number of TLHs is 5, theunsatisfied demand is almost close to its minimum value as a result of which both the upstream
and the downstream transportation cost from SPs to TLHs and from TLHs to PODs is quite
high at this point.

60

Figure 3.4 shows that eight TLHs provides the minimum total cost and minimum unsatisfied
demand; increasing the number of TLHs beyond eight raises the total cost, whereas total
unsatisfied demand remains the same, perhaps owing to the limited availability of reliefmaterials in the TLHs and supply points. Thus, we performed a sensitivity analysis to examine
the extent to which the available quantity of emergency relief in the TLHs and supply points

900

Costs (in 10,000 USD)

600

800

500

700
600

400

500

300

400
300

200

200

100

100
0

0

0

1

2

3

4

5

6
7
8
9
10
11
Number of temporary logistics hubs

Unsatisfied demand (in 10,000 units)affects costs and demand satisfaction.

Total cost
Fixed cost
Shipping cost from SP to TLH
Shipping cost from TLH to DP
Figure 3.4: Change in the cost attributes and unsatisfied demand with a changing number of
TLHs
Figure 3.5 shows the location choices when varying the number of TLHs. From the figure we
can observe that, TLH candidate located in Nuwakot is the most important location as it iscommon to all the solutions which is followed by TLH candidate in Sindhupalchok,
Kavrepalanchok, Makwanpur, Kathmandu, Gorkha, Sindhuli, Ramechhap, Dhading,Okhaldhunga and Dolakha.

61

Figure 3.5: Change in location choices with changing number of TLHs
Table 3.5: Sensitivity of the available quantity of relief materials in the TLHs
Scenarios

Total unsatisfied
demandTotal cost

Shipping
cost fromSP to TLH

Shipping
cost from
TLH to DP(in 1000 units)(in 1000 USD)
Original case

512.104686.681325.65

1053.84

Scenario I

482.104691.151324.66

1059.30

Scenario II

452.104693.32

1336.61

1049.52

Scenario III

422.104697.68

1348.481042.01

Scenario IV

392.104697.82

1361.191029.43

Scenario V

362.104701.761375.49

1019.09

Table 3.5 shows the results of the sensitivity analysis over the available quantity ofemergency relief materials in the TLHs. The table illustrates the cost attributes and total
unsatisfied demand. Each scenario represents an increase in the available units of reliefmaterials by 10,000 units in each step. In each scenario, the model resulted in eight optimal
TLHs. With an increase in the availability of emergency relief materials in the TLHs, the results
show that total unsatisfied demand decreases at the cost of increased total costs, while the fixed
cost remains the same. This sensitivity analysis allows us to conclude that keeping the locations
62

the same, an increase in the availability in the TLHs decreases total unsatisfied demand andincreases total cost. This cost can be attributed to increases in downstream transportation costs.
The sensitivity analysis of the model over the varying quantity of emergency relief materials
available in the supply points shows no significant reduction in total costs or unsatisfied

Costs (in 10,000 USD)

600

900
800

500

700

400

600
500

300

400

200

300
200

100

100

0

0
0

1

2

3
4
5
6
7
8
Number of temporary logistics hubs

9

10

11

Unsatisfied demand (in 10,000 units)demand upon increasing the available units.

Total cost with multi-sourcing
Total cost with single-sourcing
Total unsatisfied demand with multi-sourcing

Figure 3.6: Comparison of single-sourcing with multi-sourcing
Additionally, we investigated the model performance over the multi-sourcing constraint.
Figure 3.6 shows the model results with and without the multi-sourcing constraint. In bothcases, the optimal number of TLHs remains the same. While the other input parameters remain
the same, the results highlight that multi-sourcing reduces total unsatisfied demand with aslightly higher cost compared with single-sourcing. This finding indicates the importance ofmulti-sourcing for minimizing total unsatisfied demand. However, the difference seems to be
not that significant. For the case of the numerical study, we consider the need for multi-sourcing
only for six major crisis hit affected area PODs located in Gorkha, Nuwakot, Dhading,Sindhupalchok, Dolakha, and Ramechhap. Only two TLHs are assigned for major crisis hit
areas and one for the crisis hit areas as the model setting for first time period which is graduallychanging over time. This small number of TLH assigned within the concept of multi-sourcing
might be the reason behind not that significant difference.
633.7 Chapter summary
Deciding on the best location for TLHs to aid humanitarian relief distribution often involves
more than one decision-maker and the trade-off between multiple objectives. In this study, wedeveloped a mathematical model to determine the optimal location for TLHs by using a multiobjective optimization model with multi-sourcing as well as time-varying demand, cost, andcapacities. We also proposed an FFRS under the GDM condition to take account of the decision
opinions of multiple decision-makers. This consideration is important to avoid issues with theownership of the TLHs that may arise because of monopolistic decision-making. The resultsof the questionnaire with humanitarian organizations show the heterogeneous nature ofdecision opinions. Although the humanitarian code dictates that minimizing human suffering
should be given utmost priority during disaster response, this alone does not necessarily holdtrue. Indeed, humanitarian organizations often have to work under a tight budget, resulting inmany trade-offs.
The model proposed herein was implemented by using data obtained from the Nepal
earthquake in 2015. The results of the optimization model clearly highlight the trade-off
relationship between minimizing total costs and unsatisfied demand. Emphasizing on
minimizing costs results in decreased demand satisfaction, whereas emphasizing minimizing
unsatisfied demand leads to increased costs. Significant TLH locations can be identified byvarying the number of TLHs. The sensitivity analysis shows the extent to which the available
quantities of emergency relief items in the TLHs and the supply points influences costs andunsatisfied demand. Higher availability in the TLHs increases demand satisfaction at the priceof increased costs. Additionally, the model was found to be less sensitive to increases in theavailability of relief materials in the supply points. Further, the analysis of the multi-sourcing
constraint reveals the reduction in total unsatisfied demand at the cost of increased costs in themulti-sourcing setting compared with single-sourcing under the same availability restrictions.
However, multi-sourcing enables supply chain agility, which is essential during disaster
response.

64

CHAPTER 4 A credibility based multi-objective temporary logistics hub
location-allocation model for relief supply and distribution under
uncertainty

4.1 Introduction
In the recent years, the world has witnessed several devastating disasters and a significant
growth in human life losses, economic losses, and material damages caused by the suddenonset natural disasters. Given their unpredictable nature, disasters and its impacts are generally
characterized by a high level of uncertainty. Humanitarian operations concerning sudden onset
disasters are inherently uncertain both in the disaster preparedness phase and disaster response
phase. In such case, depending on the scale of the disaster, preparedness alone may not always
be sufficient which makes response phase one of the most important and critical components
of disaster management. The main focus in the response phase is on meeting the basic needsof the people until more permanent and sustainable solutions can be found. In doing so
selecting where and when to locate response facilities and how to allocate demand to the open
facilities is an important task.
Disaster response operations are inherently complicated. Several factors contributes to thecomplexity faced during the response period; time-varying and uncertain nature of the disaster
impact, presence of multiple objectives, qualitative attributes, existence of multiple actors aresome of the major factors. These factors can significantly affect the overall performance of therelief chain network. Uncertainty has been one of the biggest challenges faced in humanitarian
operations. Uncertainty may arise due to randomness or/and impreciseness. Uncertainty may
relate to knowing the exact location of the disaster or in the values of the parameters like cost,transportation time, and demand. Uncertainty in this study refers to epistemic uncertainty
arising due to lack of knowledge of decision-maker about the actual value hence contributing
to impreciseness. Multiple objectives are a distinguishing feature of humanitarian operation
where a balance is always sought between the humanitarian and cost based objectives.
Additionally, location decision requires evaluation of qualitative attributes like transportation
accessibility, open space availability, manpower to name a few of them.

65Despite these complexities related to the post-disaster conditions and lack of sufficient
information about the extent of the damages, disaster response facilities must be set up quickly
because of the urgency of the situation. The decision on whether to open a facility or not, where
to locate them, and how to allocate the demand to the opened facility is purely based on theamount and the quality of information available during the decision-making time. The lack ofsufficient historical data for the uncertain parameters as well as the high computational
complexity of stochastic programming models make the use of this approach somehow
impossible and at the same time unreasonable especially in the real life cases (Pishvaee et al.
2011). On the contrary, fuzzy mathematical programming is a flexible tool for handling
epistemic uncertainty that comes from lack of knowledge of decision maker about the actual
value of parameters.
As the related literature shows, previous works addressing the issue of temporary facility
location problem do not take account of the time-varying and uncertain nature of the parameters,presence of multiple objectives, qualitative attributes, and existence of multiple actors
simultaneously during the response phase.
In contrast to conventional approach, where post-disaster challenges are accounted in the predisaster phase (i.e. before the actual occurrence of the disaster) using the scenarios of disasters,in this study we focus on determining the location of TLHs by considering actual post disasterchallenges occurring after the disaster using a credibility based fuzzy chance constrained
programming while minimizing total cost and maximizing total demand coverage. The
essential idea of fuzzy chance constrained programming is to optimize some critical value witha given confidence level subject to some chance constraints, in a fuzzy environment.
Essentially, it does not contribute additional uncertainty but requires information on theconfidence interval and the spread of the symmetrical triangular fuzzy number which in turnprovides a better way to account for epistemic uncertainty.
The TLHs considered in this study operate on a tactical level. Therefore, it is important to makesure it can cover PODs within the desired proximity while minimizing the total costs. Moreover,
the TLH location selection model incorporates qualitative aspects like transportation
accessibility and availability of open space into consideration. The evaluation of thesequalitative aspects are purely based on the judgement provided by the experts (or decisionmakers) which is often the case in the post-disaster phase. A fuzzy factor rating system undergroup decision-making condition is applied to illicit information from the experts. In summary,66

this study contributes to the existing literature by developing a credibility based multi-objective
temporary logistic hub location model for post-disaster relief network design under uncertainty
which captures both quantitative and qualitative aspects of location modeling.
4.2 Problem description
The relief chain network presented in this study is of multi-echelon, single productconsisting of three layers: (1) supply points which represents all the points of entry to theaffected country and permanent warehouses, (2) TLHs which acts an intermediator between
the supply points and the point of distribution (POD), and (3) PODs which represents theaggregate demand location for demands arising from one district on a geographical region.
Figure 1.4 shows the underlying structure of the humanitarian relief chain and positioning of
the TLH within. The relief supplies enter the country via various points of entry (eg: sea, air,land) which are handled and arranged at TLHs and finally distributed to the PODs. Therefore,
the decision to be made is on tactical level. The location of supply points and PODs are known
in the post-disaster phase.
The establishment of TLH is required to distribute emergency relief to the PODs over the entire
planning horizon. Each TLH has a known limit in the amount of emergency relief that can bedelivered. Each POD is allowed to receive relief from only one TLH. The shipment ofemergency relief between supply point, TLH, and POD incurs a variable transportation cost
proportional to type of vehicle used, the quantity, distance, and the time period of operation.
Further, establishment of a TLH incurs a fixed operation cost which can represent the cost of
manpower, utilities, and rent needed to keep the facility operational. Establishment of TLH
takes place in the beginning of each period. In the immediate aftermath of disaster it is almost
impossible to determine the precise values of the parameters due to the impreciseness.
Therefore, these parameters are assumed to be uncertain. Along the discrete and finite time
horizon, these parameters are changing in a known way. An increase or decrease in especiallytotal demand for emergency relief in a particular geographical region may requireestablishment of TLHs to be demand responsive.
The decisions to be addressed under the given circumstances include determining the locations,
numbers, their capacities, the sequence of establishment of TLHs and allocation of POD’s toopen TLHs as well as aggregate relief flow between them. Moreover, when designing ahumanitarian relief chain it is important to make sure the established facilities can cover the67

demand areas within stipulated coverage distance while also minimizing total cost. We have
implemented the concept of time-varying coverage provided by the TLHs. Figure 4.1 shows
an illustration of the concept of time-varying coverage. For humanitarian operations, as
important as it is to follow humanitarian code of conduct, one has to acknowledge the fact thatthese operations often operate within the confines of a limited budget. Moreover, qualitative
aspects like transportation accessibility and open space availability should be considered toensure operational sustainability of the established TLHs. The model formulation epitomizes
situation more prevalent in developed countries where relief supplies are abundant to meet thedemand.

Where,
Dt

time varying coverage distance of TLHs in each period
location of PODs
Figure 4.1: Illustration of concept of time-varying coverage

4.3 Mathematical model formulation
4.3.1 Assumptions


The demand points, supply points, and the candidate temporary logistic hubs and the
distance between them are known.

The weight capacity of the vehicles used for carrying relief are known.
68

Different types of relief are allowed to be loaded in a vehicle to serve the affectedareas.



Information in terms of disaster-induced damage conditions and casualties associatedwith each affected area, can be obtained during the response period but are imprecise.



Costs, demand, and available relief parameters are assumed imprecise/fuzzy in natureand changing by time in a known way during the entire planning horizon.



Relief supplies are available abundantly.

4.3.2 Nomenclature
The notations used in the mathematical model are as follows:
SetsT

set of time periods {t|t= 1, 2, …, e}I

set of supply points {i|i= 1, 2, …, f}J

set of temporary logistic hubs {j|j= 1, 2, …, g}K

set of affected area demand points {k|k= 1, 2, …, h}Parameters𝐶̃𝑖𝑗𝑡𝑚 unit transportation cost of shipping emergency relief package from supply point totemporary logistics hub in period t for vehicle type m ($/kmcar)
𝐶̃𝑗𝑘𝑡𝑚 unit transportation cost of shipping emergency relief package from temporary
logistics hub to point of distribution in period t for vehicle type m ($/kmcar)
𝐹̃𝑗a constant operational cost of having a TLH open (operating) in location j during
period t𝑄̃𝑖𝑡available quantity of relief at supply point i ∈ I in period t

𝑄̃𝑗𝑡

available quantity of relief at TLH j ∈ J in period t𝑎𝑗𝑘𝑡a binary parameter equal to 1 if sjk<=Dmax, 0 otherwise

sjk

distance between TLH and POD

Dmax

the maximum coverage distance of TLH j in period t𝑑̃𝑘𝑡

demand at each point of distribution j ∈ J in period t

Ptotal number of temporary logistic hubs
69

𝛼confidence level

𝑇𝑗𝑡

a value representing transportation accessibility in candidate location j in period t

𝑂𝑗𝑡

a value representing availability of open spaces in candidate location j in period t𝑁𝑇threshold value for transportation accessibility in candidate j𝑁𝑂threshold value for availability of open spaces in candidate j

Variables
𝑟𝑖𝑗𝑡

amount of relief packages shipped from supply points i ∈ I to temporary logistics
hubs j ∈ J in period t ∈ T

𝑞𝑗𝑘𝑡

amount of relief packages shipped from temporary logistics hubs j ∈ J to affected area
points of distribution k ∈ K in period t ∈ T

𝑦𝑗𝑡binary variable that equals 1 if TLH is open in location j at the beginning of period t
and 0 otherwise

𝑥𝑗𝑘𝑡binary variable that equals 1 if POD k is served by TLH j in period t and 0 otherwise

𝑧𝑘𝑡binary variable that will be 1 if TLH 𝑗 covers POD at 𝑘 in time period t and 0
otherwise

4.3.3 Formulation
Minimize,
O1 = ∑𝑗 𝐹̃𝑗 𝑦𝑗𝑡 + ∑𝑖 ∑𝑗 ∑𝑡 𝐶̃𝑖𝑗𝑡𝑚 𝑟𝑖𝑗𝑡 + ∑𝑗 ∑𝑘 ∑𝑡 𝐶̃𝑗𝑘𝑡𝑚 𝑞𝑗𝑘𝑡

(4.1)

Maximize,O2 =∑𝑘 𝑑̃𝑘𝑡 𝑧𝑘𝑡(4.2)

Constraints,∑𝑗 𝑎𝑗𝑘𝑡 𝑦𝑗𝑡 ≥ 𝑧𝑘𝑡∀𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(4.3)∑𝑗 𝑥𝑗𝑘𝑡 = 1∀𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(4.4)ℎ𝑦𝑗𝑡 − ∑𝑘 ∑𝑡 𝑥𝑗𝑘𝑡 ≥ 0∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.5)

𝑥𝑗𝑘𝑡 ≤ 𝑦𝑗𝑡∀𝑗 ∈ 𝐽, 𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇

(4.6)

70

∑𝑘 𝑞𝑗𝑘𝑡 = ∑𝑖 𝑟𝑖𝑗𝑡∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.7)∑𝑖 𝑟𝑖𝑗𝑡 ≤ 𝑄̃𝑖𝑡∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.8)∑𝑗 𝑟𝑖𝑗𝑡 ≤ 𝑄̃𝑗𝑡

∀𝑖 ∈ 𝐼, 𝑡 ∈ 𝑇(4.9)∑𝑘 𝑞𝑗𝑘𝑡 ≤ 𝑄̃𝑗𝑡

∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.10)∑𝑗 𝑦𝑗𝑡 ≤ 𝑃∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.11)∑𝑗 𝑞𝑗𝑘𝑡 ≥ 𝑑̃𝑘𝑡

∀𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(4.12)

𝑦𝑗𝑡 = 0, ∃ 𝑗 ∈ {𝑗: 𝑇𝑗𝑡 ≤ 𝑁𝑇 }(4.13)

𝑦𝑗𝑡 = 0, ∃ 𝑗 ∈ {𝑗: 𝑂𝑗𝑡 ≤ 𝑁𝑂 }(4.14)

𝑟𝑖𝑗𝑡 ≥ 0∀𝑖 ∈ I, 𝑗 ∈ J, 𝑡 ∈ T(4.15)

𝑞𝑗𝑘𝑡 ≥ 0∀𝑗 ∈ J, 𝑘 ∈ K, 𝑡 ∈ T(4.16)

𝑧𝑘𝑡 ∈ {0,1}∀ 𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(4.17)

𝑦𝑗𝑡 ∈ {0,1}∀𝑗 ∈ J(4.18)

𝑥𝑗𝑘𝑡 ∈ {0,1}∀𝑗 ∈ J, 𝑘 ∈ K, 𝑡 ∈ T(4.19)The objective function (4.1) minimizes the total cost which includes a fixed operating cost ofopen TLHs and the transportation cost from supply points to TLHs and from TLHs to the PODs.
The objective function (4.2) maximizes the total demand coverage.
Constraint (4.3) is the coverage constraint, it ensures that a POD is covered only when one ormore TLHs are located within Dmax distance units of POD. Constraint (4) ensures that POD’s
are served by only one TLH. Constraint (4.5) guarantee that each selected TLH can deliver toseveral PODs. Constraint (4.6) make sure that demand is allocated to open facilities only.
Constraint (4.7) is the flow conservation constraint. Constraints (4.8), (4.9), and (4.10) are theavailability constraints. Constraint (4.11) limits on the maximum number of TLHs that can be
opened. Constraint (4.12 ensures that all the demand is met. Constraint (4.13) and (4.14) are
the subjective constraints. These constraints prevent allocating facilities in the neighborhoods
71whose transportation accessibility, open space availability and disaster vulnerability is below
the required level. Constraints (4.15), (4.16), (4.17), (4.18), and (4.19) depict the nature ofdecision variables.
4.4 Solution strategy
4.4.1 Determine the values of qualitative attributes
Availability of open spaces and transportation accessibility plays an important role inensuring establishment and operational sustainability of the TLHs. However, determining its
values to enable quantitative evaluation is a cumbersome task. We use modified version of
fuzzy multi-attribute group decision-making approach to determine the values of the qualitative
attributes. The methodology includes five sequential steps starting with (1) selection ofdecision-makers, (2) determining the degree of importance of decision-makers, (3) computing
the importance weight of the attributes (4) collecting decision opinions to assess candidate
TLHs with respect to individual attributes and computing the aggregated fuzzy ratings, (5)constructing a fuzzy rating matrix, (6) deriving the total fuzzy scores for candidate TLHs and(7) computing the crisp values of attributes. The crisp values of the attributes thus computed
are therefore used as the value representing open space availability and transportation
accessibility in candidate location j in period t.
4.4.2 Convert the multi-objective possibilistic model to single objective model
One of the most popular approach to solving multi-objective optimization involves
formulating a single objective optimization problem that is related to the multi-objective
problem by means of a real-valued scalarizing function. Besides the weighted sum method, theepsilon constraint method is probably the best known technique to solve multi-objective
optimization problems (Ehrgott, 2005). The epsilon-constraint method has several advantages
over the weighing method (for a detailed explanation of the advantages please refer to Mavrotas(2009)). In the epsilon constraint method, one of the objective function is optimized using theother objective functions as constraints, incorporating them in the constraint part of the model.
In the ideal situation, the value of the epsilon is determined by the decision-maker. Anotheralternative is to obtain the upper bound by solving the single objective optimization model. Byparametrical variation in the right hand side of the constrained objective function the efficientsolution of the problem can be obtained. For the mathematical model formulated in section72

4.3.3, epsilon constraint method can be applied either to minimize total cost or to maximize
total demand coverage while subjecting other objective as a constraint.
4.4.3 Apply fuzzy chance constrained programming approach to the possibilistic model andobtain its crisp equivalent
The essential idea of fuzzy chance constrained programming is to optimize some criticalvalue with a given confidence level subject to some chance constraints in a fuzzy environment.
Among the three different credibility-based fuzzy mathematical programming models i.e.
expected value model; chance constrained programming model; and dependent chanceconstrained programming model (see Yang and Liu (2007) for details of three models), we
employ chance constrained programming model in this study. Chance-constrained
programming, which was initiated by Charnes and Cooper (1959), offers a powerful means formodeling uncertain decision systems. Chance constrained programming is able to control thesatisfaction degree of chance constraints by adding a constraint for each objective function.
However, it needs additional information on the ideal value of the objective function todetermine the right hand side of the added constraints. Inclusion of fuzzy concept in chanceconstrained programming provides a means of allowing the decision-maker to consider
objectives and constraints in terms of the possibility of their attainment (Liu and Liu, 2002)
while accounting for the epistemic uncertainty in parameter values. In doing so, a constraint
is added for each objective function where the ideal value of the objective function can beobtained from the decision-makers involved in the location decision making or by obtaining
the optimal value of the objective.
Based on the existing literature there are generally three prominent fuzzy measures to deal withthe possibilistic chance constraints (Liu, 2009). These include possibility, necessity, andcredibility measure. The main advantage of these measures is to specify an occurrence degree
for each fuzzy (i.e. possibilistic) event in the interval [0, 1] with varying optimistic andpessimistic attitudes. The possibility measure indicates the possibility (i.e. the most optimistic)level of an uncertain event’s occurrence that involves possibilistic parameters. The necessity
measure shows the corresponding minimum possibility level under the most pessimistic view.
Meanwhile, the credibility measure represents the certainty degree of occurring an uncertain
event. Liu (2008) extended the chance-constrained programming to fuzzy decision systems
using the credibility measure, which is called credibility–based fuzzy chance-constrained
programming. Credibility measure is self-dual, meaning that if a credibility value of a fuzzy73

event achieves 1, decision-maker believes the fuzzy event will surely happen. Therefore, it has
been used to convert the possibilistic chance constraints into their crisp counterparts as it can
provide results that would be more reliable than possibility and necessity measures (Tofighi etal. 2016).
The possibilistic model developed in Section 4.3.3 can be reformulated by employing
credibility based fuzzy chance constrained programming in two ways depending on the choiceof objective. Here we present the reformulation when minimizing total cost as:Max𝑓̅

(4.20)(4.1) ≡ Cr{∑𝑗 𝐹̃𝑗 𝑦𝑗𝑡 + ∑𝑖 ∑𝑗 ∑𝑡 𝐶̃𝑖𝑗𝑡 𝑟𝑖𝑗𝑡 + ∑𝑗 ∑𝑘 ∑𝑡 𝐶̃𝑗𝑘𝑡 𝑞𝑗𝑘𝑡 ≥ 𝑓}̅ ≥ 𝛼1(E1)(4.2) ≡ 𝐶𝑟(∑𝑘 𝑑̃𝑘𝑡 𝑧𝑘𝑡 ≥ 𝜀) ≥ 𝛼2(E2)(4.8) ≡ Cr(∑𝑖 𝑟𝑖𝑗𝑡 ≤ 𝑄̃𝑖𝑡 ) ≥ 𝛼3∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(E3)(4.9) ≡ Cr(∑𝑗 𝑟𝑖𝑗𝑡 ≤ 𝑄̃𝑗𝑡 ) ≥ 𝛼3∀𝑖 ∈ 𝐼, 𝑡 ∈ 𝑇(E4)(4.10) ≡ Cr(∑𝑘 𝑞𝑗𝑘𝑡 ≤ 𝑄̃𝑗𝑡 ) ≥ 𝛼3∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(E5)(4.11) ≡ Cr(∑𝑗 𝑞𝑗𝑘𝑡 ≥ 𝑑̃𝑘𝑡 ) ≥ 𝛼4∀𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(E6)⇒ (4.3) – (4.7), (4.11), and (4.13) - (4.19)
In the above formulation, Cr(. ) Denotes the credibility of the event in ( . ) and 𝛼1 , 𝛼2 , 𝛼3 , and𝛼4 are the predetermined confidence levels within which chance constraints should be fulfilled.
Application of fuzzy measures constitutes conversion of the original possibilistic chanceconstraints to their crisp counterparts. Defuzzification is a method that can be used to covert
the possibilistic chance constraints to their crisp counterparts. In defuzzification, the fuzzy
chance constraints are converted to their respective crisp equivalents with respect to thepredetermined confidence level. Then the equivalent crisp model can be solved using
traditional solution process. Let us consider a triangular fuzzy parameter ζ = (ζ1 , ζ2 , ζ3 ) and areal number r. From the definition of possibility, necessity, and credibility measures on fuzzy
event, these measures about two events, ζ ≤ 𝑟 and ζ ≥ 𝑟 are expressed as:

74

1,

if 𝑟 ≤ ζ2 ,

ζ3 −𝑟

Pos{ζ ≥ r} = {ζ −ζ ,3

if ζ2 ≤ 𝑟 ≤ ζ3 ,2

0,

if 𝑟 ≥ ζ3 ,1,

if 𝑟 ≥ ζ2 ,𝑟−ζ1Pos{ζ ≤ r} = {ζ −ζ ,2

if ζ1 ≤ 𝑟 ≤ ζ2 ,

1

0,

1,

(4.23)

if 𝑟 ≤ ζ1 ,

ζ2 −𝑟

Nec{ζ ≥ r} = {ζ −ζ ,if ζ1 ≤ 𝑟 ≤ ζ2 ,1

0,

if 𝑟 ≥ ζ2 ,1,

if 𝑟 ≥ ζ3 ,𝑟−ζ2Nec{ζ ≤ r} = {ζ −ζ ,3

if ζ2 ≤ 𝑟 ≤ ζ3 ,

2

0,
1

1,
2ζ2 −ζ1 −𝑟
2(ζ2 −ζ1 )ζ3 −𝑟(4.25),

if ζ1 ≤ 𝑟 ≤ ζ2 ,if ζ2 ≤ 𝑟 ≤ ζ3 ,0,

if 𝑟 ≥ ζ3 ,3

(4.26)

if 𝑟 ≤ ζ1 ,,2(ζ −ζ ){(4.24)

if 𝑟 ≤ ζ2 ,Cr{ζ ≥ r} = 2 (Pos{ζ ≥ r} + Nec{ζ ≥ r})i.e. Cr{ζ ≥ r} =(4.22)

if 𝑟 ≤ ζ1 ,Nec{ζ ≥ r} = 1 − Pos{ζ ≥ r}2

(4.21)

2(4.27)

Similarly, we can also obtain,
0,
𝑟−ζ1

,

if ζ1 ≤ 𝑟 ≤ ζ2 ,,2(ζ −ζ )if ζ2 ≤ 𝑟 ≤ ζ3 ,1,

if 𝑟 ≥ ζ3 ,2(ζ2 −ζ1 )𝑟−2ζ2 +ζ3

Cr{ζ ≤ r} =if 𝑟 ≤ ζ1 ,

3

{

2

(4.28)

Pos{ζ ≤ r}, Nec{ζ ≤ r}, and Cr{ζ ≤ r}show the possibility, necessity, and credibility degrees
to what extent ζ is not greater than r respectively. Similarly, Pos{ζ ≥ r}, Nec{ζ ≥ r}, andCr{ζ ≥ r} show the possibility, necessity, and credibility degrees to what extent ζ is not lessthan r respectively. Based on (4.27) and (4.28), it can be proven that that for 𝛼 ≥ 0.5 (see Zhu
and Zhang, 2009),75

Cr{ζ ≥ r} ≥ 𝑟⇔𝑟 ≤ (2𝛼 − 1)ζ1 + (2 − 2𝛼)ζ2 )(4.29)

Cr{ζ ≤ r} ≥ r⇔r ≥ (2 − 2α)ζ2 ) + (2α − 1)ζ3

(4.30)

Based on equation (4.29) and (4.30), the above credibility-based fuzzy chance constrainedmodel can be converted to the following crisp equivalent model.
(E1) ≡ ( ∑𝑗((2 − 2𝛼2 )𝐹𝑗(2) + (2𝛼2 − 1)𝐹𝑗(3) )𝑦𝑗𝑡 + ∑𝑖 ∑𝑗 ∑𝑡((2 − 2𝛼2 )𝐶𝑖𝑗𝑡(2) +(2𝛼2 − 1)𝐶𝑖𝑗𝑡(3) )𝑟𝑖𝑗𝑡 + ∑𝑗 ∑𝑘 ∑𝑡((2 − 2𝛼2 )𝐶𝑗𝑘𝑡(2) + (2𝛼2 − 1)𝐶𝑗𝑘𝑡(3) )𝑞𝑗𝑘𝑡 ) ≥ 𝑓 ̅(4.31)(E2) ≡ ∑𝑘((2 − 2𝛼1 )𝑑𝑘𝑡(2) + (2𝛼1 − 1)𝑑𝑘𝑡(3) )𝑧𝑘𝑡 ≥ 𝜀(4.32)(E3) ≡ ∑𝑖 𝑟𝑖𝑗𝑡 ≤ ((2𝛼3 − 1)𝑄𝑖𝑡(1) + (2 − 2𝛼3 )𝑄𝑖𝑡(2) )∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.33)(E4) ≡ ∑𝑗 𝑟𝑖𝑗𝑡 ≤ ((2𝛼3 − 1)𝑄𝑗𝑡(1) + (2 − 2𝛼3 )𝑄𝑖𝑡(2) )∀𝑖 ∈ 𝐼, 𝑡 ∈ 𝑇(4.34)(E5) ≡ ∑𝑘 𝑞𝑗𝑘𝑡 ≤ ((2𝛼3 − 1)𝑄𝑗𝑡(1) + (2 − 2𝛼3 )𝑄𝑗𝑡(2) )∀𝑗 ∈ 𝐽, 𝑡 ∈ 𝑇(4.35)(E6) ≡ ∑𝑗 𝑞𝑗𝑘𝑡 ≥ ((2 − 2𝛼4 )𝑑𝑘𝑡(2) + (2𝛼4 − 1)𝑑𝑘𝑡(3) )∀𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇(4.36)⇒ (4.3) – (4.7), (4.11), and (4.13) - (4.19)
Taking into account the nature of the problem, all the uncertain parameters are modelled assymmetric triangular fuzzy numbers. Use of symmetrical fuzzy numbers allows decisionmakers to choose the spread of the fuzzy number which in turn enables accounting for
epistemic uncertainty prevalent in predicting the values of the parameters. Symmetrictriangular fuzzy number can be uniquely defined by 𝐴̃ = (ζ𝑠 , ζ𝑐 ) where, ζ𝑠 is the spread value,and ζ𝑐 is the center value of 𝐴̃. If all the fuzzy parameters are considered as symmetrictriangular numbers, equivalent crisp model can be reformulated as,𝑐(E1) ≡ ( ∑𝑗((2 − 2𝛼2 )𝐹𝐽𝑐 + (2𝛼2 − 1)(𝐹𝐽𝑐 + 𝐹𝐽𝑠 ))𝑦𝑗𝑡 + ∑𝑖 ∑𝑗 ∑𝑡((2 − 2𝛼2 )𝐶𝑖𝑗𝑡
+
𝑐
𝑠
𝑐
𝑐
(2𝛼2 − 1)(𝐶𝑖𝑗𝑡+ 𝐶𝑖𝑗𝑡))𝑟𝑖𝑗𝑡 + ∑𝑗 ∑𝑘 ∑𝑡((2 − 2𝛼2 )𝐶𝑗𝑘𝑡+ (2𝛼2 − 1)(𝐶𝑗𝑘𝑡+𝑠𝐶𝑗𝑘𝑡))𝑞𝑗𝑘𝑡 ) ≥ 𝑓 ̅(4.37)(E2) , (E3), (E4), (E5), and (E6) can be formulated similarly.
⇒ (4.3) – (4.7), (4.11), and (4.13) - (4.19)

76

4.5 Numerical illustration and analysis
Numerical illustration aims at demonstrating the utility and relevance of the model andsolution methodology developed above in real life disaster cases. In doing so, this study uses
April 2015 Nepal earthquake for the numerical illustration. Details of the impacts of theearthquake can be referred from chapter 3 section 3.6.1.
4.5.1 Relief chain configuration
The study considers seven points of entry (6 land and 1 air) to the country as the supply
points. A total of 12 districts are selected as candidates for TLH establishment. All the 14
districts severely affected by the earthquake are considered as the location of PODs. Figure 4.2
shows the spatial location of the supply points, candidate TLHs, and PODs. An operational
horizon of 7 periods with each period lasting for a week is considered for conducting the
response operations. A single package relief delivery system is considered. A single emergency
relief package is assumed to weigh 10 kg and include essential items such as meals, a basic
medical kit, blankets, baby supplies, and clothing. It is assumed that a single emergency relief
package is sufficient to sustain an individual for a week.

77

Figure 4.2: Spatial location of supply points, candidate TLHs, and PODs
4.5.2 Nature of input parameters
In the case of humanitarian relief chain design after disaster, there is an inherent
impreciseness (i.e. epistemic uncertainty) in the data. This type of uncertainty includes thosedata such as demand of relief item, cost of transportation, accessibility issues, availability
issues, and situation of road network. Moreover, these data are also time dependent as a resultof which its value changes based on the changes in response environment. Table 4.1 shows thenature of input parameters used in this study. Transportation cost, relief demand, available
relief in TLHs, and available relief in supply points, and fixed operation costs are considered
to be changing with time while also enduring uncertainty in its value. The imprecise parameters
are considered as symmetric triangular fuzzy numbers for which the provided data represents
the central value of the associated fuzzy number. The fuzzy numbers can then be constructedby considering desired spread, whereas the spread itself can be determined by close
consultation with the experts in decision making. The experts may rely either on available dataor on their own knowledge or both. And the symmetric triangular fuzzy numbers wereconstructed by considering 15 percent spread in both sides of the central value. For the purpose78

of this numerical illustration the confidence level is considered to be 80 percent within which
the chance constraints are to be fulfilled. The coverage distance is assumed to gradually
increase from 100km in the first period to 200km in the seventh period within the operational
horizon. The operational horizon is considered to be finite and deterministic and coverage isassumed to gradually change over time but in a known fashion.
Table 4.1: Nature of input parameters
Parameters
Transportation cost
Relief demand
Available relief in TLHs
Available relief in Supply points
Fixed operation cost
Operational horizon
Coverage

NatureDynamic(Time varying)

Uncertain

FiniteDeterministic

Dynamic(Time varying)

4.5.3 Results
We ignore the first 72 hours of disaster response acknowledging the reality of real-life
emergency response operation. Because of the time needed and complexity of finding anappropriate location, assuming that TLHs could be established within 72 hours is unrealistic.
Hence, our model is valid for the response situation after the first 72 hours. The model wascoded in Lingo 17.0 Optimization modeling software. All the experiments were run on a
personal computer with an Intel (R) Core (TM) i5-7500 CPU (3.40 GHz) and 16 GB of RAM.
All the test problems were computed in under 10 minutes.
The result shows the optimal number of TLHs that need to be operational in each period alongwith their spatial location for the entire planning horizon and the allocation of the selected
TLHs to the PODs when minimizing total cost. The values of the qualitative parameters(availability of open space and transportation accessibility) is obtained using FMAGDM. A
comparison of the results of multi-objective optimization with uncertainty in parameters anddeterministic parameters is also presented. Sensitivity analysis brings light on the impact of theparameters on the overall results.

79

Figure 4.3: Optimal location of TLHs considering multiple objectives with uncertainty inparameters when minimizing total cost
Figure 4.3 shows the number, the spatial location, and the sequence of establishment of TLHs
considering objective of minimizing total cost under uncertainty in relief demand, cost, andavailable relief. In the figure, T1…T7 represents time period of the operational horizon. Amongthe twelve candidates, TLH in Dolakha, Kathmandu, and Sindhuli is selected to operate forseven periods and Gorkha, Nuwakot, Okhaldhunga, and Sindhupalchok is selected to operate
for six periods. Similarly, TLH in Dhading and Makwanpur is selected to operate for five
periods and TLH in Kavreplanchok is selected to operate for four periods starting from second
period ending in fifth period. Finally, TLH in Ramechhap is selected to be operational in fourth
period. The candidate TLH location in Rasuwa is the only candidate that is not selected to be
operational. One of the possible reasons could be the limited transportation accessibility of
Rasuwa within and outside the district in real life. A total of 13.76 million demands are covered
with total cost of 1.058 million USD.

80

Table 4.2: Allocation of relief supplies from supply points to TLHs (in 10,000 kg)
Supplypoints

TLH

T1

Dhading
164.8
Tribhuwan Kathmandu
632.0
international
Okhaldhunga
22.2
airportSindhuli
Biratnagar Ramechhap
133.0
Bhairahawa Gorkha
Dhading
Dolakha190.9
Kavrepalanchok
Tatopani
Makwanpur
91.7
Okhaldhunga
10.1
Sindhuli
64.6
DhadingNuwakot
157.3
InarwaSindhupalchok 141.2

T2

T3

T4

T5

T6

T7

143.8 81.9 54.6 54.6
675.2 737.1 764.4 764.4 759.8 415.8
33.9
25.3 30.5
169.0
186.1 226.0 212.7 199.4 139.6
87.0 194.4 147.2 192.7
267.3 155.6 305.4 286.4 200.4 60.1
209.5 330.6 246.8 183.6
128.3 155.8 146.7 137.5
45.2 54.8 51.6 48.4
90.4 109.8 103.3 96.9 42.5
3.9
61.9
220.3 267.5 251.7 236.0 338.3
197.6 240.0 225.9 211.7 148.2

Table 4.2 shows the allocation of the emergency relief from supply point to TLHs and Table
4.3 shows the allocation of TLHs to different PODs in different periods of operation. Given
the same limit on the available quantities of emergency relief in all the supply points which is
gradually increasing over time, from Table 4.2 it can be observed that out of seven supply
points five supply points located in Tribhuwan international airport, Biratnagar, Bhairahawa,
Tatopani, and Inarwa is selected under the given circumstances to minimize total cost while
ensuring maximum demand coverage under uncertainty in parameters. Similarly, from Table
4.3 it can be observed that among twelve candidate TLHs, eleven of them are selected to be
operational in different periods. Among all the TLHs selected, the one located in Kathmandu
is serving many PODs. With Kathmandu being the capital of the country it has ease ofaccessibility to many of the affected areas and the results closely approximates reality.

81

Table 4.3: Allocation of relief supplies from TLHs to POD (in 10,000 kg)
TLH
Dhading

POD
T1
T2
T3
T4
T5
T6
T7
164.8
230.8
280.2
263.7
247.3
Dhading
91.5 128.1 155.6 146.4 137.3 96.1 28.8
Dolakha
Dolakha99.4 139.2
159.0 149.1 104.4 31.3
Ramechhap
Gorkha133.0 186.1 226.0 212.7 199.4 139.6
Gorkha66.4
41.0 69.7 20.9
Bhaktapur
51.9
Dhading
41.9
Gorkha380.2 532.3 646.4 608.4 570.4 399.3 119.8
Kathmandu
87.4 26.2
Kavrepalanchok 83.3
Kathmandu
102.1 142.9 90.7 156.0 153.1 107.2 32.1
Lalitpur96.2 28.9
Makwanpur
42.9
Nuwakot
6.7
Rasuwa44.5
Sindhupalchok
93.0 106.3 106.3 58.7
Bhaktapur
Kavrepalnchok Kavreplanchok
116.6 141.5 133.2 124.9
82.8
7.3
Lalitpur
Makwanpur
91.7 128.3 155.8 146.7 137.5
Makwanpur
173.1
DhadingNuwakot
136.1 190.5 231.4 217.8 204.1 142.9
Nuwakot
21.2 29.7 36.1 34.0 31.9 22.3
RasuwaOkhaldhunga Okhaldhunga
32.3 45.2 54.8 51.6 48.4 33.9
Ramechhap
169.0
Ramechhap
10.2
Okhaldhunga
Sindhuli64.6 90.4 109.8 103.3 96.9 67.8 20.3
Sindhuli
Sindhupalchok Sindhupalchok 141.2 197.6 240.0 225.9 211.7 148.2
To illustrate the significance of considering uncertainty in parameter values when modeling
TLH location-allocation problem, Figure 4.4 shows the model results when minimizing total
cost while ensuring maximum demand coverage with deterministic parameters. The
deterministic model results in a total cost of 0.912 million USD with a total coverage of 12.626
million demands. Comparison of Figure 4.3 and Figure 4.4 revels the dynamics in terms of thenumber and location of TLHs and that incorporation of uncertainty in parameter value leads todifference in the number and spatial location of the TLHs. A difference can be seen in the total
number of TLHs operational in period one, two, four, and five. An increase in hub number canbe observed in the case with uncertainty in parameters compared to the deterministic parameter
case.

82

Figure 4.4: Optimal location of TLHs considering multiple objectives with deterministic
parameters when minimizing total cost
Table 4.4 elucidates the difference in the number of TLHs operational with and without theconsideration of uncertainty in parameters. In the figure, T1…T7 represents time period. From
Table 4.4, it can be observed that the total number of TLHs that should be operational underconsideration of epistemic uncertainty is larger than the deterministic case. The increase in thenumber of TLHs may be attributed to the demand uncertainty and time-varying nature and may
as well be pertinent to actual needs in the affected areas. Irrespective of the consideration of
uncertainty, a gradual growth and then respective decline in the number of TLHs operational
can also be observed. From this comparison, it can be concluded that inclusion of uncertainty
in parameter plays an important role in location selection process.

83

Table 4.4: Comparison of the results of multi-objective model with uncertainty in parametersand deterministic parameters
DemandTotal cost
TLH
Model
Nature of coverage(100
operational T1 T2 T3 T4 T5 T6 T7
objective parameters
(1000
USD)
periods
units)
Minimize
total cost

Uncertain

13763.06 10583.46

Deterministic 12626.66

9120

60

9

10 11 10 10

7

3

56

8

9

7

3

11

9

9

Sensitivity analysis has been performed to understand the impact of number of TLHs on total
cost and demand coverage and the overall network structure. Table 4.5 shows the sensitivityof the model results to the number of TLHs. It can be observed that increasing the number of
TLHs leads to both increase in demand coverage and increase in total cost. Maximum demand
coverage is obtained with ten hubs operating for seventy periods with a demand coverage of
13.76 million units and a total cost of 0.112 million USD. If we compare the results of the
maximum coverage under limit on number of TLHs and under the optimal condition wheremodel decides the number and the operational periods, we can observe that total demand iscovered with lesser number of TLHs and at lower total costs under the optimal condition.
However, it is worth to note that under the optimal condition the number of TLHs operating isvarying in each period unlike a fixed number under the constrained situation. This signifies thetime-varying nature of the TLH establishment and need for time-varying sequencing of theestablishment process.

84

Table 4.5: Sensitivity analysis on the number of TLHs
Transportation
DemandFixedTransportation
Total cost
cost fromcoverage
operatingcostfrom TLH
Operational(100 USD)
supply point to
Number(1000 units)
cost
to POD
periods
TLH
4
28 13496.91 14150.95
4578
1856.184
5151.725
5
35 13310.77 12434.37
3815
1594.346
7025.0286
42 13496.91 11585.91
4578
1856.184
5151.7257
49 13496.91 11260.45
5341
1934.512
3984.9418
56 13496.91 11175.34
6104
2248.004
2823.3369
63 13656.6
11146.92
6867
2290.011
1989.913
10
70 13763.06 11188.95
7630
2419.268
1139.67711
77 13763.06 11384.63
8393
2590.631
40112
84 13763.06 12083.61
9156
2653.928
273.6777
TLHs

To further understand the impact of confidence level and spread of the symmetric triangularfuzzy numbers on the attainment of objectives, sensitivity analysis was performed. Figure 4.5
shows the sensitivity analysis on confidence level (α) with 15 percent spread on thesymmetrical triangular fuzzy number and epsilon constraint for demand coverage at greaterthan or equal to 10 million units. Figure 4.6 shows the sensitivity on the spread of the symmetrictriangular fuzzy number with 80 percent confidence level and epsilon constraint for demand
coverage at greater than or equal to 10 million units. From figure 4.5 it can be observed that
increase in the confidence level leads to increase in both total cost and demand coverage. Thisconfidence level ensures the attainment level of the constraints with given degree of confidence.
Similar trend can be observed from figure 4.6 as well, an increase in the spread of the triangularfuzzy number leads to increase in both total cost and total demand coverage.

85

Figure 4.5: Sensitivity analysis on confidence level (α)

Figure 4.6: Sensitivity analysis for spread of symmetric triangular fuzzy number864.5 Chapter summary
Uncertainty and time-varying nature are the two key features of disaster response
operations. This time-varying and uncertain nature of the demand and other parameters during
the disaster response period plays an important role in the overall location selection process
and the corresponding allocation decisions. Additionally, the time-varying nature of theseparameters demands the corresponding variation in the location and allocation decisions as
well. In this study, we have developed a multi-objective mathematical model considering
uncertain and time-varying nature of parameters while also including the qualitative parametersin the quantitative modeling to determine the time-varying locations and the corresponding
allocation of the TLHs within the operational horizon of seven periods. The mathematicalmodel minimizes total cost (operational and transportation cost) while maximizing the demand
coverage under time-varying coverage distance. Each TLH’s demand coverage is assumed to
be gradually changing depending on the time of operation which in turn depends on the factors
like transportation accessibility and available relief.
The model proposed herein was implemented by using data obtained from the April 2015 Nepal
earthquake. The results of the optimization model shows the total cost, associated demand
coverage, number, and spatial location of the TLHs and their corresponding allocations. The
results of the optimization model also shows that, while the time-varying nature of relief
demand and the coverage levels of TLH remaining the same, the time periods when the TLHs
are operational are different under different circumstances of multi-objective uncertain modeland multi-objective deterministic model. Changes in the location of TLHs was observed with
the introduction of uncertainty in parameters when compared to the deterministic model. The
results also show the allocation of emergency relief from supply points to TLHs and from TLHs
to PODs varying based on time periods and highlights the role of selected supply points and
TLHs for emergency relief supply and delivery. Inclusion of qualitative attributes in the
optimization model makes sure that minimum standards are met to enable establishment andoperation of TLHs in the selected locations.
Sensitivity analysis provided us with a wider understanding of the impact of limiting number
of TLHs, confidence level within which objectives and constraints must be fulfilled, the spreadof the symmetrical triangular fuzzy number on the coverage and cost objectives. It can beconcluded that increase in these parameters lead to increase in both the demand coverage andtotal cost. Additionally, the fuzzy factor rating system used under group decision-making
87condition also enables accommodating multiple decision-makers in the decision-making
process. Often during the chaotic response period a single decision-maker may not have all theinformation regarding various parameter. Therefore, inclusion of multiple decision-makers in
obtaining the values of these parameters plays an important role.

88CHAPTER 5 Fuzzy multi-attribute group decision-making for ordering
the establishment of temporary logistics hubs

5.1 Introduction
A typical location problem includes determining how many, where, and how to locate andallocate the demand for open facilities. However, disaster response operation in most emerging
countries is often resource constrained and requires the effective allocation of resources(mobile storage units) to ensure their effective utilization. In location decision-making,traditional network models take into account quantitative factors and aim to minimize the total
cost or to maximize profitability or coverage. Non-quantitative criteria—such as, manpower
qualifications, geographical characteristics, disaster vulnerability, availability of open spaces,
and road accessibility issues—are also important in deciding location. While optimization
approaches can be used for evaluating quantitative factors, this evaluation of qualitative factors
is often accompanied by ambiguity and vagueness (Önüt et al. 2010). This is particularly so in
the aftermath of a disaster, when the environment is chaotic, and there is limited informationand time. Moreover, Montibeller and Yoshizaki (2011) state that intangible factors can change
a network configuration resulting from a mathematical model.
Furthermore, in the aftermath of a disaster the decision-making process typically involves
multiple decision-makers with varying interests and opinions. Indeed, the growing complexity
and uncertainty of decision situations make it less and less possible for a decision-maker toconsider all relevant aspects of a problem, thereby necessitating the participation of multiple
experts in the decision-making process (Ben-Arieh and Chen, 2006). As such, achieving aproper balance among them is a significant challenge. Essentially, disaster managers have to
make myriad reactive operational decisions to solve complex dilemmas with little to no
information under immensely stressful conditions as they respond to emergencies. Thishighlights the need for a simple and inclusive methodology. Under these circumstances, anappropriate decision-making strategy would require that the resolutions and opinions of a groupof decision-makers be taken into account when evaluating the subjective and objective
attributes in the TLH selection process.
Within the extant literature, however, there is a general lack of studies that amalgamates
optimization with a multi-criteria decision-making approach, which enables assessing both89

qualitative and quantitative aspects, to model location problem. On the one hand, studies using
an optimization approach to the problem of location selection hardly include qualitative
attributes. On the other hand, studies focusing on location selection by incorporating qualitative
attributes barely focus on the temporary nature of disaster response facilities and the need toincorporate optimization techniques. There is also a scarcity of studies that concentrate on
issues related to ordering the establishment of TLHs in addition to their location and allocation
strategies when the resources are limited. Moreover, few studies focus specifically on
temporary facilities for relief distribution. Indeed, while the study of Maharjan and Hanaoka(2018) has incorporated multiple decision-makers in a multi-objective optimization for TLH
location selection, it does not consider the order of its establishment.
In this chapter we address the gaps in the existing literature and aid in the decision-making
process by developing a methodology that determines the order of establishment of TLHs, andwhich considers location problems in doing so. The proposed methodology operates in threestages. The first stage uses an optimization model to determine the number and spatial locationof the TLHs. In the second stage, a fuzzy factor rating system under group decision-making isused to rate the importance of attributes. Finally, in the third stage, a fuzzy multi-attribute groupdecision-making approach is used to determine the order of establishment of selected TLHs.
As such, this study aims to develop a methodology that determines the order of establishment
of TLHs that incorporates an optimization model and a multi-criteria decision-making
approach. The methodology allows evaluating quantitative aspects and several qualitative
attributes while considering the temporary nature of disaster response facilities under thepresence of multiple-actors.
5.2 Fuzzy multi-attribute group decision-making
Known for its utility in evaluating imprecise attributes, the fuzzy multi-attribute groupdecision-making approach uses fuzzy set theory to deal with the vagueness and imprecision indecision-making. It also uses the logic and principle of the simple additive weighing method
in factor rating systems to derive total scores for individual alternatives, which allows ranking
by order of preference (Heragu, 1997; Heizer and Render, 2004) in GDM conditions. Thisapproach has been proven to be simple but efficient in dealing with qualitative dimensions ofalternative selection problem by Chou et al. (2008). Furthermore, while we are unsuccessful inmaking quantitative predications, we are comparatively efficient at qualitative forecasting.
Fuzzy decision theories attempt to deal with the vagueness—that is, fuzziness—inherent in the90

subjective or imprecise determination of preferences, constraints, and goals (Yager and Filey,1994). In addition to its abundant application in commercial logistics, fuzzy group decision
making is a popular approach used for facility location problems (cf. Kahraman et al., 2003;
Chou et al., 2008; Ertuğrul, 2011). However, their application in humanitarian logistics isnominal.
5.3 Model formulation
Consider the occurrence of a large-scale disaster that causes significant infrastructural
damage and injury and results in large number of affected people. The scale of the disaster will
attract responses from different humanitarian, governmental and non-governmentalorganizations, as well as local community groups, thereby creating a multi-actor scenario.
Depending on the scale of the disaster, the number of humanitarian actors can range from a
few dozens to several hundred. Effective disaster response requires the establishment of TLHs
that can manage, sort, and store incoming emergency relief materials intended for distribution
to affected people in different geographical locations immediately after the disaster. In largescale disasters, we can assume a situation where the mobile storage units used as TLHs arelimited in number in the immediate aftermath. To facilitate the response to urgent emergency
relief demands in affected areas while enabling the effective utilization of scarce mobile storage
units, this study develops a mechanism to determine the order of establishment of TLHs.
Based on the aforementioned prerequisites, the methodology for determining the order of
establishment of TLHs involves: an optimization model, to calculate the number and the spatial
location of TLHs; a mechanism establishing the importance weight of the subjective attributes;
and a fuzzy multi-attribute group decision-making approach, to ascertain their order of
establishment. In the first stage, the optimization model calculates the location alternatives for
TLHs by minimizing total unsatisfied demand over the entire planning horizon. Moreover, toselect an appropriate location, several qualitative attributes—including the availability of
manpower, basic infrastructure facilities, security, and accessibility issues—need to beevaluated immediately after a disaster has occurred. While quantitative factors can be modeledusing optimization techniques, qualitative factors are often difficult to incorporate and evaluate.
As such, the main purpose of the second mechanism is to synthesize the importance weight of
the attributes that will be used to evaluate the resulting location alternatives when multiple
decision-makers exist. Finally, in the third step, the results obtained from the first stage
optimization model are used as alternatives for subjective evaluation. The last two steps can be91

operated recursively to accommodate the varying numbers and opinions of decision-makers.
This methodology is thus a development of that of Maharjan and Hanoaka (2018), and isintended to assist decision-makers in the design of emergency logistics plan. The next
subsection provides the details of each mechanism.
5.3.1 Selection of location alternatives for TLHs
This mechanism aims to determine the number and spatial location of TLHs. We haveformulated an optimization model with the objective of minimizing total unsatisfied demand
under time-varying demand and changing level of available emergency relief. The proposed
approach allows us to accurately capture the changing levels of relief demand and supplies
over the planning horizon. Within this optimization model, the establishment of TLHs isrequired to meet the demand of affected people over the entire relief time horizon. Each district
or demand point has an associated demand for emergency relief materials. A demand point
represents the aggregated demands of one district. Along the discrete time horizon, demands
from the affected zone changes in a known way related to information availability, changes in
the number of affected people, and the recovery of affected people—and demand can increase,decrease, or stagnate as a consequence. The amount of emergency relief materials available in
TLHs is affected by its capacity, as well as external availability issues. This amount can be lessthan or equal to the capacity of TLHs—that is, it cannot exceed the capacity of TLHs. Ourmodel is deterministic—the location and the affected areas of the disaster are known before thedecision to open a TLH is made. The following section provides further detail of themathematical model, notations, parameters, and variables.
NomenclatureT

Set of time periods.

I

Set of supply points.

J

Set of temporary logistic hubs (TLHs).

K

Set of affected area demand points.

𝑄𝑆𝑖𝑡

Maximum available quantity of emergency relief materials at supply point i ∈ I inperiod t [kg].

𝑄𝐻𝑗𝑡

Maximum available quantity of emergency relief materials at TLH j ∈ J in period t [kg].

𝑑𝑘𝑡Demand of the affected area’s demand point k in period t [kg].

𝑛𝑘𝑡Number of TLHs allocated to demand point 𝑘 in period t.
92

M

A very large number.

𝑟𝑖𝑗𝑡

Amount of emergency relief materials shipped from supply point i ∈ I to TLH j ∈ J inperiod t ∈ T.

𝑞𝑗𝑘𝑡

Amount of emergency relief materials shipped from TLH j ∈ J to the affected area’s
DP k ∈ K in period t ∈ T.

𝑦𝑗

Binary variable that equals 1 if the facility at j is selected as a TLH and 0 otherwise.

𝑧𝑗𝑘𝑡

Binary variable that equals 1 if TLH 𝑗 serves demand point 𝑘 in period t and 0
otherwise.

The optimization problem is formulated as follows:
Minimize the unmet demand,∑k ∑t dkt − ∑j ∑k ∑t q jkt(5.1)

Constraints,∑k q jkt = ∑i rijt∀j ∈ 𝐽, t ∈ 𝑇(5.2)∑j rijt ≤ QSit∀i ∈ 𝐼, t ∈ 𝑇(5.3)∑i rijt ≤ QHjt

∀ j ∈ 𝐽, t ∈ 𝑇(5.4)∑k q jkt ≤ QHjt

∀j ∈ 𝐽, t ∈ 𝑇(5.5)∑j yj ≤ P

(5.6)

∑j q jkt ≤ dkt∀k ∈ 𝐾, t ∈ 𝑇(5.7)

zjkt ≤ yj∀j ∈ 𝐽(5.8)∑j zjkt ≤ nkt∀ k ∈ 𝐾, t ∈ 𝑇(5.9)

q jkt ≤ Mzjkt∀j ∈ 𝐽, t ∈ 𝑇(5.10)

rijt ≥ 0∀i ∈ 𝐼, j ∈ 𝐽, t ∈ 𝑇(5.11)

q jkt ≥ 0

∀j ∈ 𝐽, k ∈ 𝐾, t ∈ 𝑇(5.12)

93yj ∈ {0,1}∀j ∈ 𝐽(5.13)

zjkt ∈ {0,1}∀j ∈ 𝐽, k ∈ 𝐾, t ∈ 𝑇(5.14)The objective function (5.1) minimizes total unsatisfied demand. Constraint (5.2) is the flow
conservation constraint. Constraints (5.3) – (5.5) are the availability constraints. Constraint(5.3) ensures that the quantity of emergency relief materials moved from the supply points to
the TLHs should be less than or equal to the maximum available quantity of emergency reliefmaterials in the supply point in each period. Similarly, constraints (5.4) and (5.5) ensure thatthe quantity of emergency relief materials moved from the supply points to the TLHs and from
TLHs to the demand points of affected areas should be less than or equal to the maximum
available quantity of emergency relief materials in the TLHs in each period. Constraint (5.6)
limits the total number of TLHs. Constraint (5.7) ensures that the quantity of emergency relief
delivered to each demand point does not exceed its demand. Constraint (5.8) ensures that ademand point is served by TLH only if the TLH is open. Constraint (5.9) enforces multisourcing, ensuring that each demand point is served by a pre-specified number of TLHs.
Constraint (5.10) obligates emergency relief distribution only between the assigned TLH andthe demand point. Constraints (5.11) – (5.14) express the nature of the decision variables usedin the model.
5.3.2 Determining the importance weight of attributes
The main purpose of this stage is to determine the importance weight of the subjective
attributes used in evaluating TLH location alternatives. In this study, we adapted the “fuzzy
factor rating system under group decision making condition” to accommodate the calculationof the importance weights of subjective attributes. The fuzzy factor rating system under groupdecision-making uses fuzzy logic to account for the inherent vagueness and uncertainty
associated with decision-making during disaster response. The modified mechanism iscomposed of six sequential steps, explained hereunder.
Step 1: Selection of attributes.
Several attributes play an important role in determining the order of establishment of TLHs. In
this study, the term “attribute” is used to refer to subjective attributes only. The attributes canbe selected based on a variety of criteria, including the socio-economic situation of the country,
94the geo-climatic situation, a literature survey, and a review of lessons learned from the reportsof past disasters. The attributes should be selected so as to ensure the sound utility andoperational sustainability of the TLHs.
Step 2: Selection of decision-makers.
Under the GDM scenario, multiple decision-makers can be chosen. The choice of decisionmakers also varies from case-to-case and country by country. A committee of decision-makers
can be formed based on their overall role in the disaster management activity. The nature ofthese decision-makers and their decision opinions can lead to the generation of different
scenarios: (1) when the decision-makers are homogeneous (1.1) their decision opinions arehomogeneous, or (1.2) their decision opinions are heterogeneous; (2) when the decision-makers
are heterogeneous (2.1) their decision opinions are homogeneous, or (2.2) their decision
opinions are heterogeneous.
Step 3: Determining the degree of importance of decision-makers.
As such, the next step is to determine if decision-makers are homogeneous or heterogeneous.
If the degree of the importance of decision-makers is equal, then the group of decision-makers
is deemed to be a homogeneous group; otherwise the group is deemed heterogeneous.
In a committee of k decision-makers (Dt, t = 1, 2, …, k) responsible for assessing m alternatives(Ai, i=1, 2, …, m), under each of the n attributes (Cj, j=1, 2, …, n), as well as importance of
attributes, the degree of importance of the decision-makers is It, t = 1, 2 ,…, k, where It ∈ [0,1]1and ∑𝑘𝑡=1 𝐼𝑡 = 1. If 𝐼1 = 𝐼2 =…= 𝐼𝑘 = 𝑘, the group of decision-makers is called a homogeneousgroup; otherwise the group is called heterogeneous group. The importance of each decisionmaker can be determined by interviewing the final decision-maker or based on their role inoverall disaster management activities.
Step 4: Collecting decision opinions and computing the aggregated fuzzy weight of individual
attributes.
The decision opinions of decision-makers can be obtained using a questionnaire interview orin person. The questionnaire uses the linguistic variables outlined in Table 5.1 to enabledecision-makers to assess the importance of the attributes. The current study uses a scale of 19 for rating in the manner employed by Liang and Wang (1991), Liang (1999), Yong (2006)95

and Chou et al. (2008). Subsequently, to compute the aggregated fuzzy rating of the individual̃𝑗𝑡 = (𝑎𝑗𝑡 , 𝑏𝑗𝑡 , 𝑐𝑗𝑡 , 𝑑𝑗𝑡 ), j = 1, 2, …., n; t = 1, 2, …., k, be the linguistic rating given
attributes, let 𝑊
̃𝑗 =to attributes 𝐶1 , 𝐶2 ,…., 𝐶𝑛 by decision-maker 𝐷𝑡 . The aggregated fuzzy rating, 𝑊(𝑎𝑗 , 𝑏𝑗 , 𝑐𝑗 , 𝑑𝑗 ), of attribute 𝐶𝑗 assessed by the committee of k decision-makers is defined as̃ j = (I1 ⊗ W̃ j1 ) ⊕ (I2 ⊗ W̃ j2 ) ⊕ . . .⊕ (Ik ⊗ W̃ jk ),
W(5.15)

where 𝑎𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑎𝑗𝑡 , 𝑏𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑏𝑗𝑡 , 𝑐𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑐𝑗𝑡 , 𝑑𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑑𝑗𝑡 .
Table 5.1: Linguistic variables and fuzzy numbers for ratings
Linguistic variables

Fuzzy numbers

Very poor(0, 0, 0, 20)

Between very poor and poor(0, 0, 20, 40)

Poor(0, 20, 20, 40)

Between poor and fair

(0, 20, 50, 70)

Fair(30, 50, 50, 70)

Between fair and good(30, 50, 80, 100)

Good

(60, 80, 80, 100)

Between good and very good

(60, 80, 100, 100)

Very good(80, 100, 100, 100)

Step 5: Computing the importance weight of attributes.
To compute the importance weight of attributes, defuzzify the fuzzy rating of the individual
attributes, compute the normalized weights, and construct the weight vector. To defuzzify thẽ𝑗 , denoted
rating of the fuzzy attributes, the signed distance is adopted. The defuzzification of 𝑊
̃𝑗 ), is therefore given byas d(𝑊̃ j ) = 1 (aj + bj + cj + dj )d(Wk(5.16)

The crisp value of the normalized weight for attributes 𝐶𝑗 , denoted by 𝑊𝑗 , is given by
̃j)
d(W
,
̃j)
d(W

Wj = ∑n(5.17)

j=1

where ∑𝑛𝑗=1 𝑊𝑗 = 1. The weight vector W = [𝑊1 , 𝑊2 , . . . , 𝑊𝑛 ] is therefore formed.
96

The crisp value of the normalized weight of the attributes 𝐶𝑗 can thus be used as the importanceweight of the attributes.
5.3.3 Identifying the order of establishment of TLHs
To facilitate the establishment of TLHs, this stage aims to determine the order in which
TLHs should be established. To do so, a fuzzy multi-attribute group decision-making approach
uses the qualitative attributes selected in the second stage to evaluate each TLH location
alternative obtained from the first stage. The following summarizes the main steps involved inthis fuzzy multi-attribute group decision-making method.
Step 1: Obtain the decision-opinions of decision-makers to assess alternatives with respect toindividual attributes, and obtain aggregated fuzzy ratings.
To assess the fuzzy ratings of location alternatives with respect to individual attributes, obtain
the decision-opinions of decision-makers using the linguistic variables outlined in Table 5.1,
and pool them together to obtain the aggregated fuzzy ratings. An interview questionnaire canbe used for the rating of alternatives.
Let 𝑥̃𝑖𝑗𝑡 = (𝑜𝑖𝑗𝑡 , 𝑝𝑖𝑗𝑡 , 𝑞𝑖𝑗𝑡 , 𝑟𝑖𝑗𝑡 ), i = 1, 2, . . . , m; j = 1, 2, . . . , n; t = 1, 2, . . . , k, be the linguistic
suitability rating assigned to alternatives 𝐴𝑖 for attributes 𝐶𝑗 by decision-maker 𝐷𝑡 . The
aggregated fuzzy rating 𝑥̃𝑖𝑗 of alternative 𝐴𝑖 for attribute 𝐶𝑗 assessed by the committee of kdecision-makers is defined asx̃ij = (I1 ⊗ x̃ij1 ) ⊕ (I2 ⊗ x̃ij2 ) ⊕ . . .⊕ (Ik ⊗ x̃ijk ),(5.18)

This can subsequently be represented and computed as𝑥̃𝑖𝑗 = (𝑜𝑖𝑗 , 𝑝𝑖𝑗 , 𝑞𝑖𝑗 , 𝑟𝑖𝑗 ), i = 1, 2, . . . , m, j = 1, 2, . . . , n
where 𝑜𝑖𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑜𝑖𝑗𝑡 , 𝑝𝑖𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑝𝑖𝑗𝑡 , 𝑞𝑖𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑞𝑖𝑗𝑡 , 𝑟𝑖𝑗 = ∑𝑘𝑡=1 𝐼𝑡 𝑟𝑖𝑗𝑡 .
Step 2: Construct a fuzzy rating matrix.
̃ can be constructed based on fuzzy ratings, and expressed concisely
The fuzzy rating matrix 𝑀
in the matrix format

97

𝑥̃11
𝑥̃21
..
̃=
𝑀
.
[𝑥̃𝑚1

𝑥̃12
𝑥̃22
..
.
𝑥̃𝑚2

.
..
.
.
.

. 𝑥̃1𝑛.. 𝑥̃2𝑛..
.
.
.
. 𝑥̃𝑚𝑛 ]where 𝑥̃𝑖𝑗 , ∀𝑖, 𝑗 is the aggregated fuzzy rating of alternative 𝐴𝑖 with respect to attribute 𝐶𝑗 .
Step 3: Derive the total fuzzy scores for individual alternatives by multiplying the fuzzy rating
matrix by its respective weight vectors.
̃ by theObtain the total fuzzy score vector by multiplying the fuzzy rating matrix 𝑀
corresponding weight vector W, i.e.,
x̃11
x̃21
..
̃ ⊗ WT =F̃ = M
.
[x̃m1

x̃12
x̃22
..
.
x̃m2

.
..
.
.
.

. x̃1nW1.. x̃2n
W2
..
.
⊗ ..
.
.
.
. x̃mn ][Wn ](5.19)

̃f1
̃f1== . = [f̃i ]m∗1 ,..
[x̃m1 ⊗ W1 ⊕ x̃m2 ⊗ W2 ⊕ ⋯ ⊕ x̃mn ⊗ Wn ][̃fm ]
x̃11 ⊗ W1 ⊕ x̃12 ⊗ W2 ⊕ ⋯ ⊕ x̃1n ⊗ Wn
x̃21 ⊗ W1 ⊕ x̃22 ⊗ W2 ⊕ ⋯ ⊕ x̃2n ⊗ Wn.
..

where 𝑓̃𝑖 = (𝑠𝑖 , 𝑡𝑖 , 𝑢𝑖 , 𝑣𝑖 ).
Step 4: Compute the crisp values using a defuzzification method.
Defuzzify the fuzzy scores 𝑓̃1 , 𝑓̃2 , . . . , 𝑓̃𝑚 by using signed distance method. The following
defuzzification equation is used to determine the crisp total scores of individual locations.
1d(f̃i ) = 4 (si + t i + ui + vi )i = 1, 2, . . . , m(5.20)

where d(𝑓̃𝑖 ) gives the defuzzified value (crisp value) of the total fuzzy score of location
alternative 𝐴𝑖 .
Step 5: Determine the order of establishment of the TLHs.

98

Finally, to determine the order of establishment of TLHs, rank the location alternatives basedon the crisp values. The location alternatives with larger crisp values should be established first,
followed by the location alternatives with lower values. The higher crisp value indicates thebetter performance of alternatives over the selected attributes.
5.4 Numerical illustration and analysis
To support the usefulness of this methodology, a numerical experiment was performed
using disaster data from April 2015 Nepal earthquake. The detail of the impacts can beenreferred from chapter 3.
5.4.1 Optimal number and the spatial location of TLHs
To determine the optimal number and location of TLHs, we considered seven supply points,
eleven candidate TLHs, and 13 demand points. The optimal solution was achieved byminimizing total unsatisfied demand over the entire planning horizon. An operational horizonof five weeks was considered with each period lasting one week. We accounted for a single
package relief delivery system. A single emergency relief package was assumed to weigh 10
kg and to include essential items such as meals, a basic medical kit, blankets, baby supplies,
and clothing. We estimated that a single emergency relief package is sufficient to sustain an
individual for a week. The demand, cost, and available units of relief supplies are assumed tobe time-varying.
The model was coded using Lingo 17.0 Optimization modeling software. All the experiments
were run on a personal computer with an Intel (R) Core (TM) i5-7500 CPU (3.40 GHz) and 16
GB of RAM. All the test problems were computed in under ten minutes. Under the given
conditions, the model resulted in a total of six TLHs with locations in Dolakha, Gorkha,
Kathmandu, Makwanpur, Okhaldhunga, and Sindhupalchok. Figure 5.1 shows the spatial
location of the selected TLHs on a map of Nepal.

99

Figure 5.1: Spatial location of temporary logistics hubs
5.4.2. Determining the importance weight of attributes
Eight attributes were identified through a combination of a survey of the literature on the
problem of facility location in humanitarian operations, the lessons learnt reports published bydifferent entities, as well as information regarding the socio-economic and geo-climatic
context of Nepal. Table 5.2 lists and describes the selected attributes.

100

Table 5.2: Description of the attributes
S.N.
1
2

Attribute
Availability of open
spacesAccessibility via
road

C1
C2

3

Accessibility via air

C3

4

Security

C4

5

Availability ofnecessary
infrastructure
Availability ofskilled manpower

C5

Disastervulnerability of
selected locations
Proximity to disaster
affected areas

C7

6

7

8

C6

C8

Description of the attribute
Determines whether there are open spaces
available to establish TLHs.
Refers to accessibility via road network, anddetermines the ease or difficulty in accessing thelocation by means of trucks, vans, etc.
Refers to accessibility issues via helicopters orplanes.
Denotes the security of the warehouse and related
facilitates around the selected location.
Refers to the availability of basic infrastructural
facilities, like electricity, water supply, etc.
Refers to the availability of the necessary
manpower to support proper functioning of TLH
in the candidate location.
Refers to the disaster vulnerability of the selected
location alternative—for example, whether thelocation is susceptible to secondary disasters.
Describes how close or far the selected location isfrom the affected areas in need of emergency
relief.

A committee of four decision-makers—D1, D2, D3, and D4—from four humanitarianorganizations active in disaster management in Nepal was formed. The decision-makers
involved in evaluating the qualitative attributes were assumed to be homogeneous—the degreeof importance is thus equal for all of the decision-makers.
Table 5.3 shows the decision-opinions of four decision-makers using the linguistic weighing
variables. The aggregated fuzzy rating of individual attributes was computed using equation(5.15) with reference to fuzzy numbers corresponding to each linguistic variable (Table 3.1).
The importance weight of the attributes was calculated by defuzzifying the fuzzy numbers
using the signed distance approach represented by equation (5.16), and the normalized weightwas calculated using equation (5.17). The aggregated fuzzy weight, crisp values after
defuzzification, and the normalized weight are shown in Table 5.3.

101

Table 5.3: The importance weight of attributes

Attributes D1
C1
C2
C3
C4
C5
C6
C7
C8

D2

D3

D4

Aggregated fuzzy
Defuzzified
weight (AFW)
value of AFW
VH VH VH H (6.5, 9.25, 9.25, 10)8.750
VH VH H VH (6.5, 9.25, 9.25, 10)8.750
M H VH VH (5.25, 8, 8, 9.5)
7.687
H M H H (4.25, 6.5, 6.5, 9.5)
6.687
VH H VH M (5.25, 8, 8, 9.5)
7.687
M VL H M (2.25,4.25, 4.25, 7.25)
4.500
H VH H H (5.5, 7.75, 7.75, 10)7.750
VH VH M H (5.25, 8, 8, 9.5)
7.687

Normalized
AFW
0.147
0.147
0.129
0.112
0.129
0.076
0.130
0.129

5.4.3 Order of establishment of TLHs
To determine the order of establishment, we used the six TLHs obtained from the first stage
as alternatives and evaluated them further using the attributes selected in the second stage byapplying the fuzzy multi-attribute group decision-making method proposed in third stage.

102

Table 5.4: Decision-makers’ evaluation and fuzzy rating matrix
AttributeAlternative
D1
DolakhaF
GorkhaB.G & V.G
Kathmandu
G
C1
Makwanpur
V.G
Okhaldhunga F
Sindhupalchok B.F & G
DolakhaB.F & G
GorkhaB.G & V.G
Kathmandu
V.G
C2
Makwanpur
B.G & V.G
Okhaldhunga F
Sindhupalchok F
DolakhaB.P & F
GorkhaV.P
Kathmandu
V.G
C3
Makwanpur
G
Okhaldhunga F
Sindhupalchok P
DolakhaG
GorkhaF
Kathmandu
B.G & V.G
C4
Makwanpur
B.F & G
Okhaldhunga F
Sindhupalchok F
DolakhaG
GorkhaB.F & G
Kathmandu
B.G & V.G
C5
Makwanpur
G
Okhaldhunga F
Sindhupalchok B.P & F
DolakhaG
GorkhaB.F & G
Kathmandu
V.G
C6
Makwanpur
G
Okhaldhunga F
Sindhupalchok B.P & F
DolakhaB.G & V.G
GorkhaF
Kathmandu
B.G & V.G
C7
Makwanpur
F
Okhaldhunga F
Sindhupalchok P

D2
D3
B.P & F
B.P & FP
B.P & F
V.P
P
P
GP
B.F & G
V.P
B.P & FF
B.P & F
GF
P
GG
G
B.P & F
B.P & FF
B.P & F
V.P
B.P & FPP
GG
B.P & F
GP
B.P & F
V.P
P
F
B.P & FG
B.F & G
G
G
G
B.F & GP
F
B.P & F
B.P & F
F
F
B.P & FP
G
B.F & G
G
F
P
B.P & FPP
P
B.P & F
B.P & FP
G
B.F & G
B.P & F
B.P & F
B.V.P & P B.P & F
PPF
B.P & F
B.F & G B.P & F
GF
GF
B.V.P & P F
B.P & F
B.P & F

D4
P
V.G
G
G
B.P & F
G
F
G
G
G
P
G
F
P
G
B.F & GP
B.P & F
F
G
G
G
B.P & FG
B.P & FF
B.F & G
G
B.P & F
B.F & GP
B.P & F
B.F & G
B.F & GP
B.F & G
B.P & F
G
F
G
B.P & F
G

Aggregated fuzzy ratings(7.5, 27.5, 42.5, 62.5)(35, 55, 67.5, 77.5)(30, 45, 45, 65)(50, 70, 70, 85)(15, 35, 50, 70)(22.5, 37.5, 52.5, 72.5)(22.5, 42.5, 57.5, 77.5)(52.5, 72.5, 77.5, 92.5)(50, 70, 70, 85)(60, 80, 85, 100)
(7.5, 27.5, 42.5, 62.5)(30, 50, 57.5, 77.5)(7.5, 22.5, 37.5, 57.5)(0, 15, 15, 35)(65, 85, 85, 100)
(37.5, 57.5, 72.5, 92.5)(7.5, 27.5, 35, 55)(0, 15, 22.5, 42.5)(30, 50, 57.5, 77.5)(45, 65, 72.5, 92.5)(60, 80, 85, 100)
(45, 65, 80, 100)
(15, 35, 42.5, 62.5)(22.5, 42.5, 57.5, 77.5)(30, 50, 57.5, 77.5)(15, 35, 50, 70)(45, 65, 85, 100)
(52.5, 72.5, 72.5, 92.5)(7.5, 27.5, 42.5, 62.5)(7.5, 27.5, 42.5, 62.5)(15, 35, 42.5, 62.5)(7.5, 27.5, 50, 70)(50, 70, 85, 100)(22.5, 42.5, 65, 85)(7.5, 22.5, 35, 55)(7.5, 27.5, 42.5, 62.5)(22.5, 42.5, 62.5, 77.5)(30, 50, 65, 85)(45, 65, 70, 85)(45, 65, 65, 85)(15, 30, 42.5, 62.5)(15, 35, 50, 70)103

Table 5.4 (contd.): Decision-makers’ evaluation and fuzzy rating matrix
AttributeAlternative
D1
DolakhaB.G & V.G
GorkhaG
Kathmandu
F
C8
Makwanpur
P
Okhaldhunga F
Sindhupalchok B.G & V.G

D2
F
B.F & G
G
G
B.P & F
B.P & F

D3
B.P & FF
B.F & GF
B.P & F
F

D4
B.P & F
B.G & V.G
F
B.F & G
B.P & F
V.G

Aggregated fuzzy
ratings(22.5, 42.5, 62.5, 77.5)(45, 65, 77.5, 92.5)(37.5, 57.5, 65, 85)(30, 50, 57.5, 77.5)(7.5, 27.5, 50, 70)(42.5, 62.5, 75, 85)

The decision-opinion of decision-makers in terms of fuzzy ratings for selected alternatives
were obtained using the linguistic variables outlined in Table 5.1. Table 5.4 shows the decisionmakers’ evaluations and the aggregated fuzzy ratings computed for each alternative, as well as
the respective criterion combination using equation (5.18). The fuzzy ratings matrix in Table
5.5 has been constructed using the aggregated ratings in Tables 5.3 and 5.4.
Table 5.5: Fuzzy rating matrix
AttributesDolakha

GorkhaC4(7.5, 27.5, 42.5,
62.5)(22.5, 42.5, 57.5,
77.5)(7.5, 22.5, 37.5,
57.5)(30, 50, 57.5, 77.5)C5(30, 50, 57.5, 77.5) (15, 35, 50, 70)

C6(15, 35, 42.5, 62.5) (7.5, 27.5, 50, 70)

C7(22.5, 42.5, 62.5,
77.5)(22.5, 42.5, 62.5,
77.5)

C1
C2
C3

C8

Kathmandu Makwanpur

Okhaldhunga Sindhupalchok(35, 55, 67.5, 77.5) (30, 45, 45, 65)(50, 70, 70, 85)(15, 35, 50, 70)(52.5, 72.5, 77.5,
92.5)(0, 15, 15, 35)(60, 80, 85, 100)

(7.5, 27.5, 42.5,
62.5)(7.5, 27.5, 35, 55) (0, 15, 22.5, 42.5)(50, 70, 70, 85)(65, 85, 85, 100) (37.5, 57.5, 72.5,
92.5)(45, 65, 72.5, 92.5) (60, 80, 85, 100) (45, 65, 80, 100)

(30, 50, 65, 85)(22.5, 37.5, 52.5,
72.5)(30, 50, 57.5, 77.5)(15, 35, 42.5, 62.5) (22.5, 42.5, 57.5,
77.5)(45, 65, 85, 100) (52.5, 72.5, 72.5, (7.5, 27.5, 42.5, (7.5, 27.5, 42.5,
92.5)
62.5)
62.5)
(50, 70, 85, 100) (22.5, 42.5, 65, 85) (7.5, 22.5, 35, 55) (7.5, 27.5, 42.5,
62.5)(45, 65, 70, 85) (45, 65, 65, 85)(15, 30, 42.5, 62.5) (15, 35, 50, 70)(45, 65, 77.5, 92.5) (37.5, 57.5, 65,85)(30, 50, 57.5, 77.5) (7.5, 27.5, 50, 70) (42.5, 62.5, 75, 85)

The normalized weight in Table 5.3 and fuzzy ratings in Table 5.5 were combined using
equation (5.19) to obtain the total fuzzy scores for each location. Table 5.6 shows the resultingscores. The crisp values of the total fuzzy scores were obtained using the defuzzification
equation (5.20), shown in Table 5.6. Finally, the alternatives were ranked based on thedefuzzified total scores and used to determine the order of establishment of TLHs (Table 5.6).

104

Table 5.6: Aggregated fuzzy number, defuzzified total score, and order of establishment
Location
Aggregate fuzzy number Defuzzified total scorealternatives
Kathmandu(47.21, 66.48, 72.38, 88.76)
68.71
Makwanpur(44.31, 64.31, 71.34, 89.87)
67.46
Gorkha(30.16, 49.51, 60.14, 77.29)
54.27
Dolakha(19.60, 38.96, 52.88, 71.58)
45.76
Sindhupalchok (19.23, 37.85, 50.46, 69.17)
44.18
Okhaldhunga (10.42, 2940, 43.04, 63.04)
36.48

Order ofestablishment
I
II
III
IV
V
VI

The results of the interviews with the decision-makers in Table 5.3 reveals the differences in theirdecision-opinions. While three of the four decision-makers revealed that the availability of open
spaces is of very high importance, one decision-maker placed comparatively lower importance on
the same attribute. The decision-opinions of different decision-makers are heterogeneous ingeneral—underscoring the importance of considering multiple decision-makers in the evaluation
process. The normalized aggregated fuzzy weight in Table 5.3 shows that the “availability of open
spaces” and “accessibility via roads” were perceived as highly important attributes, while the“availability of skilled labor” was deemed least important.
The order of establishment of TLHs can be determined with reference to the defuzzified total scoresprovided in Table 5.6. A higher value of a defuzzified total score means that the selected TLH
performs better than its alternatives, and should thus be established first to achieve maximum
effectiveness. Based on the decision-opinions of four decision-makers considered homogeneous, thefinal order of establishment should see the first TLH installed in Kathmandu, followed by
Makwanpur, Gorkha, Dolakha, Sindhupalchok, and finally Okhaldhunga. The spider chart in Figure
5.2 illustrates the performance of the selected TLHs over the selected attributes. As seen in Figure
5.2, the location alternative of Kathmandu performs the best among the six selected TLHs, andtherefore should be established first. While Kathmandu lags behind other alternatives in terms ofopen space availability, accessibility via roads, and proximity to disaster affected areas, it performs
better overall.

105

GorkhaKathmandu

Kavrepalanchok

Nuwakot

Sindhuli

Sindhupalchok

C1
100
C8

80

C2

60

40
20
C7

C3

0

C6

C4
C5

Figure 5.2: Performance of TLHs over all attributes
In order to understand the importance of including multiple actors and their impact on the overall
decision-making process, we performed further calculations under different scenarios. Table 5.7
provides a comparison of the results in terms of variation in the order of establishment under three
scenarios: single actor, multi-actor homogeneous, and multi-actor heterogeneous. When the decisionmaking process is conducted by only one decision-maker, the order of establishment is as follows:
Kathmandu, Makwanpur, Dolakha, Gorkha, Okhaldhunga, and Sindhupalchok. In the homogenous
multi-actor scenario, the order of establishment is: Kathmandu, Makwanpur, Gorkha, Dolakha,
Sindhupalchok, and Okhaldhunga. Meanwhile, in a heterogeneous multi-actor scenario it the order
is: Kathmandu, Makwanpur, Gorkha, Sindhupalchok, Dolakha, and Okhaldhunga. This highlights
the importance of considering multiple decision-makers and their influence over the decision-making
process—as is the case in reality.

106Table 5.7: Comparison of single and multiple actor scenarios
Selected locations

DolakhaGorkhaKathmandu
Makwanpur
Okhaldhunga
Sindhupalchok

Order of establishment
Single-actor
Multi-actor
Homogeneous
Heterogeneous
III
IV
V
IV
III
III
I
I
I
II
II
II
V
VI
VI
VI
V
IV

5.5 Chapter summary
Recently, temporary facilities for disaster response has been receiving growing attention
from scholars and practitioners alike. However, location selection and ordering are immenselycomplex due to the lack of information, growing number of humanitarian responders, and theneed to evaluate subjective attributes during the chaotic disaster response period. This study
has combined an optimization model with fuzzy multi-attribute group decision-making todevelop a methodology for determining the order of establishment of TLHs. This is a threestage process: the multi-period optimization problem determines the number and spatial
location of TLHs by minimizing the total unsatisfied demand, the fuzzy factor rating system
calculates the importance weight of subjective attributes, and the fuzzy multi-attribute groupdecision-making method ascertains the order of establishment of the selected TLHs by
considering eight subjective attributes.
The proposed methodology was implemented using data obtained from the April 2015 Nepal
earthquake. Of the eleven candidate locations assumed to fulfill the time-varying demand overthe entire planning horizon, the optimization model pinpointed six locations: Dolakha, Gorkha,
Kathmandu, Makwanpur, Okhaldhunga, and Sindhupalchok. Interviews with decision-makers
revealed the differences in their opinion regarding the prominence of different attributes. Thisdifference in decision-opinion was also observed when evaluating the performance of selected
locations versus the attributes. Further analysis showed that the order of establishment varies
significantly when the locations are evaluated under different scenarios. In this study, the orderof establishment under the three scenarios of single actor, homogeneous multiple actors, andheterogeneous multiple actors were found to differ considerably. This led us to conclude that
it is essential to consider real life scenarios when making decisions regarding TLHs.

107

Though we have used a single objective optimization approach for generating the optimal TLH
number and their spatial location alternatives in this chapter, the multi-objective optimization
models both the deterministic one and the possibilistic one can also be used to generatealternatives. Depending on the actual need of the situation appropriate mathematical model
can be used in the first phase.

108

CHAPTER 6 Summary and Conclusion

6.1 Facility location in perspective
Figure 6.1 shows the facility location problem in perspective. Through this dissertation we
have addressed a temporary logistics hub establishment problem with a finite horizon with both
single and multiple objectives considering time-varying uncertain and time-varying
deterministic nature of parameters using both qualitative and quantitative modeling approach.

Figure 6.1: Facility location problem in perspective
6.2 Summary and Conclusion
In the recent years, the field of humanitarian logistics has been receiving burgeoning
attention from both academics and practitioners. However, review of the extant of literature
reveals a general lack of studies focusing on temporary logistical facilities that enables
streamlining post-disaster operations to minimize suffering of affected people. Thisdissertation started with a broader aim of introducing the concept of temporary logistics hubs
and its significance in post-disaster operation especially focusing on developing countries
where preparedness lags behind actual needs. In doing so we studied different dimensions of
TLHs ranging from determining their location, allocation, timing of establishment, andordering of establishment and developed models and methodology for determining them.
Furthermore, methodologies were also developed to enable evaluation of qualitative andquantitative attributes, and decision-making approaches which plays a vital role in enabling109

comprehensive analysis of multiple aspects of TLH location problem and its operationalsustainability. The following sections summaries what has been achieved through each chapter
in retrospective to the objectives of this study.
Chapter three – One of the key decisions to make regarding TLHs is to determine and decideon where to locate them to achieve desired objective/s. Unlike commercial operations,humanitarian operations often have more than one objective which necessitates use of multiobjective optimization. However, use of this approach requires knowing the weights assigned
to different objectives which is often complicated. Furthermore, humanitarian response
operations often requires engagement of wide range of actors ranging from governmentorganizations to national and international non-governmental organization, and community
organizations where the decision-makers have to make myriad of decisions under pressure andimpreciseness while ensuring agility of relief chain. To address these issues in this chapter wedeveloped a multi-objective location model with the objectives of minimizing total cost andunsatisfied demand with multi-sourcing feature and a FFRS under GDM. The FFRS under
GDM is used to determine the weight of objectives which is capable of accommodating
decision-opinion of multiple decision-makers. The results of the numerical illustration using
April 2015 Nepal earthquake shows trade off relationship between the two objectives andvarying decision-opinion of different decision-makers when the decision-makers wereconsidered homogeneous. Sensitivity analysis shows higher availability of emergency relief inthe TLHs increases demand satisfaction at the price of increased costs. Further, the analysis of
the multi-sourcing constraint reveals the reduction in total unsatisfied demand at the cost ofincreased costs in the multi-sourcing setting compared with single-sourcing under the same
availability restrictions. Despite the increased cost, multi-sourcing enables supply chain agility,
which is essential during disaster response.
Chapter four – Disaster response operations are often carried out immediately after its
occurrence, during which time the information regarding precise values of the parameters isstill evolving. The entire decision-making ability/process is tainted with high degree of
uncertainty. Under these circumstances, knowing not only where and how many TLHs toestablish, but also when to establish them is necessary while taking account of the uncertainty
in parameter value. In this chapter we develop a possibilistic multi-objective optimization
model that determines the location of TLHs and allocation of open TLHs to the demand points.
The model minimizes total cost while maximizing total demand coverage using epsilon

110constraint method. A credibility based fuzzy chance constrained programming approach is used
to account for possibilistic parameters and FMAGDM is used to evaluate availability of open
spaces and transportation accessibility during the immediate aftermath. The results of thenumerical illustration shows the location, number of TLHs along with their sequence (timing)of establishment and allocation of the open facilities to PODs. Sensitivity analysis provided us
with a wider understanding of the impact of limiting number of TLHs, confidence level within
which objectives and constraints must be fulfilled, the spread of the symmetrical triangularfuzzy number on the coverage and cost objectives. It can be concluded that increase in theseparameters lead to increase in both the demand coverage and total cost. Additionally, the fuzzy
factor rating system used under group decision-making condition also enables accommodating
multiple decision-makers in the decision-making process. Often during the chaotic response
period a single decision-maker may not have all the information regarding various parameter.
Therefore, inclusion of multiple decision-makers in obtaining the values of these parameters
plays an important role.
Chapter five – This chapter introduces the concept of the order of establishment of TLHs.
Determining the order of establishment plays an important role in ensuring maximum
utilization of the mobile storage units which are used as TLHs when they are in limited
availability which is often true during the initial phase of post-disaster operation. Order of
establishment can be determined after their optimal number, their corresponding spatial
location and allocation strategies, and their timing of establishment have been determined. It is
worth noting that the concept introduced in this chapter is almost non-existent in the existing
literature. From the methodological point of view, often studies have used either optimization
approach or multi-criteria decision-making approach to deal with location problems. In thischapter we attempt to take the benefit obtained by amalgamating an optimization approachwith multi-criteria decision-making approach where the optimization model determines the
optimal numbers and locations of TLHs and FMAGDM is used to determine their order of
establishment. While both the mathematical models developed in chapter three and four candetermine the optimal number and location of the TLHs we have developed a single objective
optimization model with the objective of minimizing total unsatisfied demand to determine theinitial results. FMAGDM approach employed here enables evaluation of qualitative attributes
affecting the ordering decision while taking account of decision-opinion of multiple decisionmakers in terms of fuzzy linguistic variables. In the numerical illustration, the decision-opinionof four decision-makers reveals availability of open spaces and transportation accessibility as
111

the two most important attributes for determining the order of establishment of TLHs. The
performance of the selected TLHs can also be observed from the results.
Generally speaking, humanitarian operations should focus on optimizing humanitarian
objectives as dictated by the humanitarian code of conduct. However, discrepancy can beobserved in the real life operations where minimizing cost becomes a significant objective. A
thorough understanding of the impact of the choice of objectives on the location selection isdesirable in this case. In this dissertation, we have developed three optimization models withdifferent objectives with the aim of understanding this. Chapter three has developed a multiobjective optimization model with the objective of minimizing total cost and total unsatisfied
demand. Similarly, in chapter four a possibilistic multi-objective model with the objectives ofmaximizing total demand coverage and minimizing total cost is developed. On the contrary, asingle objective optimization model with the objective of minimizing total unsatisfied demandis developed in chapter five. As a summary, in terms of the choice of objectives this dissertation
has explored location selection with wide range of objectives which can provide managerial
insights on the impact of choice of objective function on TLH location selection decision.
In retrospect to the objectives of this dissertation we have developed three different models todetermine the optimal number, their spatial location, allocation of selected TLHs, and theirorder of establishment while also accounting for features like multi-sourcing, incorporating
multiple actors in the decision-making process, uncertainty arising due to impreciseness in thisdissertation. While multi actor approach to optimization modelling is almost insignificant in
the literature of humanitarian logistics, the interview with the logistics experts from different
humanitarian organizations revealed difference in their decision opinion highlighting thesignificant of incorporating them in the decision-making process.
6.3 Comparison of results
In chapter three, model results of the numerical illustration has selected eight optimal TLHs
with locations in Gorkha, Kathmandu, Kavrepalanchok, Makwanpur, Nuwakot, Ramechhap,
Sindhuli, and Sindhupalchok to operate for the entire planning horizon of five periods. In
chapter four, time-varying locations in eleven candidate TLH locations in Dhanding, Dolakha,
Gorkha, Kathmandu, Kavrepalanchok, Makwanpur, Nuwakot, Okhaldhunga, Ramechhap,
Sinduli, and Sindhupalchok are selected for establishment of TLHs within an operational
horizon of seven periods. Among the twelve candidates, TLH in Dolakha, Kathmandu, and112

Sindhuli is selected to operate for seven periods and Gorkha, Nuwakot, Okhaldhunga, andSindhupalchok is selected to operate for six periods. Similarly, TLH in Dhading and
Makwanpur is selected to operate for five periods and TLH in Kavreplanchok is selected tooperate for four periods starting from second period ending in fifth period. Finally, TLH in
Ramechhap is selected to be operational only in fourth period. In chapter five, a total of six
TLHs with locations in Dolakha, Gorkha, Kathmandu, Makwanpur, Okhaldhunga, andSindhupalchok are selected to operate for the entire planning horizon of five periods.
It is worth to note that, the features of the mathematical model and the objectives of concern
are different in each chapter, consequently the optimal choice of TLH location and their
numbers are also different. Although, chapter three and chapter five deals with static nature of
TLHs and chapter four with time-varying nature, TLH candidate locations in Dolakha andKathmandu are selected to operate for the entire planning horizon in all three chapters whichsignifies the importance of these locations in the overall humanitarian response operation
irrespective of the choice of objectives and modelling features. However, from the results, it
can also be concluded that, the choice of objective function and the solution methodology inaddition to other model features has considerable impact on the location selection decision.
6.4 Practical implication and applicability
Based on the insights gained in the course of this dissertation, this section discusses what
implications the research findings have for the actors/decision-makers for improving
humanitarian operations.


Large scale humanitarian operations usually see involvement of more than one
actor/stakeholder/decision-maker in real life. However, an inability to accommodate
the actors in the establishment decision-making may have its consequences. Therefore,
practical implication of involving multiple decision- maker early in the decisionmaking process enables coordination by synthesizing a representative outcome from adecision-maker’s judgements. This further helps to develop a sense of ownership of theestablished TLHs and its operations. This sense of ownership is important to maximize
the utilization of the established hubs while enabling coordination.



The application of group decision-making approach also enables minimizing
discrepancy caused by lack of information of information asymmetry. When thedecision is made by a group more accurate information can be obtained while reducing
113

redundancy in information and operation. The practical implication of involving
multiple decision-makers early in the decision making process allows synthesis
information from more than one decision-maker during the information scarce response
phase.
The trade-off between non-commensurable objectives provides decision-makers with
ample alternatives and combinations from which to choose when deciding on theavailable quantity of emergency relief goods as well as the number and location of the
TLHs.



The methodology developed herein can provide disaster managers with an effectivemeans to ascertain the location sequencing of TLHs under impreciseness in values ofparameters which is often the case in real life response operations. Time-varying
location sequencing allows the humanitarian relief chain network to be responsive tothe changes in the factors pertinent to increasing the efficiency and effectiveness ofhumanitarian operations.

When the resources for establishment of TLHs are limited and their effective utilization
is vital which is often the case in the immediate aftermath of the disaster (eg: after April
2015 Nepal earthquake) particularly in developing countries where the investment on
disaster preparedness is minimal, determining the order of establishment of TLHs
especially useful of the decision-makers who have to make myriad of decisions withlimited information and time.

The evaluation of TLH location alternatives based on the qualitative attributes allows
for ensuring operational sustainability of the established hubs. Based on theperformance of TLH over the selected attributes, insightful suggestions can be made tostrengthen the performance over the weaker attributes.



Although, all the numerical illustrations have been performed with earthquake case, themodels and methodologies developed within the scope of this dissertation have broader
applicability in real life disaster cases. Especially, the methodology developed in
Chapter 4 is applicable to moving disaster like floods where time-varying nature of
TLHs are key to the effectiveness of humanitarian operation.

6.5 Recommendation for future establishment of TLHs
In response to Nepal earthquake 2015 nine storage hubs were made available in different
parts of the country. Specific spatial location of the hubs can be observed in Figure 1.1. Table

114

6.1 shows the name/location of the hubs, date of identification, number of organizations using
it, volume of relief stored in each hubs.
Table 6.1: Details of storage hubs during Nepal earthquake 2015
S.N.

Location of storage hubs

Date of

Number ofVolume ofidentification

organizations

relief (m3)1Kathamndu

Pre-established86

16,1102

Gorkha (Deurali)2015 May 1

47

6,278

3

Sindhupalchok (Chautara)

2015 May 8

19

3,511

4

Chitwan (Bharatpur)

2015 May 11

5

1,492

5

Kavrepalanchok (Dhulikhel) 2015 May 12

15

4175

6

Dhading (Dhading Besi)

NA

12

955

7

(Nuwakot) Bidur

NA

10

1,700

8

Rasuwa (Dhunche)

NA

4

183

9

Dolakha (Charikot)

NA

8

1,904

Recommendations made for future establishment of TLHs are in reference comparison withthe actual logistics strategy adopted during Nepal earthquake 2015. Concisely translating thefindings of this study to practical world and policy implications for future establishment of
TLHs, the following points were found important to consider:
1. Response to Nepal earthquake 2015, saw establishment of transit hubs in
Kavrepalanchok and Chitwan as the first response strategy which later acted as supply
sources to regional storage hubs in Gorkha, Shindhupalchok, Dhanding, Nuwakot,
Rasuwa, and Dolakha. In the ideal situation, these hubs should have been established
as a part of preparedness phase. Doing this could have saved both time, effort, andmoney.
Therefore, in the context of disaster response operation, special attention needs to be
paid to strengthen disaster preparedness. This can translate to substantial reduction intransportation cost and improvement in overall relief delivery. Disaster preparedness
can be strengthened by establishing warehousing facilities for storage of emergency
relief, identifying reliable supply sources and open spaces etc.
2. The response to Nepal earthquake 2015 can be summarized (Table 6.2) as establishingstorage hubs in major crisis hit districts except for hubs in Kathmandu, Kavrepalanchok,115

and Chitawan. This may severely hinder effectiveness of the overall response operation.
Therefore, future establishment decision-making should aim at avoiding ad hoc
decision-making and adopt a systematic approach.
Table 6.2: Summary of the TLH selection

3. The significance of objective selection for distribution network design wasdemonstrated by the varying numbers and corresponding spatial locations of TLHs withthe varying types of objectives (Table 6.2). Therefore, it is desirable to determine
mutually acceptable objective/s in the preparedness phase. The choice of objectives
may vary conditional to the nature of disaster and type of decision-making entities
involved.
4. One of the main shortcoming faced in the operation of storage hubs during Nepal
earthquake is the problem of ownership of the established hubs. Organizations were
only found to be interested in using the storage hubs but not taking the responsibility ofensuring its operation. The interview with the decision-makers clearly illustratedifference in their decision-opinions. Therefore, future establishment decisions should
focus on incorporating multiple decision-makers in location decision-making.
5. Future establishment of TLHs should focus on determining appropriate order of
establishment. Nepal earthquake faced challenges with actual operation of establishedhub due to lack of sufficient and relevant equipment and handling capacities likeforklifts. Although, detailed information on how long did it take for the problem to besolved, it determining the order of establishment of TLJs becomes instrumental in the
successful operation of those established.

116

6. Establishment of TLHs needs be addressed in holistic view including quantitative andqualitative criteria incorporating multiple actors to ensure effective utilization andsustainable operation of TLHs. Depending on the scale of disasters, response operations
are often beyond the capability of single entity. Moreover, response operations indeveloping countries frequently face epistemic uncertainty. Incorporation of multiple
actors can lead to possible reduction in accuracy, information asymmetry withenhanced cooperation.
6.6 Scope of future work
The scope of the future work is geared towards addressing the limitation encountered in the
conduct of this study. Though the concept, methodological development, and findings of thisdissertation contribute to the body of the literature, based on the insights gained in the courseof the study, the following specific topics lend themselves to future research.
Operational horizon: The length of disaster response operation plays an important role indetermining the operational horizon of TLHs. However, determining the exact duration is acumbersome task which depends on factors like economic status of the country/region, levelof development, severity of disaster etc. Future research could focus on determining the exact
length of operational horizon. This may enable efficient and effective utilization of mobile
storage units in case of multiple disaster cases.
Importance of decision-makers: Real life decision-making involves active participation of
more than one decision-makers. These decision-makers may have varying degree ofimportance based on their hierarchy and/or knowledge. Developing a method to determine therelative importance of decision-makers and incorporating it into the model is thus a possible
extension.
Confidence level: As the complexity of the response operation is growing, determining thedesired confidence level to ensure optimum service is of great value. Future researchers could
examine in greater detail the nature of the confidence level used in chapter four and possible
method to elicit its value.
Level of uncertainty: The level of uncertainty in the parameter values in our current study(chapter four) is represented by the spread of the symmetric triangular fuzzy number which has
been assumed to be 15 percent. However, it is quite challenging to determine its precise value
117

and its nature (time-varying or not). A coordinated approach with constant participation ofdecision-maker could be a possible avenue to further research on this topic.
Accounting for uncertainty: There is an extant of literature in humanitarian logistics using
stochastic or robust approach to model uncertainty. However, the nature of uncertainty
prevalent in post-disaster stage is often ignored. Through this study an attempt has been madeto account for uncertainty arising due to impreciseness using possibility distribution. Future
research could explore this avenue by developing/employing other approaches to account forthis type of uncertainty.

118

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APPENDIX
APPENDIX A
Transportation cost from supply points to candidate TLHs per km per vehicle (in USD)
Supplypoints
TIA

KAKAD

BIRAT

Candidate
TLHs
DHA

T1

T2

T3

T4

T5

T6

T7

0.167

0.167

0.155

0.149

0.143

0.143

0.143

DOL

0.267

0.267

0.248

0.238

0.228

0.228

0.228

GOR

0.290

0.290

0.269

0.259

0.249

0.249

0.249

KTM

0.010

0.010

0.009

0.009

0.008

0.008

0.008

KAV

0.051

0.051

0.047

0.046

0.044

0.044

0.044

MAK

0.014

0.014

0.013

0.012

0.012

0.012

0.012

NUW

0.163

0.163

0.151

0.145

0.139

0.139

0.139

OKH

0.155

0.155

0.144

0.138

0.133

0.133

0.133

RAM

0.414

0.414

0.384

0.369

0.354

0.354

0.354

RAS

0.243

0.243

0.226

0.217

0.209

0.209

0.209

SIN

0.257

0.257

0.238

0.229

0.220

0.220

0.220

SIND

0.290

0.290

0.269

0.259

0.249

0.249

0.249

DHA

1.070

1.070

0.994

0.956

0.917

0.917

0.917

DOL

0.831

0.831

0.772

0.742

0.712

0.712

0.712

GOR

1.172

1.172

1.088

1.047

1.005

1.005

1.005

KTM

0.937

0.937

0.870

0.837

0.803

0.803

0.803

KAV

0.837

0.837

0.777

0.747

0.717

0.717

0.717

MAK

0.933

0.933

0.866

0.833

0.800

0.800

0.800

NUW

0.782

0.782

0.726

0.698

0.670

0.670

0.670

OKH

1.058

1.058

0.983

0.945

0.907

0.907

0.907

RAM

0.661

0.661

0.613

0.590

0.566

0.566

0.566

RAS

1.154

1.154

1.071

1.030

0.989

0.989

0.989

SIN

0.717

0.717

0.666

0.641

0.615

0.615

0.615

SIND

0.600

0.600

0.557

0.536

0.514

0.514

0.514

DHA

0.925

0.925

0.859

0.826

0.793

0.793

0.793

DOL

0.684

0.684

0.635

0.611

0.586

0.586

0.586

GOR

1.027

1.027

0.954

0.917

0.880

0.880

0.880

KTM

0.792

0.792

0.735

0.707

0.679

0.679

0.679

KAV

0.692

0.692

0.642

0.618

0.593

0.593

0.593

MAK

0.745

0.745

0.692

0.665

0.638

0.638

0.638

NUW

0.635

0.635

0.590

0.567

0.544

0.544

0.544

OKH

0.913

0.913

0.848

0.816

0.783

0.783

0.783

RAM

0.514

0.514

0.477

0.459

0.440

0.440

0.440

RAS

0.990

0.990

0.919

0.884

0.849

0.849

0.849

SIN

0.570

0.570

0.530

0.509

0.489

0.489

0.489

SIND;

0.453

0.453

0.420

0.404

0.388

0.388

0.388

127

BHAIRA

DHA

0.545

0.545

0.506

0.487

0.467

0.467

0.467

DOL

0.937

0.937

0.870

0.837

0.803

0.803

0.803

GOR

0.368

0.368

0.342

0.329

0.316

0.316

0.316

KTM

0.541

0.541

0.502

0.483

0.464

0.464

0.464

KAV

0.582

0.582

0.541

0.520

0.499

0.499

0.499

MAK

0.531

0.531

0.493

0.474

0.455

0.455

0.455

NUW

0.384

0.384

0.357

0.343

0.329

0.329

0.329

OKH

0.610

0.610

0.566

0.544

0.522

0.522

0.522

RAM

0.939

0.939

0.872

0.838

0.805

0.805

0.805

RAS

0.592

0.592

0.550

0.529

0.508

0.508

0.508

SIN

0.825

0.825

0.766

0.737

0.707

0.707

0.707

SIND

0.708

0.708

0.657

0.632

0.606

0.606

0.606

DHA

0.380

0.380

0.353

0.340

0.326

0.326

0.326

DOL

0.192

0.192

0.178

0.172

0.165

0.165

0.165

GOR

0.504

0.504

0.468

0.450

0.432

0.432

0.432

KTM

0.227

0.227

0.211

0.203

0.195

0.195

0.195

KAV

0.169

0.169

0.157

0.151

0.144

0.144

0.144

MAK

0.221

0.221

0.206

0.198

0.190

0.190

0.190

NUW

0.372

0.372

0.346

0.333

0.319

0.319

0.319

OKH

0.367

0.367

0.340

0.327

0.314

0.314

0.314

RAM

0.504

0.504

0.468

0.450

0.432

0.432

0.432

RAS

0.457

0.457

0.425

0.408

0.392

0.392

0.392

SIN

0.347

0.347

0.322

0.310

0.297

0.297

0.297

SIND

0.380

0.380

0.353

0.340

0.326

0.326

0.326

NEPALGUNJ DHA

0.994

0.994

0.923

0.887

0.852

0.852

0.852

DOL

1.439

1.439

1.336

1.285

1.233

1.233

1.233

GOR

0.868

0.868

0.806

0.775

0.744

0.744

0.744

KTM

1.041

1.041

0.966

0.929

0.892

0.892

0.892

KAV

1.084

1.084

1.006

0.968

0.929

0.929

0.929

MAK

1.037

1.037

0.963

0.926

0.889

0.889

0.889

NUW

0.884

0.884

0.821

0.789

0.758

0.758

0.758

OKH

0.984

0.984

0.914

0.879

0.843

0.843

0.843

RAM

1.439

1.439

1.336

1.285

1.233

1.233

1.233

RAS

1.049

1.049

0.974

0.937

0.899

0.899

0.899

SIN

1.325

1.325

1.230

1.183

1.136

1.136

1.136

SIND

1.207

1.207

1.121

1.078

1.035

1.035

1.035

DHA

0.447

0.447

0.415

0.399

0.383

0.383

0.383

DOL

0.557

0.557

0.517

0.497

0.477

0.477

0.477

GOR

0.398

0.398

0.369

0.355

0.341

0.341

0.341

KTM

0.537

0.537

0.499

0.480

0.460

0.460

0.460

KAV

0.557

0.557

0.517

0.497

0.477

0.477

0.477

TATOPANIINARWA

128

MAK

0.531

0.531

0.493

0.474

0.455

0.455

0.455

NUW

0.116

0.116

0.107

0.103

0.099

0.099

0.099

OKH

0.496

0.496

0.460

0.443

0.425

0.425

0.425

RAM

0.680

0.680

0.632

0.607

0.583

0.583

0.583

RAS

0.939

0.939

0.872

0.839

0.805

0.805

0.805

SIN

0.443

0.443

0.411

0.396

0.380

0.380

0.380

SIND

0.333

0.333

0.309

0.298

0.286

0.286

0.286

129

APPENDIX B
Transportation cost from TLHs to PODs per km per vehicle (in USD)
Candidate
TLHs
PODs

T1

T2

T3

T4

T5

T6

T7

1.4*G(T1) 1.4*C(T1) 1.3*C(T1) 1.2*C(T1) 1.2*C(T1) 1.2*C(T1) 1.2*C(T1)
DHA

DOL

GOR

BKT

1.386

1.305

1.468

1.223

1.223

1.223

1.223

DHA

0.000

0.000

0.000

0.000

0.000

0.000

0.000

DOL

3.083

2.902

3.265

2.721

2.721

2.721

2.721

GOR

1.273

1.198

1.348

1.123

1.123

1.123

1.123

KTM

1.160

1.092

1.228

1.023

1.023

1.023

1.023

KAV

1.669

1.571

1.767

1.473

1.473

1.473

1.473

LTP

1.245

1.171

1.318

1.098

1.098

1.098

1.098

MAK

2.263

2.130

2.396

1.997

1.997

1.997

1.997

NUW

0.877

0.825

0.929

0.774

0.774

0.774

0.774

OKH

6.308

5.937

6.679

5.566

5.566

5.566

5.566

RAM

4.088

3.847

4.328

3.607

3.607

3.607

3.607

RAS

1.559

1.468

1.651

1.376

1.376

1.376

1.376

SIN

4.597

4.326

4.867

4.056

4.056

4.056

4.056

SIND

2.404

2.263

2.546

2.122

2.122

2.122

2.122

BKT

1.697

1.597

1.797

1.498

1.498

1.498

1.498

DHA

3.083

2.902

3.265

2.721

2.721

2.721

2.721

DOL

0.000

0.000

0.000

0.000

0.000

0.000

0.000

GOR

5.276

4.965

5.586

4.655

4.655

4.655

4.655

KTM

1.924

1.810

2.037

1.697

1.697

1.697

1.697

KAV

1.414

1.331

1.498

1.248

1.248

1.248

1.248

LTP

1.839

1.731

1.947

1.622

1.622

1.622

1.622

MAK

2.999

2.822

3.175

2.646

2.646

2.646

2.646

NUW

2.857

2.689

3.025

2.521

2.521

2.521

2.521

OKH

7.058

6.643

7.473

6.228

6.228

6.228

6.228

RAM

1.004

0.945

1.063

0.886

0.886

0.886

0.886

RAS

3.542

3.333

3.750

3.125

3.125

3.125

3.125

SIN

5.346

5.032

5.661

4.717

4.717

4.717

4.717

SIND

1.386

1.305

1.468

1.223

1.223

1.223

1.223

BKT

2.164

2.037

2.291

1.909

1.909

1.909

1.909

DHA

1.273

1.198

1.348

1.123

1.123

1.123

1.123

DOL

5.276

4.965

5.586

4.655

4.655

4.655

4.655

GOR

0.000

0.000

0.000

0.000

0.000

0.000

0.000

KTM

1.938

1.824

2.052

1.710

1.710

1.710

1.710

KAV

2.447

2.303

2.591

2.159

2.159

2.159

2.159

LTP

2.023

1.904

2.142

1.785

1.785

1.785

1.785

MAK

2.037

1.917

2.157

1.797

1.797

1.797

1.797

NUW

1.655

1.558

1.752

1.460

1.460

1.460

1.460

OKH

6.096

5.737

6.455

5.379

5.379

5.379

5.379

RAM

4.866

4.579

5.152

4.293

4.293

4.293

4.293

RAS

2.342

2.204

2.479

2.066

2.066

2.066

2.066

130

KTM

KAV

MAK

NUW

SIN

4.385

4.127

4.643

3.869

3.869

3.869

3.869

SIND

3.182

2.995

3.370

2.808

2.808

2.808

2.808

BKT

0.226

0.213

0.240

0.200

0.200

0.200

0.200

DHA

1.160

1.092

1.228

1.023

1.023

1.023

1.023

DOL

1.924

1.810

2.037

1.697

1.697

1.697

1.697

GOR

1.938

1.824

2.052

1.710

1.710

1.710

1.710

KTM

0.000

0.000

0.000

0.000

0.000

0.000

0.000

KAV

0.509

0.479

0.539

0.449

0.449

0.449

0.449

LTP

0.099

0.093

0.105

0.087

0.087

0.087

0.087

MAK

1.103

1.038

1.168

0.973

0.973

0.973

0.973

NUW

0.962

0.905

1.018

0.849

0.849

0.849

0.849

OKH

5.177

4.872

5.481

4.568

4.568

4.568

4.568

RAM

2.928

2.756

3.100

2.583

2.583

2.583

2.583

RAS

1.756

1.653

1.859

1.549

1.549

1.549

1.549

SIN

3.479

3.275

3.684

3.070

3.070

3.070

3.070

SIND

1.245

1.171

1.318

1.098

1.098

1.098

1.098

BKT

0.283

0.266

0.300

0.250

0.250

0.250

0.250

DHA

1.669

1.571

1.767

1.473

1.473

1.473

1.473

DOL

1.414

1.331

1.498

1.248

1.248

1.248

1.248

GOR

2.447

2.303

2.591

2.159

2.159

2.159

2.159

KTM

0.509

0.479

0.539

0.449

0.449

0.449

0.449

KAV

0.000

0.000

0.000

0.000

0.000

0.000

0.000

LTP

0.424

0.399

0.449

0.374

0.374

0.374

0.374

MAK

1.584

1.491

1.677

1.398

1.398

1.398

1.398

NUW

1.443

1.358

1.528

1.273

1.273

1.273

1.273

OKH

5.643

5.311

5.975

4.980

4.980

4.980

4.980

RAM

2.419

2.276

2.561

2.134

2.134

2.134

2.134

RAS

2.129

2.004

2.254

1.879

1.879

1.879

1.879

SIN

3.932

3.701

4.163

3.469

3.469

3.469

3.469

SIND

0.735

0.692

0.779

0.649

0.649

0.649

0.649

BKT

1.301

1.225

1.378

1.148

1.148

1.148

1.148

DHA

2.263

2.130

2.396

1.997

1.997

1.997

1.997

DOL

2.999

2.822

3.175

2.646

2.646

2.646

2.646

GOR

2.037

1.917

2.157

1.797

1.797

1.797

1.797

KTM

1.103

1.038

1.168

0.973

0.973

0.973

0.973

KAV

1.584

1.491

1.677

1.398

1.398

1.398

1.398

LTP

1.160

1.092

1.228

1.023

1.023

1.023

1.023

MAK

0.000

0.000

0.000

0.000

0.000

0.000

0.000

NUW

2.065

1.944

2.186

1.822

1.822

1.822

1.822

OKH

4.059

3.821

4.298

3.582

3.582

3.582

3.582

RAM

4.003

3.767

4.238

3.532

3.532

3.532

3.532

RAS

2.741

2.580

2.902

2.418

2.418

2.418

2.418

SIN

2.348

2.210

2.486

2.072

2.072

2.072

2.072

SIND

2.320

2.183

2.456

2.047

2.047

2.047

2.047

BKT

1.160

1.092

1.228

1.023

1.023

1.023

1.023

131

OKH

RAM

RAS

DHA

0.877

0.825

0.929

0.774

0.774

0.774

0.774

DOL

2.857

2.689

3.025

2.521

2.521

2.521

2.521

GOR

1.655

1.558

1.752

1.460

1.460

1.460

1.460

KTM

0.962

0.905

1.018

0.849

0.849

0.849

0.849

KAV

1.443

1.358

1.528

1.273

1.273

1.273

1.273

LTP

1.047

0.985

1.108

0.924

0.924

0.924

0.924

MAK

2.065

1.944

2.186

1.822

1.822

1.822

1.822

NUW

0.000

0.000

0.000

0.000

0.000

0.000

0.000

OKH

6.110

5.751

6.470

5.391

5.391

5.391

5.391

RAM

3.861

3.634

4.088

3.407

3.407

3.407

3.407

RAS

0.683

0.642

0.723

0.602

0.602

0.602

0.602

SIN

4.413

4.153

4.673

3.894

3.894

3.894

3.894

SIND

2.178

2.050

2.306

1.922

1.922

1.922

1.922

BKT

5.361

5.045

5.676

4.730

4.730

4.730

4.730

DHA

6.308

5.937

6.679

5.566

5.566

5.566

5.566

DOL

7.058

6.643

7.473

6.228

6.228

6.228

6.228

GOR

6.096

5.737

6.455

5.379

5.379

5.379

5.379

KTM

5.177

4.872

5.481

4.568

4.568

4.568

4.568

KAV

5.643

5.311

5.975

4.980

4.980

4.980

4.980

LTP

5.219

4.912

5.526

4.605

4.605

4.605

4.605

MAK

4.059

3.821

4.298

3.582

3.582

3.582

3.582

NUW

6.110

5.751

6.470

5.391

5.391

5.391

5.391

OKH

0.000

0.000

0.000

0.000

0.000

0.000

0.000

RAM

8.062

7.588

8.536

7.114

7.114

7.114

7.114

RAS

6.797

6.397

7.197

5.997

5.997

5.997

5.997

SIN

2.758

2.596

2.920

2.434

2.434

2.434

2.434

SIND

6.379

6.004

6.754

5.628

5.628

5.628

5.628

BKT

2.702

2.543

2.860

2.384

2.384

2.384

2.384

DHA

4.088

3.847

4.328

3.607

3.607

3.607

3.607

DOL

1.004

0.945

1.063

0.886

0.886

0.886

0.886

GOR

4.866

4.579

5.152

4.293

4.293

4.293

4.293

KTM

2.928

2.756

3.100

2.583

2.583

2.583

2.583

KAV

2.419

2.276

2.561

2.134

2.134

2.134

2.134

LTP

2.843

2.676

3.010

2.508

2.508

2.508

2.508

MAK

4.003

3.767

4.238

3.532

3.532

3.532

3.532

NUW

3.861

3.634

4.088

3.407

3.407

3.407

3.407

OKH

8.062

7.588

8.536

7.114

7.114

7.114

7.114

RAM

0.000

0.000

0.000

0.000

0.000

0.000

0.000

RAS

4.549

4.281

4.816

4.014

4.014

4.014

4.014

SIN

6.351

5.977

6.724

5.604

5.604

5.604

5.604

SIND

2.390

2.250

2.531

2.109

2.109

2.109

2.109

BKT

1.843

1.734

1.951

1.626

1.626

1.626

1.626

DHA

1.559

1.468

1.651

1.376

1.376

1.376

1.376

DOL

3.542

3.333

3.750

3.125

3.125

3.125

3.125

GOR

2.342

2.204

2.479

2.066

2.066

2.066

2.066

132

SIN

SIND

KTM

1.756

1.653

1.859

1.549

1.549

1.549

1.549

KAV

2.129

2.004

2.254

1.879

1.879

1.879

1.879

LTP

1.732

1.630

1.834

1.528

1.528

1.528

1.528

MAK

2.741

2.580

2.902

2.418

2.418

2.418

2.418

NUW

0.683

0.642

0.723

0.602

0.602

0.602

0.602

OKH

6.797

6.397

7.197

5.997

5.997

5.997

5.997

RAM

4.549

4.281

4.816

4.014

4.014

4.014

4.014

RAS

0.000

0.000

0.000

0.000

0.000

0.000

0.000

SIN

5.089

4.789

5.388

4.490

4.490

4.490

4.490

SIND

2.865

2.696

3.033

2.528

2.528

2.528

2.528

BKT

3.649

3.434

3.864

3.220

3.220

3.220

3.220

DHA

4.597

4.326

4.867

4.056

4.056

4.056

4.056

DOL

5.346

5.032

5.661

4.717

4.717

4.717

4.717

GOR

4.385

4.127

4.643

3.869

3.869

3.869

3.869

KTM

3.479

3.275

3.684

3.070

3.070

3.070

3.070

KAV

3.932

3.701

4.163

3.469

3.469

3.469

3.469

LTP

3.508

3.301

3.714

3.095

3.095

3.095

3.095

MAK

2.348

2.210

2.486

2.072

2.072

2.072

2.072

NUW

4.413

4.153

4.673

3.894

3.894

3.894

3.894

OKH

2.758

2.596

2.920

2.434

2.434

2.434

2.434

RAM

6.351

5.977

6.724

5.604

5.604

5.604

5.604

RAS

5.089

4.789

5.388

4.490

4.490

4.490

4.490

SIN

0.000

0.000

0.000

0.000

0.000

0.000

0.000

SIND

4.668

4.393

4.942

4.118

4.118

4.118

4.118

BKT

1.018

0.958

1.078

0.899

0.899

0.899

0.899

DHA

2.404

2.263

2.546

2.122

2.122

2.122

2.122

DOL

1.386

1.305

1.468

1.223

1.223

1.223

1.223

GOR

3.182

2.995

3.370

2.808

2.808

2.808

2.808

KTM

1.245

1.171

1.318

1.098

1.098

1.098

1.098

KAV

0.735

0.692

0.779

0.649

0.649

0.649

0.649

LTP

1.160

1.092

1.228

1.023

1.023

1.023

1.023

MAK

2.320

2.183

2.456

2.047

2.047

2.047

2.047

NUW

2.178

2.050

2.306

1.922

1.922

1.922

1.922

OKH

6.379

6.004

6.754

5.628

5.628

5.628

5.628

RAM

2.390

2.250

2.531

2.109

2.109

2.109

2.109

RAS

2.865

2.696

3.033

2.528

2.528

2.528

2.528

SIN

4.668

4.393

4.942

4.118

4.118

4.118

4.118

SIND

0.000

0.000

0.000

0.000

0.000

0.000

0.000

133

APPENDIX C
Distance from supply point to candidate temporary depots (in kilometers)

S.N.
Supply Points
1 TIA
2 Kakadbhitta, Jhapa
3 Biratnagar, Morang
4 Bhairahawa, Kapilbastu
5 Tatopani, sindhupalchok
6 Nepalgunj, Banke
7 Inarwa, Parsa

Dhading
DHA

Candidate temporary logistics hubs
Dolakha Gorkha Kathmandu Kavrepalanchok Makwanpur Nuwakot Okhaldhunga Ramechhap Rasuwa Sindhuli Sindhupalchok
DOL
GOR
KTM
KAV
MAK
NUW
OKH
RAM
RAS
SIN
SIND
85
136
148
5
26
83
79
211
131 124.15
148
83
546
424
598
478
427
399
540
337
366 588.71
306
467
472
349
524
404
353
324
466
262
291 505.16
231
393
278
478
188
276
297
196
311
479
421 302.09
361
354
194
98
257
116
86
190
187
257
177 233.37
194
83
507
734
443
531
553
451
502
734
676 535.33
616
609
228
284
203
274
284
59
253
347
226 479.31
170
326

APPENDIX D
Distance from candidate temporary depots to point of distribution (in kilometers)
Candidate temporary
S.N.
logistics hubs
1 Dhading
2 Dolakha
3 Gorkha
4 Kathmandu
5 Kavrepalanchok
6 Makwanpur
7 Nuwakot
8 Okhaldhunga
9 Ramechhap
10 Rasuwa
11 Sindhuli
12 Sindhupalchok

Point of distribution
Dhading Dolakha Gorkha
Kathmandu
Kavrepalanchok
Lalitpur Makwanpur Nuwakot
Okhaldhunga
RamechhapRasuwa
Sindhuli Sindhupalchok
98
0
218
90
82
118
88
160
62
446
289
110.24
325
170
120
218
0
373
136
100
130
212
202
499
71
250.4
378
98
153
90
373
0
137
173
143
144
117
431
344
165.56
310
225
16
82
136
137
0
36
7
78
68
366
207
124.15
246
88
20
118
100
173
36
0
30
112
102
399
171
150.54
278
52
92
160
212
144
78
112
82
0
146
287
283
193.78
166
164
82
62
202
117
68
102
74
146
0
432
273
48.26
312
154
379
446
499
431
366
399
369
287
432
0
570
480.56
195
451
191
289
71
344
207
171
201
283
273
570
0
321.6
449
169
130.27110.24250.4
165.56124.15150.54 122.47
193.7848.26 480.56
321.6
0359.77202.55
258
325
378
310
246
278
248
166
312
195
449
359.77
0
330
72
170
98
225
88
52
82
164
154
451
169
202.55330
0Bhaktapur

134

APPENDIX D
Coverage of PODs by TLHs
T1
TLHs PODs
Distance
DHA Bhaktapur
98
Dhading0
Dolakha218
Gorkha90
Kathmandu
82
Kavrepalanchok
118
Lalitpur88
Makwanpur
160
Nuwakot
62
Okhaldhunga
446
Ramechhap
289
Rasuwa110.24Sindhuli
325
Sindhupalchok
170
DOL Bhaktapur
120
Dhading
218
Dolakha0
Gorkha373
Kathmandu
136
Kavrepalanchok
100
Lalitpur130
Makwanpur
212
Nuwakot
202
Okhaldhunga
499
Ramechhap
71
Rasuwa250.4
Sindhuli
378
Sindhupalchok
98
GOR Bhaktapur
153
Dhading
90
Dolakha373
Gorkha0
Kathmandu
137
Kavrepalanchok
173
Lalitpur
143
Makwanpur
144
Nuwakot
117
Okhaldhunga
431
Ramechhap
344

T2
100KM
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0

T3
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0

T4
T5
T6 T7
150KM
175KM 200KM
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
135

Rasuwa
Sindhuli
Sindhupalchok
KTM Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
KAV Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
MAK Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok

165.56
310
225
16
82
136
137
0
36
7
78
68
366
207
124.15
246
88
20
118
100
173
36
0
30
112
102
399
171
150.54
278
52
92
160
212
144
78
112
82
0
146
287
283
193.78
166
164

0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0

0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0

0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0

0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0

1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1

1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1

1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
136

NUW Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
OKH Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
RAM Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
RAS Bhaktapur
Dhading
Dolakha

82
62
202
117
68
102
74
146
0
432
273
48.26
312
154
379
446
499
431
366
399
369
287
432
0
570
480.56
195
451
191
289
71
344
207
171
201
283
273
570
0
321.6
449
169
130.27110.24
250.4

1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0

1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0

1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0

1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0

1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0

1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0

1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
137

GorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
SIN
Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok
SIND; Bhaktapur
Dhading
DolakhaGorkhaKathmandu
Kavrepalanchok
Lalitpur
Makwanpur
Nuwakot
Okhaldhunga
Ramechhap
RasuwaSindhuli
Sindhupalchok

165.56124.15150.54122.47193.7848.26
480.56321.6
0359.77202.55
258
325
378
310
246
278
248
166
312
195
449
359.77
0
330
72
170
98
225
88
52
82
164
154
451
169
202.55
330
0

0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1

0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1

0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1

0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1

1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1

1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1

1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1

138

APPENDIX F
Lingo code for model in Chapter 5!Two objective model, minimizing costs and mzximizing total demand
coverage;!TIME = T1, T2, T3, T4, T5, T6, T7;
MODEL:SETS:
SUPPLY;TEMPDEPOT: F;
DEMANDPT;TIME;SPXTP(SUPPLY, TIME): SCAP;TDXTP(TEMPDEPOT, TIME):TCAP, y;
DPXTP(DEMANDPT, TIME):

DEM, z, NSUP;XLINK( TEMPDEPOT, DEMANDPT, TIME): x;
ZLINK(TEMPDEPOT, DEMANDPT,TIME):COEFF;SPXTDXTP( SUPPLY, TEMPDEPOT, TIME):C1, R;
TDXDPXTP(TEMPDEPOT, DEMANDPT, TIME):C2, Q;
ENDSETSDATA:
SUPPLY = TIA
Kakad Birat Bhaira! Supply Point capacities;
SCAP = 900
900
900
900
900
950
950
950
950
950
1100 1100 1100 1100 1100
1200 1200 1200 1200 1200
1100 1100 1100 1100 1100
1000 1000 1000 1000 1000
1000 1000 1000 1000 1000

Tatopani
900
950
1100
1200
1100
1000
1000

900
950
1100
1200
1100
1000
1000;

TEMPDEPOT = DHA
DOL
GOR
KTM
SIND; ! The distn centers;
F = 100
100
100
100
100;

KAV

MAK

100

TCAP =750
750
810
810

Nepalgunj

Inarwa;

NUW

OKH

RAM

RAS

SIN

100

100

100

100

100

100

750

750

750

750

750

750

750

750

750

750

810

810

810

810

810

810

810

810

810

810

139

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

840

830

830

830

830

830

830

830

830

830

830

830

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

820

840
840
830
820
820;
! Shipping costs from Supply point to Candidate temporary logistic hubs ineach period;
C1= @OLE('E:\IJDRR_Credibility_2018.04.24.xlsx', '_CC1');!Listing the name and number of PODs (Demand nodes) which is 13 in ourcase;
DEMANDPT= BKT
DHA
DOL
GOR
KTM
KAV
LTP
MAK
NUW
OKH
RAS
SIN
SIND;
DEM=

RAM

@OLE('E:\IJDRR_Credibility_2018.04.24.xlsx', '_DD');

COEFF=@OLE('E:\IJDRR_Credibility_2018.04.24.xlsx', '_COEFF1');
C2=@OLE('E:\IJDRR_Credibility_2018.04.24.xlsx', '_C22');!Confidence level;
a=0.8;!Spread of Triangular fuzzy number;
m=0.3;ENDDATA!The objective is to calculate maximum coverage attainable over the entire
planning horizon;[OBJ] MIN = TCT;
TCT = FXT + SPT + SPD;FXT = @SUM(TDXTP(J,P): (F(J)*(1-m+2*m*a)*y(J,P)));SPT = @SUM(SPXTDXTP( I,J,P): (C1(I,J,P)*(1-m+2*m*a)*R(I,J,P)));
SPD = @SUM( TDXDPXTP( J,K,P): (C2(J,K,P)*(1-m+2*m*a)*Q(J,K,P)));!CONSTRAINTS;
CVR>=10000;
CVR =@SUM(DPXTP(K,P): (DEM(K,P)*(1-m+2*m*a))*z(K,P));!Coverage constraint;@FOR(TIME(P):@FOR(DEMANDPT(K):@SUM(TEMPDEPOT(J):COEFF(J,K,P)*y(J,P))>=z(K,P)));! Supply Constraints at SP I;@FOR(TIME(P):@FOR(SUPPLY(I):@SUM(TEMPDEPOT(J): R(I,J,P)) <= (SCAP(I, P)*(1+m-2*m*a))
)
);

140

! Aggregate capacities at each TLH J;@FOR(TIME(P):@FOR(TEMPDEPOT(J):@SUM(SUPPLY(I): R(I,J,P)) <= (TCAP(J,P)*(1+m-2*m*a)*y(J,P))));@FOR(TIME(P):@FOR( TEMPDEPOT(J):@SUM(DEMANDPT(K): Q(J,K,P)) <= (TCAP(J,P)*(1+m-2*m*a)*y(J,P))));! TD balance (inbound = outbound)constraints for Commodities at TLH J;@FOR(TIME(P):@FOR(TEMPDEPOT(J):@SUM(SUPPLY(I): R(I,J,P)) = @SUM(DEMANDPT(K): Q(J,K,P))));!Demand constraints;@FOR(TIME(P):@FOR(DEMANDPT(K):@SUM(TEMPDEPOT(J): Q(J,K,P)) >=(DEM(K,P)*(1-m+2*m*a))));! Ensures POD'S are served by only one TLH in time period P;@FOR(TIME(P):@FOR(DEMANDPT(K):@SUM(TEMPDEPOT(J): x(J,K,P))= 1));!Ensure each TLH can deliver to several PODs;@FOR(TIME(P):@FOR(TEMPDEPOT(J):@SUM(DEMANDPT(K):X(J,K,P))<=14*y(J,P)));!Ensure demand is allocated to open facilities only;@FOR(TIME(P):@FOR(TEMPDEPOT(J):@FOR(DEMANDPT(K):x(J,K,P)<=y(J,P))));@For( TDXTP(J,P):@BIN(y(J,P)));@For( DPXTP(K,P):@BIN(Z(K,P)));@FOR( XLINK(J,K,P): @BIN(x(J,K,P)));@FOR (SPXTDXTP(I,J,P):R(I,J,P) >=0);@FOR (TDXDPXTP(J,K,P):Q(J,K,P) >=0);DATA:@TEXT() = ' ';141

@TEXT() = 'Solution to Uncertainty MOO Problem';@TEXT() = "Total cost=", TOTCOST;@TEXT() = ' ';@TEXT() = "OPEN TLH: TLH Opened in Period";@TEXT() = "TLH Period";@TEXT() = @WRITEFOR(TDXTP(J,P)|y(J,P)#GT#0:'
TIME(P),' ',y(J,P),@NEWLINE(1));', TEMPDEPOT(J),' ',@TEXT() = ' ';@TEXT() = "Shipment: SP to TLH";@TEXT() = "SP TLH Period";@TEXT() = @WRITEFOR(SPXTDXTP(I, J, P)|R(I, J, P)#GT#0:'',SUPPLY(I),'', TEMPDEPOT(J),'', TIME(P),'',R(I, J, P),@NEWLINE(1));@TEXT() = ' ';@TEXT() = "Shipment: TLH to DP";@TEXT() = "TLH DP Period";@TEXT() = @WRITEFOR(TDXDPXTP(J,K,P)|Q(J,K,P)#GT#0:'',TEMPDEPOT(J),'', DEMANDPT(K),'', TIME(P),'',Q(J,K,P),@NEWLINE(1));@TEXT() = ' ';ENDDATA
END

142