Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

Inter-ward, Risk-diversified Allocation Modelfor Storing of Disaster Relief Goods

Tetsuro Kajihara1, Muneta Yokomatsu2, Hideyuki Ito3, and Wisinee Wisetjindawat4
1
2

Japan Railway Central,

Disaster Prevention Research Institute, Kyoto University,
3

P&I Logistics,

4 Nagoya Institute of Technology,(Received Apr 30, 2015 Accepted:Jun 16, 2016)

Abstract
This study focuses on the concept of an inter-ward, risk-diversified spatial allocation model for the
storage of relief goods to reduce the cost of the relief goods policy. The study proposes the model, andshows the feasibility and efficiency of the suggested logistics policy by applying it to a case study of the
Shonai River, Nagoya City. The simulation results show that one day’s worth of stocked relief goods ineach shelter is sufficient for sustaining all evacuees for three days in any disaster scenario, and reduces
the total costs of the relief goods policy. The study further illustrates the applicability of the model towide-area disasters.
Key words Disaster, Relief Goods, Humanitarian Logistics, Shelter

1. INTRODUCTION
Evacuation has been one of central issues of humanitarian disaster management in the aftermath of large
disasters. Not only behaviors for escaping from hazard, but, by extending the focus to a period of several
months after a disaster, improvement of quality of lives in shelters such as public schools and community
centers has recently been investigated. While awareness of the necessity of various sorts of goods inshelter life, not only public provision but voluntary supplies of goods, has increased in these several
decades, this sometimes even causes confusion when on-site coordinators classify and allocate those
goods to evacuees in need. Matching methods of treating goods and evacuees with various needs andpreferences are expected to be improved.
Focusing exclusively on a period of several days after the occurrence of disaster, the relief goods
problem is characterized in a somewhat different way: we should consider disruption of transportation
while the list of necessary goods is shorter because it is a period where evacuees concentrate on surviving
and, for that purpose, necessary goods are in large part common and include water, foods to intake
calories, blankets, and so on.
The Cabinet Office, Government of Japan, suggests that society should stock sufficient relief
goods to sustain the assumed numbers of evacuees for at least three days after a disaster (Cabinet Office11

T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawata). Considering the suggestion, many local governments recognize that each local government should
guarantee that all evacuees can survive for three days with relief goods stocked within the jurisdiction.
For example, Nagoya City is considering an alternative to stocking three days’ worth of relief goods in its
storehouses for the estimated number of evacuees, which amounts to four million meals, which is a huge
number to manage and is associated with high costs.
Compared with other risks like traffic accidents and diseases, disaster risk is characterized as acollective risk, meaning that it brings damage simultaneously to many people in an affected area.
However, some disaster risks are more localized, considering inherent geographical characteristics. For
example, a dike of a river usually breaks at one point because the breakpoint releases water pressure,which results in flooding of only one side of the river basin and deep inundation in the area close to thebreakpoint. If communities on the other side of the river have goods that are not used by the local people
there, they can be transported for the use of evacuees in the affected area. This kind of post-disasterprocurement could also be applied at the inter-city (or municipality, village, etc.) level, since no relief
goods stock is touched in the unaffected area.
As a matter of fact, many relief goods are often transported from unaffected to damaged areas
after a disaster. Some local governments in Japan create agreements with private companies or other local
governments, although these mutual assistances are not accounted for in their planning for relief supplies
in many cases, meaning that each local government does not recognize the cooperation by otherorganizations regarding stocked relief goods. For example, it was found in the authors’ interview that,
although Nagoya City has an agreement concerning disaster relief activities with the Associated General
Constructors of Nagoya City, the city government itself tries to stock three days’ worth of relief goods forthe estimated number of evacuees. One of the reasons behind this is that the city government cannot
realize the feasibility of external support in the aftermath of disaster, and thinks that it is responsible forguaranteeing three-day survival by its own stocks. Hence, our proposal of the model must be associatedwith a demonstration of feasibility. We deal with a case study with actual data and reveal somequantitative results.
Recently, the issue of humanitarian logistics has attracted attention, and some literature provides
academic review, lists essential factors, and tries to structure them to characterize this new academic area
(e.g., Kovács et al., 2011). Mathematical models such as application of linear programming and others
have been developed mainly in the area of operations research with focuses such as the decision-making
problem of helicopter logistics (Barbarosoğlu et al., 2002), a multi-commodity and multi-nodal
framework (Haghani et al., 1996), coordination of transportation of commodities and wounded people (Yiet al., 2007), disaster-affected area grouping and relief co-distribution (Sheu, 2007), and so forth. In otherareas like logistics and disaster management, quantitative studies are relatively new, and include focusessuch as strategic pre-positioning of relief supplies (Balcik et al., 2008; Duran et al., 2011), optimal
inventory control under uncertainty (Beamon et al., 2006), relationship between operation costs and fundraising (Wakolbinger et al., 2011; Toyasaki et al., 2014), and so forth. A lack of inter-organizational
cooperation and coordination is pointed out in various articles and practitioner reports (Thomas et al.,2007; van Wassenhove, 2006; Oloruntoba, 2010), while several methodologies are developed such as the“service provider approach” (Schulz, 2010) that is applied to the international horizontal cooperation
scheme of the UN Humanitarian Response Depot (UNHDP). A multi-agent simulation model is also
developed to describe the collective performance of complex humanitarian response systems in the casestudy of the UNHDP system (Mochizuki et al., 2015).
We share the idea of horizontal cooperation with the preceding studies above, while we point out
the layered structure of the network-based stock policy: inter-ward and inter-region. Moreover, we follow
a Japanese context, whereby relief goods policy is constrained by the condition that the relief goods
should be provided to all evacuees for three days after disaster under any damage scenario that can occur.
Furthermore, in a case study of the Shonai River, Nagoya City, we apply the results of a flood simulationof the Shonai River developed by the Shonai River Office, to identify hazard, the results of Ito et al.

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33(2015) who define a list of necessary goods for three days with their volumes and prices, and actual
values of parameters related to shelters and transportation in Nagoya City. We explicitly deal with thecost minimization problem, where the objective function is the total cost of the relief goods policy definedas the sum of the cost of stocking relief goods and the cost of transportation. With verification withquantitative results, we aim to provide helpful knowledge for local people and those responsible for relief
goods policy.
The remainder of the paper is organized as follows. Section 2 introduces basic ideas and key
concepts of the study based on interview surveys. Section 3 sets up a model and identifies areas of thecase study. Section 4 conducts numerical simulation and derives implications. And Section 5 concludes
and suggests future research directions.
2. FOCUS AND CONDITIONS FOR RELIEF GOODS LOGISTICS
2.1 Problems Observed in Past Disasters
After the Chūetsu Earthquake that occurred in Japan in 2004, some shelters lacked relief goods, whileothers had a surplus (Cabinet Office a, 2007). Photo 1 was taken in a school gym, which was used as a
distribution center for relief goods, seven days after the earthquake (Mainichi Newspaper a, 2004). As isevident, a large volume of relief goods was transported to the school gym; however, these were not wellmanaged: the quantity of relief goods was too large, the packing styles of relief goods differed, and thedelivery included unwanted relief goods. Most relief goods shown in Photo 1 were wasted and disposedof. A similar problem occurred during the Hokkaido Earthquake in 1993. Unwanted relief goods weighed
more than 1,200 tons, which cost 120 million yen to dispose of. In contrast, in both earthquakes, someshelters experienced a shortage of relief goods, which could not be transported and delivered consequent
to severely damaged roads.

Photo 1. Distribution Center (Source: Mainichi Newspaper, 2004)
In the case of the 2011 Great East Japan Earthquake, many shelters lacked relief goods following
widespread fuel shortages and a badly functioning truck transportation system (Japan Trucking
Association, 2012). Relief goods in short supply included powdered milk, diapers, and allergen-free foods.
Diverse evacuees and types of stocked relief goods should be considered.
The “Great East Japan Earthquake report” of the Ministry of Land, Infrastructure, Transport andTourism (MLIT) describes relief goods as follows (MLIT, 2011):“To transport relief goods, we tried using large-capacity ships or helicopters with high mobility.
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T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat
However, we could not implement these methods, because of bad weather and the difficulty in securingtrucks from a port or airport to the relief goods supply base.”“In this disaster, most relief goods were transported by truck. However, it is necessary to establish
a plan that enables us to choose a wide variety of transportation, regardless of the disaster that occurs.”
These descriptions imply that unplanned incidences can occur after a disaster. Specifically, Sendai
Airport, a relief goods supply base, was severely damaged in the Great East Japan Earthquake. Thisrendered air transportation impossible, and goods had to be transported by truck. Relief goods should be
dispatched immediately; thus, it is necessary to secure a base that cannot be damaged in any disaster.
Furthermore, resilient modes of transportation are essential.
On the other hand, the authors visited two places in Tohoku that were used as shelters, Iwate
Prefectural Ofunato High School and Ishinomaki Senshu University, and conducted interviews withpersons in charge of the shelters at the time. Points of their statements are itemized in the appendix. The
following is a summary of their findings on relief goods management.
Iwate Prefectural Ofunato High School:“Fortunately, the shelter was equipped with some bedclothes, such as blankets. However, they
were not enough. Students first distributed these commodities among elderly people, women, andchildren. The students did not complain about the lack of commodities, as they knew each other before
the disaster. Problems might have occurred if they had been strangers.”“The water supply was stopped and evacuees were forced to use residual water in the water tank.
Consequently, a lack of water became a concern. Furthermore, they did not know when the water supply
would be restored. From two days after the disaster, they left the shelters to search for water, andtransported spring water back to the shelter on a cart in plastic bottles. They then used these bottles ofwater for the toilets. Clearly, the shelters were faced with many problems; however, evacuees managed toutilize the limited goods stocked in the shelter through trial and error.”“There was a surplus of relief goods at the shelter from the second day after the disaster. For
example, too many rice balls were transported from other regions, and the evacuees could not eat themall.”IIshinomaki Senshu University:“Evacuees housed in the shelter ran short of water and made a request to Ishinomaki City tosupply it. The next day, too much water was delivered. In addition, a volunteer unexpectedly sent morewater to the shelter.”“From three to four days after the disaster, there was enough food and water thanks to volunteers
and NPOs. However, baby goods, sanitary goods, pet goods, and cigarettes were in short supply.”“The toilets did not function, and the evacuees had to use portable toilets.”“Relief goods were transported through long-distance transportation within two days of thedisaster. The evacuees were able to feel safer and more secure, because they felt connected to otherregions. They were surprised at how quickly transportation companies and road networks were restored.”
It was pointed out that evacuees could not help to allocate and share goods that they found at the
shelters for survival until relief goods were transported from unaffected areas. On the other hand, after therelief goods started to arrive at the shelters, the amounts of some kinds of goods were way beyond thoseneeded.

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

Considering the above findings, this study proposes a model where basic relief goods that are
critically important for surviving for one day are stocked at each shelter and the logistics for redistributionof the goods after the second day are controlled for quantity with a guarantee of mobility. CI model andba are not provided here. This study first describes the networking process as a spiral phenomenon, in
which new knowledge is generated by transactions both within a volunteer group and between different
organizations. Then, the words of network members and the observed facts are evaluated through the
SECI process.

2.2 Classification of Relief Goods and Estimation of Volume
Description of our model of relief goods management starts with identification of necessary goods. Figure
1 identifies three types of relief goods needed during three stages that follow a disaster.

Figure 1. Classification of Relief Goods
The relief goods needed during the first stage can be termed “basic relief goods.” Municipalities
have different viewpoints regarding what types of goods should be stocked as basic relief goods, although
they do stock similar types. For example, Table 1 summarizes the inventory of relief goods bymunicipalities in Aichi Prefecture, Japan, which includes Nagoya City (Aichi Prefecture). According toTable 1, biscuits, instant noodles, rice, canned foods, bottles of drinking water, powdered milk, and otherfoods are stocked. These commodities are classified as basic relief goods. Furthermore, equipment needed
to guard the privacy of evacuees, such as toiletries and room partitions, should also be stocked. These
relief goods are necessary in terms of protecting the dignity of evacuees. In addition, they are helpful inpreventing the spread of diseases in shelters.

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T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat
Table 1. Inventory of Stocked Relief Goods in Aichi Prefecture, Japan

Tables 1 and 2 show a sample list of basic relief goods. Ito et al. (2015) provides a detailed
discussion on a variety of needs based on a variety of attributes such as gender, age group, allergies, andso on. These special needs must differ among communities both in their variety and quantity dependingon the composition of the people. Therefore, community members in each community should discuss anddetermine a list of special types of basic relief goods in terms of quality and quantity.

Table 2. Sample List of Basic Relief Goods

We estimate the quantity of basic relief goods to be stocked like Table 3 below. It is important toestimate the volume because space for storage is not limitless.

Table 3. Calculation of Basic Relief Goods for 1,000 Evacuees per Day

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

Table 3 shows that the volume needed for relief goods for 1,000 evacuees per day is estimated tobe approximately 35 m3. Given that the height of the shelter is 2 m, 17.4 m2 is needed. Nagoya City
assumes about 2 m2 to be the standard space in a shelter per person, and the space for 1,000 evacuees is
2,000 m2. Therefore, the space needed to stock relief goods occupies only 17.4 m2 of 2,000 m2 in the
shelter. The volume of relief goods supplied from the second day after the disaster can be reduced from35.5 m3 to 5.03 m3, since blankets, baby bottles, and room partitions are only distributed on the first day.
It should be emphasized that the volume of blankets occupies 73% of the entire volume of all basic relief
goods. It follows that replacing this blanket with a lighter one increases the space available to store otherimportant goods. The same idea can be applied to other relief goods. For example, candy is high incalories and low in volume; therefore, as long as safety for small children is ensured, it may be efficient interms of calories per volume.

2.3 Transportation of Relief Goods
We now consider how to transport relief goods after a disaster occurs. The logistics of damaged areas andunaffected areas differ greatly because of damaged infrastructure. We must also prepare a distribution
center that efficiently connects logistics in damaged areas to those in unaffected areas. Figure 2 outlines
the logistics regarding relief goods. The figure depicts the “Distribution center,” “Logistics in damaged
areas,” and “Logistics in unaffected areas.”

Figure 2. Logistics for Relief Goods after a Disaster
Logistics in unaffected areas remain as they are under regular conditions. Relief goods aretransported from unaffected areas to a distribution center soon after a disaster has occurred. If a
distribution center is appropriately located, transporting relief goods should not be difficult.
At the distribution center, logistics ensure that relief goods are suitably repackaged for efficienttransportation to damaged areas. Goods are transported to appropriate shelters in terms of quantity andquality. These processes should be conducted quickly. In previous disasters, relief goods could not betransported because facilities did not function effectively. In the early stages following a disaster, basic
relief goods should be transported especially quickly to ensure the survival of evacuees. This facility must
begin working just after a disaster occurs and for 24 hours without interruption.
In damaged areas, infrastructure also gets damaged, rendering it impossible to transport relief
goods under normal conditions. Transportation methods appropriate for different types of disasters should
be prepared for damaged areas. If we cannot use trucks in a damaged area, we must use bicycles ortrolleys. If roads are flooded, we must use boats for transportation. Photo 2 shows an emergency drill in
Chiba Prefecture (Chiba City). Trolleys were used to transport goods. Photo 3 shows Nagoya City after
the Tokai Heavy Rain. Here, boats were used to transport evacuees and relief goods (Mainichi Newspaperb).
Considering the urgency of supplying basic relief goods, helicopters are an effective
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T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat
transportation method. Although helicopters have relatively small capacity, they can quickly transportrelief goods to isolated shelters. Thus, we must improve the operation of helicopters and use themefficiently. For example, we should consider ways to reduce loading time and the number of takeoffs andlandings and improve methods of supplying relief goods to shelters by helicopter.
The logistical difficulties in damaged areas on March 16, 2011 were reported (Asahi Newspaper).
A large volume of relief goods was transported to areas surrounding the destination; however, damaged
roads made it impossible to transport them to the destination itself.

Photo 3. Utilization of Boats(Source: Mainichi Newspaper)

2.4 Two Viewpoints regarding Relief Goods Logistics
In the following section, two viewpoints are applied: “non-uniform distribution of disaster damage” and“inter-ward network for storage of relief goods,” based on which we formulate a model to analyze theefficiency of the network stocking policy that we propose.
In Nagoya City, each shelter stocks the same quantity of relief goods. This tactic may bereasonable from an equality viewpoint. However, disaster strikes locally, and the distribution of disasterdamage is non-uniform. For example, a tsunami damages low-elevation areas, not elevated areas. Thus,an efficient tactic seems to be stocking varied quantities of relief goods in each shelter depending on the
non-uniform distribution of disaster damage.
Some shelters are often short of relief goods after a disaster occurs. In this situation, relief goods
are transported from unaffected to damaged areas. Suppliers are various organizations such as volunteers,
private companies, or local governments. Moreover, the networks formed by these organizations can help
compensate for shortages of relief goods. However, this type of cooperation is seldom considered before adisaster occurs. Here, an efficient tactic is that local governments in certain areas stockpile goods andcompensate each other’s shortages when needed.

3. A MODEL SETTING AND PARAMETERS FOR A CASE STUDY
3.1 Nagoya City and the Shonai River
We formulate a model based on the concepts that are proposed in the previous section, and apply it toareas of the Shonai River basin, Nagoya City, Japan. Nagoya City is the capital of Aichi Prefecture andthe largest city in Japan’s Chubu region that is located in the center of the Pacific coast of the main islandof Japan. As of 2014, the population of the Chukyo metropolitan area totaled 8.74 million people, and thatof Nagoya City, 2.27 million. The area of Nagoya City measures 326.43 km2 (Nagoya City a). The Shonai

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

River is a Class-1 river flowing through Gifu Prefecture and Aichi Prefecture in Japan’s Chubu region. In
this case study, the target areas are five wards around the Shonai River: Nakagawa Ward, Nakamura
Ward, Nishi Ward, Kita Ward, and Minato Ward. These target areas face a flood risk from the Shonai
River.
Figure 3 depicts the eight areas assumed in this case study to be at risk of a dike break along the
Shonai River. Furthermore, in this case study, Komaki Airport is assumed to be a relief goods supply base.

Figure 3. Map Depicting Eight Cases and the Supply Relief Goods Ba
We conducted an interview survey in June, 2014, with officers of departments that are in charge ofmanagement of disaster relief goods in Nagoya City, who told us that, currently, following the abovementioned government policy (Cabinet Office c), the Nagoya City government was planning to increase
the quantity of meals stocked in its storehouses. It currently assumed that the quantity of meals should be
the amount that equals “the assumed number of evacuees” multiplied by “three-day meals per one
evacuee.” For example, if 400 thousand evacuees stay in a shelter and take meals three times a day forthree days, the quantity of meals stored in all shelters will be 3.6 million in total. However, this policy
raises various problems. For example, many goods have a shelf life and the space for storage of the relief
goods is limited, resulting in an increase in associated costs.
We numerically test our hypothesis that Nagoya City does not need to stock a large amount ofrelief goods but that local governments transporting relief goods from unaffected to damaged areas seems
to be more effective. In this case study, from a cost perspective, we compare two policies: 1) the “Planned
Policy,” that is, Nagoya City’s currently proposed policy; and 2) our proposed “Network Policy.”

3.2 Policy on Stocking Relief Goods
If a disaster occurs, evacuees at isolated shelters will have to survive on stocked relief goods until new
goods can be transported from other areas. In this case study, based on a flood simulation calculated by
the MLIT, we assume that it takes 24 hours for relief goods to be transported from other areas.
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T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat
The quantity of stocked relief goods at each shelter should exceed the number of assumed
evacuees at each shelter. If each shelter stocks this quantity of relief goods, every evacuee can survive forat least the first day, even in the case of flooding. The quantity of relief goods is provided in Table 3.
In severely damaged areas, evacuees may have to stay at the shelter for more than two days after
the disaster. Here, relief goods will be transported from an unaffected to the damaged shelter.

3.3 Target Shelters and Number of Evacuees
The number of target shelters is 301 in five wards. These shelters are depicted on Nagoya City’s hazard
map (Nagoya City b). In Table 4, the second column provides the names of shelters, while the thirdcolumn gives the capacity of the shelter in Flood Scenario 1. In this case study, we define the capacity ofshelters as the assumed number of evacuees for the sake of brevity.
Table 4. Assumed Number of Evacuees, Shelter Type, and Flood Depth in Flood Scenario 1(Abstract)

3.4 Dike Break Point and Flood Depth of Each Shelter
In this case study, four areas are assumed to be dike break points. Furthermore, since each has a left and aright side, eight points are assumed in total. We show them in Figure 3.
We calculate the flood depth of the target areas by using the flood simulation software developedby the MLIT. The software can calculate the flood depth of target areas at 15-minute intervals after thedike breaks. The probability of this type of heavy rain is once every 200 years. A dike break point can beselected from every 1.0 km from the break point along the Shonai River. The size of meshes forcalculation is 50 m x 50 m. These calculation results have already been applied to Nagoya City’s hazard
map.
In this case study, we calculated the flood depth for eight flood scenarios, and used the flood depth
for each shelter at four points in time, namely the peak hour, six hours, 24 hours, and 48 hours after thedike breaks. Figure 4 illustrates an example of simulation results for Flood Scenario 5, which shows theJournal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

flood depth at the sixth hour after the dike break. In Table 4, the fifth to eighth columns show the flood
depth of Shelters 11 to 20 in Flood Scenario 1.

Figure 4. Example of Flood Simulation
3.5 Classification of Shelters According to Flood Depth
Based on the simulation results, we classify the five types of flood impacts as in Figure 5. The severity
ranges from Type A (high) to Type E (low). Type-E shelters are not flooded, while Type-A shelters arestill flooded 24 hours after the dike breaks. As such, Type-A shelters are the most severely damaged. Also,
flood depth will determine whether or not the relief goods stocked in one shelter are to be distributed toevacuees in that shelter.
In Type-E shelters, the stock of relief goods will not be distributed to evacuees, because thesurrounding areas are not damaged and citizens do not need to evacuate to a shelter. Thus, Type-E
shelters will have surplus stock, and as such, become a relief goods donor.
In Type-C and Type-D shelters, the stock of relief goods at a shelter are to be used itself. Here,citizens will evacuate and stay at a shelter for less than 24 hours after the dike breaks.

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Figure 5. Classification of Shelters
In Type-A and Type-B shelters, the stock (which is prepared for one day) will be used.
Furthermore, it is assumed that citizens will evacuate for 72 hours after the dike breaks (Japan
Automobile Federation). Consequently, they will need relief goods for two more days (the second andthird days after the dike breaks). To compensate for the shortage, goods stored in Type-E shelters can betransported to Type-A and Type-B shelters via a hub. Flooded roads reduce the possibility of reaching
Type-A shelters by truck. Therefore, transportation to Type-A shelters should be conducted by helicopter.
It is still possible to reach Type-B shelters by truck and, hence, small two-ton-trucks are to be used inorder to guarantee accessibility to narrow roads. The type of helicopter is assumed to be the “Bell 204B.”
In Table 4 above, the fourth column shows the classification of Shelters 11 to 20 in Flood Scenario 1.
Notably, the classification was conducted for each of the eight flood scenarios; therefore, one shelter isclassified into a different type for each scenario.
4. OPTIMIZATION PROBLEM
4.1 Objective Function
For planning of disaster relief goods, plural possible scenarios of dike breaks in terms of geographicalbreak point should be equally taken into account. In other words, it is not appropriate to determine thepolicy for storage and transportation by considering only one disaster scenario. We should determine
many scenarios as a bundle so that all evacuees can survive in any scenario.
The objective is to minimize total cost, C (unit: yen), which is composed of several types of costs
as is illustrated in Figure 6, and represented by the sum of the storage cost of relief goods, , and the
expected transport cost, :(1)
There are two sorts of control variables in this cost minimization problem: the quantity of stocks ofrelief goods in all the shelters, and the quantity of relief goods transported from one shelter to another after theJournal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

inundation heights of all areas are known. Namely, the former is determined before occurrence of a flood, andthe latter, after occurrence of each flood event. Concretely, the quantity of relief goods stocked in Shelter i iswhere the subscript i is the index of shelter; the quantity of relief goods transported from
represented bywhere the subscript k
Shelter i to the distribution center by truck in Scenario s is represented byrepresents the distribution center; the quantity of relief goods transported from the distribution center to Shelteri by truck in Scenario s is represented by; the quantity of relief goods transported from the distribution
center to Shelter i by helicopter in Scenario s is represented by.

Figure 6. Outline of Total Cost

(2)
The problem is solved backward. First, the planner can obtain the optimized policy for Scenario s bysolving the following cost minimization problem:
The stock of relief goods is classified into consumable goods (called Goods 1), and durable goods(called Goods 2). The total storage cost of relief goods is the sum of the storage cost of Goods 1,, andthat of Goods 2,

:
(3)
(4)

(5)
where AS1 and AS2 represent the unit storage cost of one set of the necessary amounts of the bundle ofand, the quantity of Goods 1
Goods 1 for Scenario s and that of Goods 2, respectively, andstored in Shelter i for Scenario s and that of Goods 2, respectively. The total number of shelters is 301.
On the other hand, the transport cost of relief goods,, is defined as the sum of the cost of, and the delivery cost,.
picking up relief goods,(6)
The cost of picking up relief goods in Scenario s is defined as the cost of transporting relief goods
from a Type-E shelter to the distribution center by truck as follows:

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T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat(7)

where B1C represents the unit transport cost of one set of Goods 1 by two-ton-truck per km (unit:
yen/(set×km)).
is the distance from Shelter i to Distribution Center k by truck (unit: km).
isthe quantity of Goods 1 transported from Shelter i to the center.
The delivery cost of relief goods in Scenario s is defined as the sum of the cost of transporting
relief goods from the distribution center to a Type-B shelter by truck and to a Type-A shelter by helicopter
as follows:(8)
andare thewhere B1H is the unit transport cost of one set of Goods 1 by helicopter per km.
anddistance from Distribution Center k to Shelter i by truck and that by helicopter, respectively.
are the quantity of Goods 1 transported from Distribution Center k to Shelter i by truck and thatby helicopter, respectively.
Secondly, the planner considers the optimal quantity of relief goods stocked in each shelter so thatit ensures that all evacuees can survive in any scenario among the eight scenarios. Therefore, the quantityof Goods x (=1,2) (unit: set/() that should be stocked in Shelter i,, is represented asfollows:,(9)

represents quantity of Goods x in Shelter i that is necessary in Scenario s. Correspondingly,
where(unit: yen), is given by
the cost of stocking relief goods,
(10)
where

is the cost of stocking relief goods that are necessary in Scenario s.
On the other hand, we assume that the transportation cost in the objective function of the cost
minimization problem is represented by the expected transportation cost:(11),
where E[ ] represents the expectation operator and we assume that the probabilities of all the scenarios are
uniform. Hence, the objective function of the optimization problem that is given by Eq.(1) is rewritten as
follows:(12)
Finally, the optimization problem is represented as follows:(13)
where M and T represent the bundle of stocks of relief goods and the bundle of transported goods,
respectively.
4.2 Constraints
We have three main constraint conditions. Firstly, in all cases, the total quantity of relief goods stocked inJournal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

all shelters should be greater than or equal to the total demand for relief goods.
(14)
where
and
are the quantity of demand for Goods 1 and Goods 2, respectively, at Shelter i in
Scenario s, and given by(15)
is the estimated number of evacuees (unit: person), andis the number of days that
whereevacuees stay at Shelter i in Scenario s (unit: day).
Secondly, we identify the upper and lower bounds for the quantity of relief goods stocked at eachshelter. It is assumed that evacuees manage to survive with the stock of relief goods at each shelter after adisaster until other relief goods are delivered to their shelter in the damaged area. Thus, the quantity ofrelief goods stocked at each shelter is set as a certain threshold to ensure that evacuees manage to survive:
(16)
where
is the number of days that it takes to deliver relief goods to a shelter after a disaster. On theother hand, with consideration given to the storage space of each shelter, the maximum quantity of relief
goods stocked at each shelter is given:(17)
Finally, we set constraint conditions of transported relief goods. The sum of the stocked relief
goods and the transported relief goods in Shelter i must be greater than the quantity of relief goods
demanded in Shelter i for all cases as follows:(18)
The constraint conditions are summarized as follows:
(19)

(20)
(21)
(22)
(23)

4.3 Parameters
andare identified by using the price of each relief good sold by private companies.
The values ofis set by using the representative price suggested by the Kanto District Bureau (Tokyo Route Truck
25

T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat
Conference Association).
is set by using the cost of helicopter transportation services provided by a
,
,
, and
are set by using the data supplied byprivate company (ARK EFI ALL).
is set by using the classification of shelters based on the flood depth at each
ZENRIN DataCom.
shelter, as in Table 4. Evacuees are assumed to stay in a Type-A or Type-B shelter for a maximum of three
is set by using the capacity of each shelter as provided by Nagoya City.
days after a disaster.
Furthermore, based on the flood data calculated by the flood simulation developed by the MLIT, we
identified DayR to be unity for all i and s, namely=1. We finally assume the limitation of space forstorage in each shelter by
4.4 Simulation Results
We call the simulation results in this section the “Network Policy.” The results are compared with those of
Nagoya City’s policy, which is named the “‘Planned Policy.” Table 5 presents an excerpt of the entire
simulation results where the numbers of stocked and transported relief goods of seven shelters that are, under three scenarios, Scenarios 1, 2, and 3, among the eight scenarios are selectively
Sheltershown due to limitation of space.
Table 6 summarizes the results of the costs in each scenario under the “Network Policy” as well as
the costs of the “Planned Policy.” Finally, Table 7 shows a comparison between the Planned and the
Network Policies. Note that, in this case study, the Planned Policy is that “in each shelter, Goods 1 should
be stored in an amount of ‘the estimated number of evacuees’ x ‘three days’, and Goods 2 should be
stored for the estimated number of evacuees”.
Now, the results of the Network Policy show that if all the shelters stock a one-day supply ofGoods 1 and Goods 2, evacuees in Types-A and -B impacted shelters can survive for three days in the
shelters, thanks to elastic transfer of goods within the inter-ward network. Moreover, owing to the
reduction in stocks of Goods 1 by 67%, the total cost of the Network Policy is lower than that of the
Planned Policy by 25%, which is equivalent to 396,572 thousand yen. This is because the unit cost of
stocking relief goods is significantly higher than the unit cost of transporting relief goods.
Another potential benefit of the Network Policy will be estimated when we consider the expiration
dates of the disaster relief goods. As a matter of fact, at least some relief goods that are not consumed
because areas are not damaged must be thrown away although some of them are used in evacuation drills.
Now, the Network Policy can decrease the amount of those goods that would be disposed of under the
Planned Policy because the Network Policy increases the probability that each good is used in someshelter. The numerical estimation of this benefit is left for future study.
In summary, by guaranteeing that relief goods are transported from shelters in unaffected areas tothose in damaged areas to compensate for possible shortages, evacuees’ demands will be met in all cases
under the Network Policy and its cost is lower than that of the Planned Policy because the cost oftransportation is significantly lower than the storage cost of relief goods.
Table 5. Excerpt of Results of the Estimated Quantities of Stocked Relief Goods (M) andTransported Relief Goods (T) for the “Network Policy” for Three Sample Scenarios

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

Table 6. Results of the Estimated Cost of the “Network Policy” for Each Scenario and the “Planned
Policy”
unit : thousand yen
S
Cost
C(Total)CS(Stocking)
CS1(Goods1)
CS2(Goods2)
CT(Transporting)CC(Collection)
CD(Distribution)

Scenario1 Scenario2 Scenario3 Scenario4 Scenario5 Scenario6 Scenario7 Scenario8

All Scenarios

Planned
Policy1192912119307111937821195504

119224511926461192232

1192192

1196218

1589200

1191900

1191900

11928141194580

1191900

1191900

1191900

1191900

11954941589200

198650198650199564

201330198650198650198650198650202244595950993250993250993250993250993250993250993250993250993250993250

1012

1171

968

924

345

746

332

292

724

0

85

99

101

97

23

46

25

27

63

0

927

1072

867

826

321

700

307

265

661

0

Table 7. Comparison between the “Planned Policy” and the “Network Policy”

4.5 Wide-area DisasterSo far, flooding of the Shonai River has been assumed to be the target disaster. In fact, Nagoya City also
has the potential to undergo a wide-area disaster such as the Nankai Trough Quake. This model can be
expanded to deal with a larger disaster such as the Nankai Trough Quake. In the above case study, we
focused on the non-uniform distribution of damage among five wards of Nagoya City; however, if the
Nankai Trough Quake occurs, these five wards will be damaged uniformly because earthquakes comprisea wide area. Thus, it is necessary to construct an “Inter-regional Network for the Storage of Relief
Goods.” One of the constraints of this policy is that areas must not be damaged uniformly when a disasteroccurs. Furthermore, the number of assumed evacuees in each of these areas must be similar because thequantity of relief goods in each area is theoretically the same. For example, we show the possibility ofdeveloping a network for the storage of relief goods for the Nankai Trough Quake. Nagoya City could
suffer from this earthquake and the resulting tsunami because it is located near the trough plate and thePacific Ocean. On the other hand, cities located on the other side of the main island of Japan are assumed
not to suffer serious damage because they are located far from the seismic center of the earthquake and atsunami would not hit. Consequently, Nagoya City should develop its network with other cities on thatside; we hypothetically identify two cities that we call K City and F City, respectively.

27

T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat

Figure 7. Inter-regional Network for the Storage of Relief Goods (G1 represents Goods 1.)
We now simulate a scenario after the Nankai Trough Quake occurs as follows: suppose an interregional network among the three cities is developed. Each city stocks relief goods at each shelter for theassumed number of evacuees for one day. We assume that these three cities are not damaged by the same
disaster. They reach the following agreement with each other: “If one city is damaged by a disaster, theother cities have to deliver relief goods to the distribution center of the damaged city.” Given that Nagoya
City would be seriously damaged by the Nankai Trough Quake, this agreement means that the evacuees inall shelters in Nagoya City would be forced to stay there for 72 hours after the earthquake occurs. They
can survive with the relief goods stored in each shelter for the first 24 hours after the earthquake occurs.
On the other hand, since K City and F City are not damaged by the earthquake, they will deliver
relief goods to the distribution center of Nagoya City within 24 hours without any logistical problems.
Then, on the second day, the goods are delivered from the distribution center to each shelter in Nagoya
City by truck and helicopter. Hence, relief goods are not in shortage in any shelter in Nagoya City as
shown in Figure 7. From the fourth day after the earthquake, we expect that relief goods will be delivered
constantly, thanks to the disaster recovery effort and the elimination of road obstacles.
On the other hand, in practice, it will be difficult to identify the names of what we call “K City”
and “F City” above, since there is no city on the Sea of Japan side whose population is as large as that of
Nagoya City. Hence, “K City” or “F City” can be a consociation of several cities, towns, or villages.
Although making of a consociation is one of the important challenges in the area of politics whose
possibility should be analyzed both practically and theoretically, as described above, this model may be
extended to deal with a larger disaster, such as earthquakes or tsunamis, to avoid a shortage of supply ofrelief goods.
5. CONCLUSION
This study described the present problems of relief goods policies based on interview surveys, formulated
an optimization problem of relief goods policy, and examined its effects. We developed a model focusing
on the non-uniform distribution of damage and an inter-ward storage network for relief goods, with real
data on the necessary amount of goods and transportation conditions, and applied it to a case study of the
Shonai River, Nagoya City, Japan to determine the quantity of stocked and transported relief goods andthe associated costs. The results showed that it is possible to guarantee three days’ worth of supplies forthe expected number of evacuees by storing one day’s worth of relief goods. It is, therefore, possible toreduce the costs of the relief goods policy with this model. This study contributes knowledge helpful tothose responsible for enacting an efficient relief goods policy that guarantees the lives of evacuees.
A foreseeable extension of this research would be to include the following points: we need to take
into account the probability that roads are damaged so that it takes greater time and cost to transport
goods in the aftermath of a disaster. It is also important to consider the scenario whereby a distribution

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33

center is damaged. The Great East Japan Earthquake damaged the public office in Rikuzen Takata City.
Therefore, it is possible that an important hub intended to function during disaster recovery activities
could be damaged. This study assumes Komaki Airport to be the only distribution center. However, it isnecessary to consider a scenario such as actually occurred in Rikuzen Takata City.
The second point is to consider the disaster relief goods’ expiration dates. As is pointed out in
Subsection 4.4, Network Policy must be further advantageous over Planned Policy if expiration dates aretaken into account. This merit should also be numerically estimated by extending the model, where atransfer strategy includes a criterion whereby goods with the shorter expiration date should be provided tothe damaged shelter.
The third point is to determine what kind of management system is needed to guarantee an
efficient relief goods network policy. For example, who should manage the collection of relief goods ineach shelter? How can community members reach agreement on a list of goods that reflects the special
circumstances of their community? From the viewpoint of community disaster prevention, each shelter
should be managed by each community. Since it is an issue of implementability of community-based
activity of disaster prevention, further discussion on risk perception, risk communication, leadership,solidarity, and activity planning is necessary.
Acknowledgements
We would like to express our gratitude to related departments of the City of Nagoya, and Mr. Hidemitsu
Yukawa, city council member of Nagoya City, for providing information on relief goods of Nagoya City.
We are also grateful to the Shonai River Management Office for giving us the calculation result of flood
depth of the Shonai River. We further wish to express our sincere thanks to Professor Takashi Sakata,president of Ishinomaki Senshu University, and Mr. Yoshihiro Yamamoto, a teacher at Ofunato Prefectural
High School.
APPENDIX Interview Survey in the Tohoku Area
As described in Chapter 2, the authors visited two places in the Tohoku region of Japan that were severely
damaged by the earthquake and resulting tsunami in the Great East Japan Earthquake of 2011, in order toobtain knowledge and lessons learned regarding relief goods. The following is a summary of interview
surveys with persons in charge of a shelter at the time.
1) Iwate Prefectural Ofunato High School
Iwate Prefectural Ofunato High School is located in Ikawacho, Ofunato City, Iwate Prefecture. This highschool was used as a shelter in the aftermath of the Great East Japan Earthquake in 2011. The authors
conducted an interview survey with a male teacher aged 29. He was at the high school when theearthquake occurred. He also managed the shelter for a week until all evacuees returned to their homes.
Points of his statements are itemized as follows.

A 60-square-meter room, usually used for club activity training camps, served as a sleeping
space.
Most high schools in Iwate Prefecture have a similar type of room. The room is usually usedduring everyday situations; thus, students can use this room efficiently in an emergency.
A shelter can be well managed with the cooperation of evacuees.
Fortunately, the shelter was equipped with bedclothes, such as blankets. However, there were
not enough of these commodities. Students first distributed these commodities among elderly
people, women, and children. The students did not complain about the lack of commodities,
as they knew each other before the disaster. Problems might have occurred if they had been
strangers. In that case, they may have had to consider rationing relief goods per person. For
example, if water supply per person is two-thirds of a bottle, distribution would have beendifficult, and there may have been complaints. Riots may have occurred if people werestarving. Without cooperation, managing the evacuation shelter would have been difficult.
Light gave evacuees a sense of security.
29

T.Kajihara, M.Yokomatsu, H.Ito, W.Wisetjindawat

A kerosene oil stove played an important role as a source of both heating and light. Because
electricity was cut, the light helped many evacuees feel safe, especially at night. Consideringthat a kerosene oil stove provided mental support to evacuees, it is more effective thanelectrical heating apparatus, which would not have been able to work during the power
outage.
In an emergency, cooperating with private organizations is effective.
Soon after the disaster occurred, an electronics store located near the high school provided
them with relief goods, such as heating apparatus. This proved helpful to evacuees.
Evacuees survived with goods stocked in shelters through trial and error.
For example, the water supply had been stopped and evacuees were forced to use residual
water in the water tank. Consequently, a lack of water became a concern. Furthermore, they
did not know when the water supply would be restored. From two days after the disaster, theyleft the shelter to search for water, and transported spring water back to the shelter on a cartin plastic bottles. They then used these bottles of water for the toilets. Clearly, the shelters
were faced with many problems; however, evacuees managed to utilize the limited goods
stocked in the shelter through trial and error.
The ability of the local government to function effectively as a base for disaster recovery
greatly impacts disaster recovery.
There was a surplus of relief goods at the shelter from the second day after the disaster. For
example, too many rice balls were transported from other regions, and the evacuees could not
eat them all. Large volumes of relief goods were transported to the shelter, as Ofunato City
Office was a well-functioning disaster recovery base. On the other hand, the Rikuzentakata
City Office was severely damaged by the tsunami, and could not function as a disasterrecovery base (Rikuzen Takata City). Consequently, relief goods could not always be
supplied to those shelters lacking food.

2) Ishinomaki Senshu University
Ishinomaki Senshu University is a private university located in Ishinomaki City, Miyagi Prefecture, Japan.
The university was used as a shelter and base of the volunteer center, Red Cross, Japan’s Self-Defense
Forces camp, and heliport after the 2011 Great East Japan Earthquake (Ishinomaki Senshu University).
The authors conducted an interview with the president of the university. When the earthquake occurred,
he was charged with managing and making all decisions regarding the shelter. Points of his statements are
itemized as follows:
The situation in the evacuation shelter changed from moment to moment, making it difficult
to understand evacuees’ needs.
For example, the evacuees housed in the shelter lacked water and requested that Ishinomaki
City supply it. The next day, too much water was supplied. In addition, a volunteer
unexpectedly sent more water to the shelter.

There was enough food and water, but other goods were in short supply.
From three to four days after the disaster, there was enough food and water thanks tovolunteers and NPOs. However, baby goods, sanitary goods, pet goods, and cigarettes werein short supply.
The president experienced many difficulties in making decisions as a private university.
The private university is not a public facility. As such, the president did not know what to do
in his capacity as the president of a private university. Despite this, he was forced to makedecisions in various scenarios. For example, although the university was not designated as ashelter, many evacuees arrived there. He accepted evacuees by his own decision, as they wereunable to evacuate to other shelters.
The sewerage treatment facility did not function, and the evacuees had to use portable toilets.
Initially, evacuees used the regular toilets. However, they began using portable toilets after
noticing that the sewerage treatment facility was not functioning. We have to consider how

Journal of Natural Disaster Science, Volume 37，Number 1，2016，pp11-33









evacuees can use toilet facilities comfortably. Problems regarding toilet facilities areimportant, as they are related to security and health problems.
Long-distance transportation was restored within two days of the disaster.
Relief goods were transported through long-distance transportation within two days of thedisaster. The evacuees were able to feel safer and more secure, because they felt connected toother regions. They were surprised at how quickly transportation companies and road
networks were restored.
A supplement with a quality energy vitamin per volume was effective.
Evacuees could not obtain natural vitamins from food, such as fruits and vegetables.
Consequently, they suffered from malnutrition and stomatitis. In these cases, supplements
were beneficial to those who were ill.
Managing warehouse stock was a lifeline for shelters.
Fortunately, one volunteer was skilled in logistics. With his help, the type and quantity ofrelief goods needed could be calculated, which helped in managing the shelter. It would be
useful to create a system whereby people skilled in logistics are dispatched to each shelter. In
medical facilities, D-MAT is organized similarly to the system I recommend here (D-MAT
Office).
In evacuation shelters, both volunteers with specialized skills and regular volunteers areneeded.
Regular volunteers are helpful, but volunteers with specialized skills are invaluable. The
university president felt that volunteers with specialized knowledge in public relations,logistics, distribution, and medicine for example would be helpful during disaster recovery.

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