# Modelling Sustainable Development Aspects within Inventory Supply Strategies

Authors: Gladys Bonilla-Enriquez; Patricia Cano-Olivos; Li-Qun Peng; Weihua Gan; Jose-Luis Martinez-Flores; Diana Sanchez-Partida
Journal: Modelling and Simulation in Engineering
 (2021)

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## Abstract

Nowadays, inventory management is a tool that must be extended to cover all aspects of the supply chain (SC). One of these aspects is Sustainable Development (SD) which emphasizes the balance between economic well-being, natural resources, and society. As inventory involves the use of natural and economic resources, the integration of SD criteria is important for a more efficient and sustainable SC. In this work, the most important SD variables associated with inventory management were identified. These variables were integrated as cost elements within a nondeterministic inventory control model to include SD criteria within inventory supply strategies. Through the assessment of the proposed integrated model, it was determined that, although SD practices involve additional investments, specific practices such as reuse/recycling and government incentives can increase revenue and profits. This is important for the development of government and business strategies to perform sustainable practices.


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## Body

## 1. Introduction

Sustainable Development (SD) has its beginnings in the 1980s when the United Nations (UN) requested an investigation about natural resources and their situation in the world in the face of the evident deterioration of the environment and natural resources. This investigation led to the report entitled “Our Common Future” [1] where the term “Sustainable Development” was defined for the first time [2]. SD integrates the concern of the resource capacity of natural systems with the social, political, and economic challenges of humanity [3].The UN and the OECD (Organization for Economic Cooperation and Development) have been working with member countries to make appropriate recommendations to reduce the impact of inefficient economic practices on the sustainable aspects of the environment and society. Within this context, the manufacture and service industries are two of the main sectors whose practices impact on the economic, environmental, and social aspects.If unattended, the impacts on these aspects are expected to worsen as more people would require products and services, compromising the availability of environmental resources for production of raw materials. Thus, finding new solutions to achieve sustainable consumption and production is of main interest for companies (however, this requires an understanding of the environmental and social effects of products and services).The distribution of materials and products throughout the SC is one of the major contributors to emissions of greenhouse compounds with high logistics costs [4]. Within this context, inventory management is the component of the SC which involves operations that impact on economic, environmental, and social aspects as it involves production and distribution operations that generate significant pollution (e.g., CO2 emissions and product waste) and economic loss due to inefficient management practices [5–7].Hence, the importance of this work consists of the development of an inventory model to integrate SD criteria within the SC to reduce economic loss and negative impacts on SD. For the development of the model, the multicriteria analysis was performed to identify the most significant factors of the environmental, economic, and social aspects that impact on the SD of inventory supply management.The advances of this work are presented as follows: in Section2, a review on SD and sustainable inventory models is presented; then, in Section 3, the analysis to determine the SD factors associated to inventory is described. Section 4 presents the development of the integrated inventory control model with the cost variables representing these SD factors. A test instance developed to assess the outcomes of the inventory model is presented in Section 5 with a discussion regarding its results. Finally, Section 6 presents our conclusions and future work.


## 2. Sustainable Inventory Models

As discussed in [8], the formulation of sustainable tools for SC requires a multidisciplinary approach. Thus, the development of an inventory model with SD criteria involves multidisciplinary complexity [2] with different policies or strategies to reduce contaminants and economic loss [6]. In this review, deterministic and nondeterministic inventory models that have addressed sustainable aspects were analyzed. Table 1 presents a detailed analysis regarding the most recent models which have included some sustainable variables within their formulations.Table 1
Review of works on inventory control with sustainable aspects (own work).
Work
Description
Variable associated to sustainability
[5]
EOQ model with the vehicle’s cost of CO2 emissions
Economic lot sizeCO2 emissions
[9]
EOQ model with the cost of CO2 emissions associated to logistics and warehousing operations
Economic lot sizeWater footprintCO2 emissionsCap-and-trade incentives
[10]
Multiobjective EOQ model with the cost of CO2 emissions
Economic lot sizeWater footprintCO2 emissionsEnvironmental and social criteria
[11]
EOQ model with facility location that integrates CO2 restrictions on multiple business units
Economic lot sizeCO2 emissions and taxesCap-and-trade incentives
[12]
EOQ and EPQ models with green costs associated to warehousing and production
Economic lot sizeCO2 emissions and taxesCap-and-trade incentives
[13]
EOQ model with carbon footprint and transportation costs
Economic lot sizeCO2 emissions
[14]
EOQ model with sustainability considerations
Economic lot sizeCO2 emissionsCarbon taxCarbon offsets and social criteriaBonney and Jaber [5] addressed the importance of analyzing the relation of inventory to the environment and whether if it is possible to create environmentally responsible inventory planning systems. Their results suggested that ordering items in larger quantities (less frequent orders) in contrast to the traditional economic order quantity (EOQ) model can lead to reducing transportation costs and consequent CO2 emissions. Furthermore, their results implied that a cost-benefit analysis can be performed by a joint cost function between the company’s benefits and the inventory costs.Hua et al. [9] addressed the trade in carbon emissions as an effective mechanism to reduce them. This was proposed by investigating how companies manage carbon footprints in inventory management under the carbon emission trading mechanism. They derived the optimal order quantity and analytically and numerically examined the impacts of carbon trade, carbon price, and carbon cap on order decisions, carbon emissions, and total cost.Bouchery et al. [10] developed a sustainable EOQ model. Their results were used to provide some insights about the effectiveness of different regulatory policies to control carbon emissions. They also used an interactive procedure which allowed the decision-maker to quickly identify the best option among these solutions. The proposed interactive procedure led to a new combination of multicriteria decision analysis techniques.Benjaafar et al. [11] used the EOQ and News Vendor models to study the extent to which carbon reduction requirements can be addressed by operational adjustments, as an alternative (or a supplement) to costly investments in carbon-reducing technologies. They also used these models to (a) investigate the impact of collaboration among companies within the same SC on their costs and carbon emissions and (b) to study the incentives that companies might have in seeking such cooperation.Tao et al. [12] researched the joint optimal decisions on lot size in a coordinated SC between a retailer and a manufacturer under the carbon tax and cap-and-trade mechanisms. The comprehensive cost-based models were proposed to capture the influence of two carbon regulatory schemes on business decisions in a coordinated two-stage SC.Battini et al. [13] linked sustainability aspects to the raw material lot size, from the beginning of the order purchase to its delivery at the buyer’s plant. Thus, the environmental impact of transportation and inventory was incorporated into the EOQ model. The approach was applied to represent data from industrial problems to assess the impact of sustainability considerations on purchasing decisions when compared to traditional approaches.Arslan and Turkay [14] discussed on sustainable aspects for the standard EOQ model with a single item at a single location with no backlogging, constant lead times, and an unlimited supply. Also, they discussed on relaxations to consider multiple items at multiple locations with planned backorders, variable lead times, finite production rates, quantity discounts, imperfect quality, and resource constraints such as warehouse space.As discussed, while companies have made efforts to increase profits by looking for the economic factor, research has provided insights regarding the importance of the environmental and social factors for this goal, and currency markets are moving in that direction [2, 15]. The works reviewed in Table 1 have demonstrated that the integration of these factors within the inventory control techniques can improve on achieving sustainability without conflicting with the economic aspect of inventory management.In this context, the proposed research contributes with an integrated inventory supply model to address a more comprehensive integration of the economic, environmental and social factors. In contrast to the works reviewed in Table1, where up to three variables were analyzed, the present work analyzes six variables associated with SD factors. These were identified and modelled as cost elements for their integration within an inventory control technique for uncertain demand, which is a common feature in nowadays markets. The advances of this model are described in the following sections.


## 3. Determination of Variables Associated to SD Factors in Inventory Management

The determination of variables associated with the SD factors can be considered a multicriteria task. This is because each factor is integrated by diverse decisions, costs, and resources that affect the sustainability of the SC. Also, depending on the context, qualitative and quantitative assessment of the importance of each factor may lead to different conclusions. In the example, in [16] it was mentioned that economic factors should be the dominant ones in inventory management. On the other hand, in [14] it was considered that environmental and social factors should be considered due to the current environmental situation.For the present work, we extended the analyses reported in [16, 17] on metrics to measure SC performance and evaluation of sustainable supply chain indicators. The work reported in [16] concluded that the most important SC metrics related to sustainability were those presented in Table 2.Table 2
Supply chain metrics: performance indicators on sustainability [16].
Social
Economic
Environmental
Health and safety
(1) Number of accidents (employees)(2) Work conditions(3) Number of accidents (nonemployees)
Quality
(1) On-time delivery(2) Customer satisfaction(3) Order fill rate(4) Product/service availability
Emissions
(1) Level of CO2 emissions(2) Level of CO2 emission from transport processes(3) Level of CO2 emission from infrastructure
Noise
(1) Noise volume(2) Time of noise emission(3) Noise emission in urban areas
Efficiency
(1) Distribution costs(2) Total costs(3) Transport costs(4) Loading capacity utilization
Natural resources utilization
(1) Energy use(2) Water consumption(3) Energy consumption/revenue
Employees
(1) Employee skills(2) Employee satisfaction(3) Percent of labor cost spent on training
Responsiveness
(1) Stock-outs(2) Product lateness(3) Lead time(4) Forecast accuracy
Waste and recycling
(1) Level of waste(2) Level of products recycled(3) Level of products reusedTo provide a more general model, we performed a focus group discussion with different professionals in the manufacturing and logistics fields for the assessment of these metrics on inventory management. In this way, the metrics presented in Table2 were extended to those presented in Table 3.Table 3
Supply chain metrics: performance indicators on sustainability (own work).
Social
Economic
Environmental
Health and safety
(1) Number of accidents (employees)(2) Number of accidents (nonemployees)(3) Number of accidents associated to company’s vehicles(4) Wireless electronics conditions(5) Toxic and hazardous emissions
Quality
(1) On-time delivery(2) Customer satisfaction(3) Order fill rate(4) Product quality(5) Supplier performance
Emissions
(1) Level of CO2 emissions(2) Level of CO2 emission from transport processes(3) Level of CO2 emission from infrastructure(4) Carbon footprint—ordering(5) Carbon footprint—holding
Waste
(1) Water pollution(2) Air pollution(3) Solid waste
Efficiency
(1) Information management costs(2) Distribution costs(3) Inventory costs(4) Transport costs(5) Loading capacity utilization
Natural resources utilization
(1) Energy use(2) Water consumption(3) Energy consumption/revenue(4) Fossil fuel consumption(5) Energy efficiency per ton kilometer
Employees
(1) Hours efficiently worked (energy optimization)(2) Clean workplace(3) Good use of work tools(4) Classification of waste in work areas(5) Disposal of work waste
Responsiveness
(1) Stock-outs(2) Lead time(3) Forecast accuracy(4) New product—time to market(5) New product—time to first date
Waste and recycling
(1) Level of waste(2) Level of products recycled(3) Level of products reused(4) Level of landfill waste(5) Level of biodegradable materials usedWith this information, we proceeded to determine the most important variables or metrics between each other based on a multicriteria analysis. For the selection of the analysis tool, we studied the work reported in [17] where the AHP technique led to determine that environmental and social factors could contribute more to the sustainability of the Indian automotive industry.


### 3.1. AHP Analysis

For our analysis, the goal of the AHP is defined as the identification of the most important alternatives to be modelled as cost variables within the proposed inventory model. For this, the SD factors are set as the criteria at level 1 of the AHP structure. Then, the aspects of each factor are considered as the subcriteria for level 2. Finally, the alternatives from which the variables will be identified and modelled are set at level 3 of the AHP structure. Figure1 presents the description of the AHP model with the associated abbreviations.Figure 1
Hierarchical structure of the information reported in Table3: (a) descriptive structure and (b) abbreviated structure (own work).
(a)
(b)Figure2 presents the weights (i.e., importance) estimated for the criteria, subcriteria and alternatives defined by the AHP structure of Figure 1. These weights were estimated based on the feedback of professionals in the manufacturing and logistics fields and the results reported in [16]. The details of the professionals’ profiles are presented in Table 4.Figure 2
Weights (importance) of criteria, subcriteria and alternatives for the AHP analysis (own work).Table 4
Profiles of eight professionals considered for the AHP analysis: SC: supply chain; IM: inventory management; SD: Sustainable Development (own work).
Field
P
1
P
2
P
3
P
4
P
5
P
6
P
7
P
8
SC
X
X
X
X
X
X
X
X
IM
X
X
X
X
X
X
X
X
SD
X
X
X
XWith this data, the AHP weights associated with the interactions between all criteria, subcriteria, and alternatives were computed. These are presented in Table5.Table 5
AHP weights obtained for the interactions between all criteria, subcriteria, and alternatives (own work).
Goal
Consistency ratio
Criteria/factors
Alternatives
L1
L2
L3
Definition of SD criteria that impact inventory through the SC
0.0516
Eco 0.5936
Eco_Q 0.2234
A_Eco_Q1 0.0075
A_Eco_Q2 0.0269
A_Eco_Q3 0.0375
A_Eco_Q4 0.0568
A_Eco_Q5 0.0947
Eco_E 0.0887
A_Eco_E1 0.0026
A_Eco_E2 0.0045
A_Eco_E3 0.0159
A_Eco_E4 0.0213
A_Eco_E5 0.0443
Eco_R 0.2815
A_Eco_R1 0.0366
A_Eco_R2 0.0895
A_Eco_R3 0.1114
A_Eco_R4 0.0245
A_Eco_R5 0.0165
0.0176
Env 0.2493
Env_E 0.0523
A_Env_E1 0.0024
A_Env_E2 0.0035
A_Env_E3 0.0133
A_Env_E4 0.0267
A_Env_E5 0.0065
Env_N 0.0599
A_Env_N1 0.0028
A_Env_N2 0.0089
A_Env_N3 0.0288
A_Env_N4 0.0036
A_Env_N5 0.0158
Env_W 0.1371
A_Env_W1 0.0076
A_Env_W2 0.0069
A_Env_W3 0.0368
A_Env_W4 0.0496
A_Env_W5 0.0362
0.0036
Soc 0.1571
Soc_H 0.0172
A_Soc_H1 0.0010
A_Soc_H2 0.0046
A_Soc_H3 0.0009
A_Soc_H4 0.0045
A_Soc_H5 0.0062
Soc_W 0.0485
A_Soc_W1 0.0298
A_Soc_W2 0.0057
A_Soc_W3 0.0130
Soc_E 0.0913
A_Soc_E1 0.0061
A_Soc_E2 0.0028
A_Soc_E3 0.0212
A_Soc_E4 0.0157
A_Soc_E5 0.0455From Table5 it is obtained that the economic criterion (Eco) is the most significant with weight=0.5936. The environment criterion (Env) is the second most significant with weight=0.2493, and the social criterion (Soc) is the least significant with weight=0.1571. For each criterion, also the most significant subcriterion is determined. For example, for Eco, the subcriterion responsiveness (Eco_R) is the most significant with weight=0.2815. Finally, for each subcriterion, the most significant alternative is obtained (marked in bold). By following the previous example, for Eco_R, the most significant alternative is lead time (A_Eco_R3) with weight=0.1114 (see abbreviations presented in Figure 1).Table6 presents the interpretation of the results of the AHP analysis of Table 5. Note that these results will support the definition of variables that will be modelled as cost elements for the proposed inventory control model with SD criteria.Table 6
Interpretation of results of the AHP analysis presented in Table5 (own work).
Goal
Criteria/factors
Final results (most significant alternative)
L1
L2
Definition of SD criteria that impact inventory through the SC
Economic 0.5936
Quality 0.2234
Customer satisfaction 0.0947
Efficiency 0.0887
Inventory costs 0.0443
Responsiveness 0.2815
Lead time 0.1114
Environmental 0.2493
Emissions 0.0523
Level of CO2 emission from transport processes 0.0267
Natural resources 0.0599
Energy consumption/revenue 0.0288
Waste and recycling 0.1371
Level of products reused 0.0496
Social 0.1571
Health and safety 0.0172
Toxic and hazardous emissions 0.0062
Waste 0.0485
Water pollution 0.0298
Employees 0.0913
Disposal of work waste 0.0455As presented, there are nine variables (alternatives) associated with the sustainability of inventories through all SD factors (criteria). To equally address the variables through the SD factors, the two most significant variables were selected from each criterion. These are summarized in Table7.Table 7
Top six SD cost variables for inventory management (own work).
Economic
Quality
C
Q
Lead time
C
LT
Environmental
Level of CO2 emission from transport processes
C
E
Level of products reused
C
PR
Social
Water pollution
C
WP
Disposal of work waste
C
DW


## 3.1. AHP Analysis

For our analysis, the goal of the AHP is defined as the identification of the most important alternatives to be modelled as cost variables within the proposed inventory model. For this, the SD factors are set as the criteria at level 1 of the AHP structure. Then, the aspects of each factor are considered as the subcriteria for level 2. Finally, the alternatives from which the variables will be identified and modelled are set at level 3 of the AHP structure. Figure1 presents the description of the AHP model with the associated abbreviations.Figure 1
Hierarchical structure of the information reported in Table3: (a) descriptive structure and (b) abbreviated structure (own work).
(a)
(b)Figure2 presents the weights (i.e., importance) estimated for the criteria, subcriteria and alternatives defined by the AHP structure of Figure 1. These weights were estimated based on the feedback of professionals in the manufacturing and logistics fields and the results reported in [16]. The details of the professionals’ profiles are presented in Table 4.Figure 2
Weights (importance) of criteria, subcriteria and alternatives for the AHP analysis (own work).Table 4
Profiles of eight professionals considered for the AHP analysis: SC: supply chain; IM: inventory management; SD: Sustainable Development (own work).
Field
P
1
P
2
P
3
P
4
P
5
P
6
P
7
P
8
SC
X
X
X
X
X
X
X
X
IM
X
X
X
X
X
X
X
X
SD
X
X
X
XWith this data, the AHP weights associated with the interactions between all criteria, subcriteria, and alternatives were computed. These are presented in Table5.Table 5
AHP weights obtained for the interactions between all criteria, subcriteria, and alternatives (own work).
Goal
Consistency ratio
Criteria/factors
Alternatives
L1
L2
L3
Definition of SD criteria that impact inventory through the SC
0.0516
Eco 0.5936
Eco_Q 0.2234
A_Eco_Q1 0.0075
A_Eco_Q2 0.0269
A_Eco_Q3 0.0375
A_Eco_Q4 0.0568
A_Eco_Q5 0.0947
Eco_E 0.0887
A_Eco_E1 0.0026
A_Eco_E2 0.0045
A_Eco_E3 0.0159
A_Eco_E4 0.0213
A_Eco_E5 0.0443
Eco_R 0.2815
A_Eco_R1 0.0366
A_Eco_R2 0.0895
A_Eco_R3 0.1114
A_Eco_R4 0.0245
A_Eco_R5 0.0165
0.0176
Env 0.2493
Env_E 0.0523
A_Env_E1 0.0024
A_Env_E2 0.0035
A_Env_E3 0.0133
A_Env_E4 0.0267
A_Env_E5 0.0065
Env_N 0.0599
A_Env_N1 0.0028
A_Env_N2 0.0089
A_Env_N3 0.0288
A_Env_N4 0.0036
A_Env_N5 0.0158
Env_W 0.1371
A_Env_W1 0.0076
A_Env_W2 0.0069
A_Env_W3 0.0368
A_Env_W4 0.0496
A_Env_W5 0.0362
0.0036
Soc 0.1571
Soc_H 0.0172
A_Soc_H1 0.0010
A_Soc_H2 0.0046
A_Soc_H3 0.0009
A_Soc_H4 0.0045
A_Soc_H5 0.0062
Soc_W 0.0485
A_Soc_W1 0.0298
A_Soc_W2 0.0057
A_Soc_W3 0.0130
Soc_E 0.0913
A_Soc_E1 0.0061
A_Soc_E2 0.0028
A_Soc_E3 0.0212
A_Soc_E4 0.0157
A_Soc_E5 0.0455From Table5 it is obtained that the economic criterion (Eco) is the most significant with weight=0.5936. The environment criterion (Env) is the second most significant with weight=0.2493, and the social criterion (Soc) is the least significant with weight=0.1571. For each criterion, also the most significant subcriterion is determined. For example, for Eco, the subcriterion responsiveness (Eco_R) is the most significant with weight=0.2815. Finally, for each subcriterion, the most significant alternative is obtained (marked in bold). By following the previous example, for Eco_R, the most significant alternative is lead time (A_Eco_R3) with weight=0.1114 (see abbreviations presented in Figure 1).Table6 presents the interpretation of the results of the AHP analysis of Table 5. Note that these results will support the definition of variables that will be modelled as cost elements for the proposed inventory control model with SD criteria.Table 6
Interpretation of results of the AHP analysis presented in Table5 (own work).
Goal
Criteria/factors
Final results (most significant alternative)
L1
L2
Definition of SD criteria that impact inventory through the SC
Economic 0.5936
Quality 0.2234
Customer satisfaction 0.0947
Efficiency 0.0887
Inventory costs 0.0443
Responsiveness 0.2815
Lead time 0.1114
Environmental 0.2493
Emissions 0.0523
Level of CO2 emission from transport processes 0.0267
Natural resources 0.0599
Energy consumption/revenue 0.0288
Waste and recycling 0.1371
Level of products reused 0.0496
Social 0.1571
Health and safety 0.0172
Toxic and hazardous emissions 0.0062
Waste 0.0485
Water pollution 0.0298
Employees 0.0913
Disposal of work waste 0.0455As presented, there are nine variables (alternatives) associated with the sustainability of inventories through all SD factors (criteria). To equally address the variables through the SD factors, the two most significant variables were selected from each criterion. These are summarized in Table7.Table 7
Top six SD cost variables for inventory management (own work).
Economic
Quality
C
Q
Lead time
C
LT
Environmental
Level of CO2 emission from transport processes
C
E
Level of products reused
C
PR
Social
Water pollution
C
WP
Disposal of work waste
C
DW


## 4. Development of the SD Inventory Model

Figure3 presents the general structure of the SC which consists of three main entities: raw material suppliers, end-product manufacturers, and end-product retailers or clients. Here, the final entities determine the global requirements (demand) of end-products to be produced and transported through the SC. These requirements are to be periodically covered by the delivery of lots of size Q which is the basis of the economic aspect of inventory control management. As presented, the availability of Q depends of different aspects of the SC which are related to the SD variables identified in Table 7.Figure 3
Economic aspects of the SC associated to inventory control.Thus, the integration of each SD variable within the inventory model considering the relationships and dependencies identified in Figure3 is performed as follows:
(i)
Quality involves producing products with the minimum defects and the features required by the customer. Within SD criteria, achieving the highest quality supports the reduction of unnecessary waste and reconditioning processes. As the rejection of a lot is based on the individual detection of defects, the quality costCQ is considered as an investment to be associated with units(ii)
Lead time is associated to prompt delivery of products or raw material. Inefficient delivery is associated with rejection rates of lots, unnecessary additional transportation costs, and CO2 emissions. In this regard, failure to comply with the lead time can be considered as a penalty cost CLT to be associated to lots(iii)
CO2 emissions are associated with transportation. If lot sizes are not adequately estimated, unnecessary additional transportation may take place which would produce CO2 emissions. Thus, the emission cost CE is considered as a cost associated with the transportation of lots(iv)
The level of products that are reused is an important sustainability aspect. This practice consists of using an item for other purposes, either similarly to the original purpose or to different ones. This is different from recycling because it does not involve reconditioning or breaking down into raw materials. Thus, it can lead to save time, money, energy, and other resources within the company [18, 19]. Depending of the effort or additional steps for reuse (i.e., change of packaging/labelling and washing), this can include a small cost with an important return value. In this case, it is considered as an incentive CPR which is dependent of a percentage of a lot(v)
Water pollution is an aspect which is commonly omitted in the practice, and it can take place in any stage of the production process (i.e., cleaning and maintenance). The water pollution costCWP is considered as a shared-cost associated with producing a unit of product(vi)
Disposal of work waste is also an aspect that is not considered in practice. This requires additional investment for green practices associated with proper disposal of units which, if the quality is not absolute, is dependent on a percentage of the lot size. Thus,CDW is considered as a cost associated with the lot sizeIn inventory management tools, there are three main costs: holding costs, ordering costs, and safety stock costs [20]. An inventory control policy must determine a balance between these costs to reduce the impact on the SC.One of the most widely used models for inventory control under uncertainty is the continuous review model or (Q, R) model [21], where Q defines the optimal lot size and R the reorder point which depends on the lead time and average demand [22].In general terms, the (Q, R) model considers the following constants and variables: Co is the order cost per lot; Ch is the holding cost per unit of product; C is the purchase cost per unit of product; p is the stock-out cost per unit of product; D is the cumulative demand for a planning horizon, and d is the average daily, weekly, or monthly demand; LT is the lead time; μLT and σLT are the mean and standard deviation of the demand during the lead time; Lz is the standard loss function; K is the expected shortage of units of products per cycle. The economic lot quantity Q and the reorder point R then are estimated as presented in Figure 4 [23].Figure 4
Estimation process of the inventory control policy under the (Q, R) model [23].Within the determination of the lot size,pK is equivalent to CLT as it is associated with the units of products not delivered per inventory cycle. Another cost to be performed each time a lot is ordered is the transportation cost. While this can be considered within Co, the CO2 emission costs are not frequently considered. In [23], a cost metric, based on the transportation distance and CO2 emissions generated per kilometer, was determined as follows:
(1)CE=ECO2×dist×tCO2,where ECO2 is the average CO2 emission per kilometer in grams, dist is the total traveled distance between the supplier and the warehouse, and tCO2 is a CO2 emission tax per gram.About costs associated with units of products, the quality costCQ can be added to Ch as an investment to keep products in conforming conditions. Also, the cost of water pollution CWP can be added to the holding cost as a shared cost between the supplier and the retailer. Figure 5 presents the adapted (Q, R) model with these four SD cost variables:Figure 5
Estimation process of the inventory control policy under the adapted (Q, R) model with four SD cost variables (own work).The last two cost variables,CPR and CDW are considered to be dependent on the lot size. Thus, these are integrated into the total cost formulation of the (Q, R) model as described below:
(2)TC=totalordercost+totalholdingcostofcycleinventory+totalholdingcostofsafetystock+totalshortagecost–totalincentiveforreuseofproducts+totaldisposalcostofwaste,where
(a)
Total order costTCo=Co×D/Q(b)
Total holding cost of cycle inventoryTCh=Ch×Q/2(c)
Total holding cost of safety stockTCh_SS=Ch×R−μLT+σLTLz(d)
Total shortage costTC_shortage=CLT×D/Q(e)
Total incentive for reuse of productsTCPR=gQ×D/Q=CPR×D/Q,0<g<1(f)
Total disposal cost of wasteTCDW=rCQ×D/Q=CDW×D/Q,0<r<1


## 5. Assessment of the Model

The textile industry is one of the most important manufacturing industries. However, it is also one of the industries that have a more negative impact on the environment and social welfare. In this case, the proposed model can be used to reduce the costs associated with these impacts.Let us consider the inventory production and distribution of cotton t-shirts of 250 grams. Based on the feedback obtained from two retailers, the annual demand for this product was estimated asD=40000 units with a delivery cost of 100 USD/lot (Co).For this product, the associated cost elements of the integrated model were estimated as follows (the same methodology can be performed for different products):(i)
Quality is assured by the implementation of diverse processes and personnel. According to [24], the salary of a quality engineer is approximately 700 USD per month. In practice, approximately 20% of the products are sampled for quality control. This leads to approximately 0.20×40000units/12months=667units per month. Considering that sampling represents approximately 30% of the activities performed by the quality engineer, the unit cost of quality CQ is estimated as 0.30×700USD/667units=0.32USD/unit(ii)
The unit costC, which considers raw material and production costs, averages 3.0 USD/unit [25].(iii)
Holding costCh is minimal as t-shirts do not require specific warehousing conditions. It is estimated as 0.05 USD/unit(iv)
Nowadays, some countries have a tax policy to regulate the contamination of water caused by textile manufacturing [26]. For this case, a t-shirt requires approximately 2,700 liters of water or 2.7 cubic meters [27]. If the task averages 0.20 USD/m3, CWP is approximated as 0.20USD/m3×2.7m3/unit=0.54USD/unit(v)
It is expected that manufacturers perform the appropriate measures to dispose of waste. Collecting and disposing of a batch of combined waste approximately costs 400 USD/ton [28]. In this case, a cost of 80 USD is considered for CDW(vi)
Reused products can be considered as refurbished or substitution products. In practice, this accounts for approximately 5% of a lot. Thus,CPR=0.05×C−refurbishedcost×Q=0.05×3.0−2.0USD×Q=0.05QUSD(vii)
For a stock-out unit of product, a costp=1.5C is considered due to loss and additional penalties. This leads to define CLT=1.5×3×K=4.5KUSD(viii)
To estimateCE, it is important to determine the transportation route from the (supplier) manufacturer to the seller (retailer). Figure 6 presents an example of the route with a length of 375 km. Based on the work reported in [29], for a standard vehicle with a cargo capacity between 1.305 tons and 1.740 tons, an emission of 225 gCO2/km is generated if diesel is consumed. This leads to an estimate total of 85.0 kgCO2 for the trip. In practice, an emission tax is established to try to reduce CO2 emissions. In this case, a reference of 0.0020 USD per gCO2/km, this results in CE=225gCO2/km×0.0005USDpergCO2/km×375km=42.1875USDFigure 6
Route between supplier and retailer for the estimation ofCE.Table8 presents the overview of the previously defined cost variables together with the additional variables for the (Q, R) model. As the lead time is defined in days, a reference of daily demand is considered for μLT and σLT. Also, as uncertain demand is considered, a coefficient of variability of 25.0% is assumed.Table 8
Overview of cost variables for the (Q, R) model with SD criteria.
D
40000
Units
C
h
0.05
USD per unit
Days
360
C
O
100.00
USD per lot
d
112
Units
C
E
42.19
USD per lot
σ
28
Units
C
Q
0.32
USD per unit
LT
10
Days
C
WP
0.54
USD per unit
μ
LT
=
d
×
LT
1120
Units
C
DW
80.00
USD per lot
σ
LT
=
σ
√
LT
89
Units
C
3.00
USD per unit
p
4.50
USD per unitOn the other hand, Table9 presents the results of the iterative process for the estimation of Q and R. As presented, convergence is achieved on the 3rd iteration. With this result, where Q=3568 units and R=1307 units, CPR=0.05×3568=178.40USD. If no costs associated with SD criteria are considered, the following results are obtained: Q=12677 and R=1360. In such cases, R does not change significantly; however, Q increases by a factor of 3.55. This is expected because if SD criteria are to be considered, more care must be taken to establish the economic lot.Table 9
Results of the (Q, R) model with SD criteria.
A
z
L
z
K
=
σ
LT
L
z
C
LT
Q
0
3536
0.9821
2.10
R
1
1307
0.0065
0.58
2.59
Q
1
3568
0.9820
2.10
R
2
1307
0.0065
0.58
2.62
Q
2
3568
0.9820
2.10
R
3
1307
0.0065
0.58
2.62
Q
3
3568
0.9820
2.10
R
4
1307
0.0065
0.58
2.62
Q
4
3568
0.9820
2.10
R
5
1307
0.0065
0.58
2.62
Q
5
3568
0.9820
2.10
R
6
1307
0.0065
0.58
2.62
Q
6
3568
0.9820
2.10
R
7
1307
0.0065
0.58
2.62Table10 presents the total cost analysis for both scenarios. As presented, even though the SD model has more costs due to waste disposal and order costs with CO2 emissions and quality assurance, one significant income may come from investment in product reuse. This practice can represent a higher incentive which can compensate for the other SD costs. This is an improvement on the standard case where product reuse is not performed.Table 10
Comparison of total annual costs of the (Q, R) model with SD criteria and the standard (Q, R) model.
(Q, R) SD model
(Q, R) model
T
C
o=
1121.08
315.53
T
C
h=
89.20
316.93
T
C
h
_
SS=
9.38
12.00
TC
_
shortage =
29.36
1.36
T
C
PR=
2000.00
T
C
DW=
896.86
Annual total inventory cost =
145.88
645.82


## 6. Conclusions and Future Work

An important aspect to perform SD practices is the economic effort needed for their implementation. As discussed, there are specific SD factors associated with inventory control that must be carefully managed in order to maintain economic benefit.For this purpose, six SD cost variables were identified and modelled within the (Q, R) model for assessment of their impact and outcomes of their implementation. As discussed by other works, implementation of SD practices can increase the costs of the company significantly. This was observed in the analysis presented in Table 10. Particularly, those associated with lots (i.e., emission cost due to transportation and waste management) represent the highest costs. However, the opportunity of product reuse can lead to significant economic benefits which can compensate these costs. This can also lead to important advantages over standard practices where SD criteria are not considered.Even though these results lead to define specific practices to obtain economic benefits from SD factors, additional work must be performed to extend on the analysis and identification of other SD criteria. In example, stored inventory can lead to emission of contaminants which can affect the workers’ health. Thus, this should be considered within the lot ordering process. Also, considering other inventory models can lead to improve the applicability in other industries.



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*Source: 5232814-2021-03-18.xml*