a multi-stage stochastic programming model for...

Scientia Iranica E (2020) 27(1), 377{395

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringhttp://scientiairanica.sharif.edu

A multi-stage stochastic programming model forsustainable closed-loop supply chain network designwith �nancial decisions: A case study of plasticproduction and recycling supply chain

A.S. Mohammadia, A. Alemtabriza;�, M.S. Pishvaeeb, and M. Zandieha

a. Department of Industrial Management, Faculty of Management and Accounting, University of Shahid Beheshti, Tehran, Iran.b. School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran.

Received 16 July 2017; received in revised form 10 July 2018; accepted 17 November 2018

KEYWORDSSupply chainmanagement;Sustainability;Stochasticprogramming;Supply chain networkdesign;Multi-objectiveoptimization.

Abstract. This paper proposes a multi-objective, multi-stage programming model todesign a sustainable closed-loop supply chain network considering �nancial decisions.A multi-product, sustainable closed-loop plastic Supply Chain Network Design (SCND)problem, which encompasses economic, environmental, and social objectives, is modeledin a mathematical manner. The decisions to be made were concerned with the locationof facilities, ow of products, loans to take, and investments to make. Uncertaintyissue was about the demand of customers and the rate of return on investment. Thedecision making model was formulated as a multi-objective, multi-stage mixed-integer linearprogramming problem and solved by implementing path formulation and augmented "-constraint methods. Computational analysis was carried out based on the subject companyto determine the signi�cance of the proposed model and the e�ciency of integrating�nancial decisions with SCND decisions.© 2020 Sharif University of Technology. All rights reserved.

1. Introduction

With recent advances, globalization, and unpredictablebehaviors of customers and competitors, the �eld ofcompetition has been converted from �rms to supplychains. Consequently, Supply Chain Management(SCM) is one of the most sought topics in logistics.Moreover, Supply Chain Network Design (SCND) isa strategic decision contributing to supply chain. In-tegrating several strategic and tactical decisions like

*. Corresponding author. Fax: +98 21 22431645E-mail addresses: [email protected] (A.S.Mohammadi); [email protected] (A. Alemtabriz);[email protected] (M.S. Pishvaee); m [email protected](M. Zandieh)

doi: 10.24200/sci.2019.21531

determining the locations, number and capacity offacilities, and material ow through the network makesSCND a complex issue in the �eld of SCM.

Previously, minimizing total cost or maximizingpro�t was the main objective of supply chain andpioneering in the economic dimension was su�cient tooutperform the rivals. However, in recent years, supplychains have become responsible for the EnvironmentalImpact (EI) and Social Impact (SI) of their activities.This concern has led to the development of a newconcept in SCM, namely Sustainable Supply ChainManagement (SSCM), which is de�ned as consideringEI and SI of supply chain activities as well as economicperformance in management of material, information,and capital ow [1,2]. With respect to the need forsustainability in SCM, some researches have proposemodels in SCND context. However, the literature on

378 A.S. Mohammadi et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 377{395

sustainable SCND that covers all the three aspectsof sustainability (i.e., economic, environmental, andsocial) is scarce [3]. Recently, Eskandarpour et al. [4]reviewed 87 papers that used mathematical modelsin the �eld of SCND and included economic factorstogether with environmental and/or social dimensions.Based on their analysis, only in 11% of the reviewedarticles all the three dimensions of sustainable devel-opment in SCND models were addressed.

To avoid sub-optimality that originates from sep-arate modeling of forward and reverse SCNs, someresearchers have focused on developing integrated for-ward and reverse SCND models [5]. Appropriatelyestablished Close-Loop SC (CLSC) can assist �rmsto decrease the undesired EI of End-Of-Life (EOL)products and to achieve more economic bene�ts byrecapturing the value of used products and increasingtheir green image in the market. The objective ofclosed-loop supply chain is closely related to that ofSSCM [4]. Accordingly, in the body of the literature onSustainable Supply Chain Network Design (SSCND),closed-loop SSCND problems have been the major issueamong researchers in the recent years [6].

An important challenge associated with SCNDproblems is to determine the manner of handling theuncertain nature of some future conditions, which mayin uence input parameters of the problem. Uncertaintycan be a�liated to economic, legal, and political issuesand it a�ects parameters like the level of demand,production cost, supply of raw materials, etc. To copewith this issue in the context of SSCND, many authorshave proposed a number of stochastic programingmodels.

Recently, a two-stage stochastic programmingapproach was applied by Giarola et al. [7] and Vermaet al. [8] to manage uncertainties in single-objectiveenvironmental supply chain design. Pishvaee et al. [9]introduced Robust Possibilistic Programming (RPP)as a programming approach to coping with uncer-tain parameters in their bi-objective model, includ-ing minimizing the total cost and maximizing SCSocial Responsibility (SR). A computational frame-work has been proposed to quantify the probablerole of uncertainty in the environmental damage forthe multi-objective optimization of sustainable sup-ply chain in [10]. A multi-objective (economic andenvironmental factors) facility location model, whichinvestigates the impact of demand and return un-certainties on the SCND by implementing scenario-based stochastic programming, has been introducedby Amin and Zhang [11]. Ruiz-Femenia et al. [12]presented a stochastic multi-scenario Mixed-IntegerLinear Program (MILP) in which demand uncertaintywas considered for the multi-objective optimization ofchemical supply chain and economic and environmentalperformances were accounted for, simultaneously. The

fact that it is better to consider uncertainty andrisk in SSCND researches has been emphasized byEskandarpour et al. [4].

According to Shapiro [13], strategic-level supplychain studies should attempt to incorporate relevantcorporate �nancial decisions in data-driven models.However, in most of the common approaches to SCNDproblems, only the physical aspects of SC are ofconcern with some perspective on �nancial decisions inthe body of literature [14]. Implementing investmentdecisions and incorporating loans in �nancial decisionsin SCND problem have been addressed in [15]. An op-timal �nancing strategy for supply chain by consideringcapital constraint is discussed in [16]. Most researchersusually take into account the �nancial aspects such as�nancial factors [14] and �nancial ows of SC, while fewstudies address �nancial decisions in the SCND modelas decision variables.

In some cases, it is enough to consider a single-period model to develop an ideal solution to the SCNDproblem. Nevertheless, problems with �nancial andcapital expenditure-related decisions should be plannedby implementing multi-period planning models [17].Furthermore, developing a multi-period setting of thismodel in addition to the nature of �nancial decisionsmay lead to multi-stage stochastic programming. Fi-nancial decision making involves a sequence of decisionsto react to outcomes that evolve over time periodsand multi-stage stochastic programming introduces aproper strategy to cope with the complexity of thisissue in the SSCND problem [18]. The method wasapplied by Nickel et al. [15] to solve an SCND problemwith �nancial decisions and uncertainty assumptionfor demand and interest rate, where uncertainty waspresented by a set of scenarios. Despite the importanceof the integrity of �nancial and physical aspects inSCND problems, to the best of the authors' knowledge,the �nancial aspect has been completely ignored byresearches in the context of sustainable SCND. A listof the above-mentioned and some other studies in the�eld of sustainable supply chain is provided in Table 1.

To �ll the gap in the literature on SSCND, a com-prehensive multi-stage stochastic mixed-integer linearprogramming model for a real-life multi-period multi-product multi-objective closed-loop SSCND problemwith �nancial decisions and risk consideration subjectto investment return rate and demand uncertainty isproposed in this article. This is the �rst time that�nancial decisions are applied to the SSCND problemin a research study. Additionally, for the �rst time,an SSCND model is developed with all the above-mentioned features of multiple objectives, multipleproducts, multiple periods, risk measure, uncertaintyissue, �nancial decisions, and closed loop and all thethree dimensions of sustainable development operatingin a simultaneous manner are followed. The proposed

A.S. Mohammadi et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 377{395 379

Table 1. Sustainable Supply Clain Network Design futures in the body of literature.A

rtic

le

Dim

ensi

ons

Unce

rtai

nty

issu

e

Unce

rtai

nty

consi

der

atio

np

olic

y

Mult

i-p

erio

d

Mult

i-pro

duct

Mult

i-ob

ject

ive

Fin

anci

aldec

isio

n

Clo

sed-

loop

Fin

anci

alri

skm

easu

re

Dep

reci

atio

nra

te

Pishvaeeet al. [3]

Eco-Env-Soc � Possibilisticprogramming

� �Babazadehet al. [19]

Eco-Env � Possibilisticprogramming

� � �

Pishvaeeet al. [9]

Eco-Soc �Robust

possibilisticprogramming

�

Giarolaet al. [7]

Eco-Env �Two-stagestochastic

programming� �

Vermaet al. [8]

Eco-Env �Two-stagestochastic

programming

Guill�en-Gos�albezand Grossmann [10]

Eco-Env �Bi-criterion

stochastic non-convexMINLP

� � �

Amin andZhang [11]

Eco-Env �Scenario-based

stochasticprogramming

� � �

Ruiz-Femeniaet al. [12]

Eco-Env �Stochastic

multi-scenarioMILP

� � �

Balaman andSelim [20]

Eco-Env �Fuzzy Goal

Programming(FGP)

� � �

Pishvaee andRazmi [21]

Eco-Env � Possibilisticprogramming

� �

Pishvaeeet al. [22]

Eco-Env �Credibility-based

fuzzy mathematicalprogramming

�

Sa�ar andRazmi [23]

Eco-Env � Auxiliary crisp � � � �Sa�ar andRazmi [24]

Eco-Env � Auxiliary crisp � � � �Guillen-Gos�albez

and Grossmann [25]Eco-Env � Bi-criterion MINLP � � �

Mohammadiet al. [26]

Eco-Env �Mixed

possibilistic-stochasticprogramming

�

Zhalechianet al. [27]

Eco-Env-Soc �Stochastic-possibilistic

programming andmodi�ed game theory

� � � �

Shaw et al. [28] Eco-Env �Bender decompositionand chance constrait

programming


Table 1. Sustainable Supply Clain Network Design futures in the body of literature (continued).A

rtic

le

Dim

ensi

ons

Unce

rtai

nty

issu

e

Unce

rtai

nty

consi

der

atio

np

olic

y

Mult

i-p

erio

d

Mult

i-pro

duct

Mult

i-ob

ject

ive

Fin

anci

aldec

isio

n

Clo

sed-

loop

Fin

anci

alri

skm

easu

re

Dep

reci

atio

nra

te

Mohseni andPishvaee [29]

Eco-Env � Robustoptimization

�Mohammedet al. [30]

Eco-Env � Robust optimization � � �Ruimin et al. [31] Eco-Env � Robust optimization � � �

Golp̂�raet al. [32]

Eco-Env � Conditional Valueat Risk (CVaR)

�

model is adopted in designing a real plastic productionand recycling supply chain as a case study throughwhich the practical value of this research will be proved.

The rest of this paper is organized as follows.The real industrial problem is de�ned and illustratedin Section 2. The problem is formulated as a multi-objective multi-stage stochastic programming modelin Section 3. Section 4 is devoted to implementingand presenting the scenario path formulation method.Section 5 deals with the results of the computationalanalysis of the problem and addresses the value ofconsidering �nancial decisions. The value of the multi-stage stochastic problem is measured in Section 6 andthe study is concluded in Section 7.

2. Problem de�nition

In the last 60 years, plastic has become one of the mostpractical materials with a wide range of applications.In 2014, around 311 million tons of plastic wereproduced all over the world and 25.8 million tons ofpost-consumer plastics waste ended up in the wasteupstream only in the European Union (EU), while30.8% of the plastic wastes are still in the land�llsin the EU [33]. Chemically speaking, some reportsstate that plastic materials take hundreds of years tobreak down in a land�ll. In Iran, 17000 tons of plasticsare produced annually. Therefore, it can be deducedthat managing EOL of di�erent plastic products is avital issue, which can a�ect all the three dimensions ofsustainable development.

The logistics network discussed in this article,as illustrated in Figure 1, is formed based on a realIranian plastic production and recycling supply chainwith �ve echelons of production and recycling center,retailers, customers, collection centers, and land�llcenters. A new product is produced by recycling EOLproducts at di�erent production and recycling centersand then, shipped to retailers based on their demandand availability of the product. Some customers return

Figure 1. The underlying structure of the concernedsupply chain network .

EOL products to retailers and retailers send them tocollection centers. The recyclable EOL products areseparated and shipped to production and recyclingcenters and the remaining are sent to the land�ll center.Uncertainty is associated with demand and returnrate, and multi-period planning horizon is considered.The problem is about �nding the optimal decision ineach period for: location of facilities, production (orcollection) technology, investments to make, loans totake, and ow of products between facilities.

Each period is divided into two consecutive phasesof before and after knowing the demand and returnrate on investments [15]. Decisions made on locationof facilities, production technology, investment, andloans should be made in the �rst phase and decisionsregarding the ow of products between facilities in thesecond phase.

It is assumed that phase-one decisions can changefrom one period to another one. Retailers, customers,and the land�ll center are already �xed and locationdecisions are about production and recycling centers,and collection centers. In addition, it is assumed thatcustomers pay their debts at the ends of time periods.This assumption contributes to better conceiving the�nancial decisions and parameters.

Financial decisions are investment- and loan-related. Various investment alternatives can be con-


sidered for a corporate which is making decisions onthe SCND problem. Investments in stock market,bonds, real state, supply chain tangible assets, andsupply chain intangible assets are considered as thealternatives in the problem. In addition, deciding onhow to leverage �nancial power of a given corporateby taking loan is another strategic �nancial decisionconsidered in the problem. Diverse loans with di�erentinterest rates, payback times, and payback policies areamong the loan alternatives. Return On Investment(ROI) was implemented as an index to evaluate �nan-cial decisions in [15]. In this study, a target was setfor ROI and its downside risk was minimized. Thispolicy is adopted in this study to evaluate and controlthe �nancial performance of the subject. Constructionand equipment depreciation rate is another �nancialparameter in uencing ROI. This parameter was notconsidered in [15] and has not been a matter of concernin the SSCND literature. Nevertheless, depreciationrate of facilities is an important parameter that cana�ect economic performance of supply chain in longterm.

Uncertainty is associated with demand and returnrates of di�erent investment alternatives. A set ofevents are considered in assessing the uncertainty ofstochastic parameters, where each event consists ofdemand sub-events and return rate sub-events (de�nedas an event that declares only one of the stochasticparameters), which are combined in one event anddemonstrate both stochastic parameters in a simulta-neous manner. For more information about scenariocreation, interested readers can refer to [34].

Each time period is divided into two phases inwhich decisions are made separately. There exist aproblem and an Objective Function (OF) in each phasewith the objective of achieving reasonable balanceamong the three dimensions of sustainability. Decisionson investments, locations, and loans should be madein the �rst phase and decision on shipment should bemade in the second phase.

2.1. Environmental Impact (EI)To move towards sustainable design in supply chainnetworks, it is necessary to implement methods andapply tools to measure EI in di�erent SCND decisions.Each product has di�erent EIs in various stages of itslife cycle. Accordingly, appropriate frameworks shouldbe applied to estimating and assessing the EIs relatedto the whole life cycle of products. Life Cycle Assess-ment (LCA) is a popular component for quantifyingand assessing the EI of a product [35]. In order toquantify and assess the EI of products, an LCA-baseddamage-oriented method named Eco-indicator 99 [36]is adopted in this study. User friendly units namedEco-indicators, which enable researchers to aggregateand calculate LCA results in an easily understandable

manner, are introduced in Eco-indicator 99. Thismethod comprises three damage categories of humanhealth, ecosystem quality, and resources [37].

2.2. Social Impact (SI) assessmentSR is a multi-disciplinary and multi-stakeholder phe-nomenon and its complex nature and extensive scopemake its measurement di�cult. However, during thepast years, many e�orts have been made to supportplanning and implementing corporate SR. A numberof standards such as ISO 26000 [38], SA 8000 [39],and AA 1000 [40] have been developed to provide acomprehensive framework for implementing SR. TheInternational Guidance Standard on SR-ISO 26000 [38]has been introduced by the ISO as an inclusive frame-work for standard implementation of SR in �rms andcorporations. ISO 2600 classi�es SR issues into sevencore subjects:

1. Organizational governance;2. Human rights;3. Labor practices;4. The environment;5. Fair operating practices;6. Consumer issues;7. Community involvement and development.

In this study, SR measures with the followingfeatures are selected:

1. Relevant to SCND decisions;2. Simply quanti�ed;3. Compatible with the social issues of the region of

the case study.

Accordingly, �rst, stakeholder categories of SC areidenti�ed. Next, the SI of supply chain on eachstakeholder category is determined based on their socialpriorities. Finally, some quantitative measures are as-signed to each SI. The information about stakeholders,their concerned SI, and relevant quantitative measuresis presented in Table 2.

2.3. Assumptions, objectives, and constraintsBased on the above-mentioned problems, the proposedmodel follows the following assumptions:

� The location decisions can change from one periodto another one;

� Retailers, customers, and land�ll centers are already�xed;

� Customers pay their debts at the ends of timeperiods;

� Meeting the whole demand of customers is notnecessary;


Table 2. Stakeholders, their concerned Social Impacts (SIs), and relevant quantitative measures.

Stakeholder Concerned SI Relevant quantitative measure(s)Workers (production andcollection workers in additionto transportation workers)

Health and safety The average number of lost days caused bydamages-average annual road accidents

Local inhabitants Delocalization, unemploymentNumber of created job opportunities-importance rate of region based ondevelopment, unemployment rate

Consumers Health and safety The fraction of potentially harmful products

Governments Delocalization, unemployment,economic development

Number of created job opportunities-importance rate of region based ondevelopment, unemployment rate

� There is no ow between facilities of the sameechelon.

The main objectives of this model consist of:

- Maximization of total revenue and servicelevel = Revenue of production and recycling centers+ Revenue of collection centers + Revenue of otherinvestments { Cost of loans { Risk of falling belowthe target ROI + Customer service level;

- Minimization of EI = EIs of production + EIs ofshipment + EIs of facility establishment;

- Maximization of SR = Introduced job opportuni-ties + Value of local development { Consumer risk {Damage to health of workers.

To accomplish the above-mentioned objectives,decision makers face the following constraints:

� Flow balance at network facilities;� Meeting capacity;� Meeting customer demand by considering service

level;� Non-negativity and binary constraints on decision

variables;� Considering the budget available at the beginning of

each period.

3. Model formulation

The indices, parameters, and variables applied to for-mulating the concerned SSCND problem are describedbelow:

Indicesi Index of potential location for

production centerj Index of retailer

k Index of potential location forcollection center

t Index of periods in the planninghorizon, t = f1; 2; � � � ; Tg

p Index of productsm Index of potential investments (indirect

in the supply chain and alternativeinvestments)

b Index of potential loansq Index of technology

Technical parameters

Kqi Capacity of production center i with

technology qKCqk Capacity of collection center k with

technology q�qpi Unit capacity consumption factor

of product p by technology q atproduction center i

"qpk Unit capacity consumption factor ofproduct p by technology q at collectioncenter k

�j Weight (importance) of retailer jDFp Maximum downfall rate of collected

product p during the recycling process(di�erence between the weights of thecollected waste material and recycledproduct due to washing of the pollutionand impurity of waste material)

MFp Minimum downfall rate of collectedproduct p during the recycling process

Economic (cost and �nancial) parameters

Ctiq Fixed cost of opening productioncenter i in period t with technology q


Qtkq Fixed cost of opening collection centerk in period t with technology q

V tijp Cost for shipping one unit of productp from production center p to retailerj in period t

V ctjkp Cost for shipping one unit of wastedproduct p from retailer j to collectioncenter k in period t

V rtkip Cost for shipping one unit of wastedproduct p from collection center k toproduction center i in period t

Rtijp Unitary revenue of product p atproduction center i shipped to retailerj in period t (i.e., selling price minuspurchasing and operation costs)

Ztkip Unitary revenue of collected product pwastage at collection center k shippedto production center i in period t (i.e.,selling price minus purchasing andcollection costs)

�tb Interest rate of loan b payback at theend of period t. This interest rate isalways de�ned for all periods. If nointerest rate arises in a period, it is setto zero

ROI Target ROI

�tm Rate of return on an investment mpaid at the end of period t

BDt Exogenous budget available at thebeginning of period t

~iq Depreciation rate related to productioncenter i with technology q in eachperiod

kq Depreciation rate related to collectioncenter k with technology q in eachperiod

& Weight of the downside risk at the OF

Environmental parametersenqp EI of producing one unit of product p

with technology qemp

ij EI of shipping one unit of product pfrom recycling center i to retailer j

expjk EI of shipping one unit of used productp from retailer j to collection center k

eypki EI of shipping one unit of collectedproduct p from collection center k torecycling center i

ecqkp EI of collecting one unit of wastedproduct p at collection center k withtechnology q

esqi EI associated with establishingrecycling center i with technology q

etqk EI associated with establishingcollection center k with technology q

Social parametersuni Unemployment rate at location iupk Unemployment rate at location kjoqi Number of introduced job opportunities

if a recycling center is opened atlocation i with technology q

jpqk Number of introduced job opportunitiesif a collection center is opened atlocation k with technology q

rdi

8>><>>:1 importance rate of location i if

its region is developed1.3 important rate of location i if

its region is undeveloped

rvk

8>><>>:1 importance rate of location k if

its region is developed1.3 important rate of location k if

its region is undeveloped

lwqi The average number of lost days ineach period due to damages during theproducing at production center i withtechnology q

lmqk The average number of lost days in

each period due to damages during thecollection at collection center k withtechnology q

raij The average of annual vehicle accidentsoccurring on the path from recyclingcenter i to retailer j

rtjk The average of annual vehicle accidentsoccurring on the path from retailer jto collection center k

rcki The average of annual vehicle accidentsoccurring on the path from collectioncenter k to recycling center i

flqp The fraction of potentially harmfulproducts p which harm the consumerwhen technology q is applied

ws The weight given to objective SI interms of health and safety of theworker

wj The weight given to objectiveSI in terms of employment anddelocalization

we The weight given to objective SI interms of economic development

wc The weight given to objective SI interms of customer health and safety


Stochastic parameters (technical andeconomic)

!t Event in period t

!0 Current state of naturet Random variable representing the

events that may occur in period t

0 Normal state in the beginning of theplanning horizon

p(t = !t) Probability of event !t

�tm(t) Rate of return on an investment mpaid at the end of period t

�tm = �tm(!t) One realization of �tm(t)

DP tjp(t) Demand for product p at retailer j in

period t

DP tjp = DP tjp(!t)One realization of DP tjp(t)

Financial decision variablesRtm Amount of money spent in the

available investment m in period t

Ltb Amount of money obtained from loanb in period t

DR Downside RiskSLj Service level for retailer j

Physical decision variables

U tiq =

8>><>>:1 if productions center i with

technology q is set operatingin period t

0 otherwise

UCtKq =

8>><>>:1 if collection center k with

technology q is set operatingin period t

0 otherwise

Xtijp Amount of product p shipped from

production center i to retailer j inperiod t

U tjkp Amount of returned materials pshipped from retailer j to collectioncenter k in period t

M tkip Amount of collected materials for

product p shipped from collectingcenter k to production center i inperiod t

In order to formulate the multi-stage mixed-integer programming model for the SSCND problem,�rst, each of the periods is divided into two phases andthen, di�erent problems are introduced for di�erentperiods (stages). Accordingly, the beginning of eachtime period is denoted by t� and the end by t+.

Beginning of period 1As mentioned in Section 2, at the beginning of eachtime period, it is necessary to make decision aboutfacility locations, investments, and loans. Problemobjectives consist of:

1. Maximizing expected pro�t at the end of period oneand in period two;

2. Minimizing EI of selected facilities at SCN;3. Maximizing SI of facility decisions.

max Q�1 =X!1

P�1 = !1� �Q+1 �U1:UC1:DP 1�

+X!1

P�1 = !1� �Q�1(�1:R1:L1);

(1)

min N�1 =Xi

Xq

u1iqes

qi +

Xi

Xq

uc1kqetqk

+we

Xi

Xq

u1iqrdi+

Xk

Xq

uc1kqrvk

!

�ws X

i

Xq

u1iqlw

qi +Xk

Xq

uc1kqlmqk

!;(2)

s.t.:

BD1�Xi

Xq

C1iqU

1iq �

Xk

Xq

Q1kqUC

1kq �

Xm

R1M

+Xb

L1b � 0; (3)

U1iq:UC

1kq 2 f0; 1g 8 i:k:q; (4)

rdi:rvk 2 f1; 1:3g 8 i:k; (5)

uni:upk 2 [0; 1] 8 i:k; (6)

R1M :L

1b � 0 8 M:b: (7)

The expected pro�t and SI of decisions are respectivelymaximized by OFs (1) and the third part of OF given inEq. (2); the total EI is minimized by the �rst part of OFgiven in Eq. (2). Budget availability for the �rst stageof the problem is assessed by Constraint (3). Availablebudget in addition to the loans cannot be lower thaninvestments and opening cost of facilities. Binaryand non-negativity restrictions on decision variables,which should be made at the beginning of the �rstperiod, are enforced by Constraints (4), (5), and(6), respectively, and importance rate of locations ispresented by Constraint (7).


End of period 1After making decisions about facility locations, invest-ments, and loans in the beginning of the �rst period,and determining the demand at the end of the period,decisions on shipment of materials among facilitiesshould be made.

max Q+1 =Xi

Xj

Xp

Xk

((R1ijp � V 1

ijp)X1ijp

+�Z1kip�V r1

kip��U1jkp:V c

1jkp��M1kip)

� (1 +ROI)T�1; (8)

min N+1 =Xi

Xj

Xq

(enqp + empij)X

1ijp

+Xj

Xk

Xp

expjkU1jkp

+Xi

Xk

Xp

(eypki + ecqkp) �M1kip; (9)

s.t.:Xp

�qpi �Xj

X1ijp � Kq

i � U1iq 8 q:i; (10)

Xp

"qpk �Xi

M1kip � KCqk � UC1

kq 8 q:k; (11)

Xi

X1ijp � DP 1

jp 8 j:p; (12)

Xk

M1kip(1�MFp)�X

j

X1ijp�

Xk

M1kip(1�DFp)

8 i: p; (13)

X1ijp:M

1kip � 0 8 i:j:p:k; (14)

MFp:DFp 2 [0; 1] 8 p: (15)

OF (8) maximizes revenue of collection centers andrecycling centers in the �rst period as well as multiplerevenues of SCN in the target ROI in order to considerROI of the earned revenue in future periods. The EIis minimized by the �rst part of given in Eq. (9) andSI of shipment decisions is maximized by the thirdpart of OF given in Eq. (9). Constraints (10) and(11) are related to capacity constraints of recyclingcenters and collection centers. Surplus supply toretailers is prevented through Constraint (12). Theamount of the ow of materials among collection andrecycling centers is balanced through Inequality (13)by considering downfall rate of collected materials atrecycling centers. Collected plastics downfall weightis the result of wiping impurities during the washingprocess at recycling centers with an important e�ect

on SC planning of plastic recycling industry. The non-negativity restriction on shipment decision variables isenforced by Constraint (14) and the permitted valuefor downfall rates is indicated by Constraint (15).

Beginning of period t 2 f2; � � � ; T � 1gAt the beginning of t 2 f2; � � � ; T � 1g, decisionsregarding locations, investments, and loans shouldbe reconsidered. Consequently, the following sub-problem must be solved at the beginning of periodt 2 f2; � � � ; T � 1g.

max Q�t =X!t

P (t = !t) �Q+t �U t:UCt:DP t�+X!t

P (t=!t) �Q�(t+1)(�t:Rt:Lt);(16)

min N�t =Xi

Xq

utiqesqi +

Xi

Xq

uctkqetqk; (17)

max S�t=wj

Xi

Xq

utiqjoqiuni

+Xk

Xq

uctkqjpqkupk

!

+we

Xi

Xq

utiqrdi+Xk

Xq

uctkqrvk

!

�ws X

i

Xq

utiqlwqi +Xk

Xq

uctkqlmqk

!:

(18)

s.t.:

BDt �Xi

Xq

CtiqUtiq �

Xk

Xq

QtkqUCtkq �

Xm

RtM

+Xb

Ltb+t�1Xt=1

Xm

�tm:Rtm�Xb

�tb:Ltb

!�0; (19)

U tiq:UCtkq 2 f0; 1g 8 i:k:q; (20)

Ltb:Rtm � 0 8 b:m:t: (21)

The expected pro�t and SI of decisions are maximizedby OFs (16) and (18). OF (17) is applied to minimizingthe total EI. In Constraint (19), revenue of the previousperiods is added to the available budget and theamount of the loans that should be paid back in periodt is subtracted from the available budget. Non-negativeand binary nature of decision variables at the beginningof period t are presented by Constraints (20) and (21),respectively.


End of period t 2 f2; � � � ; T � 1gmax Q+t=

Xi

Xj

Xp

Xk

((Rtijp � V tijp)Xtijp

+�Ztkip�V rtkip��U tjkp:V ctjkp��M t

kip)

� (1 +ROI)T�t; (22)

min N+t =Xi

Xj

Xq

(enqp + empij)X

tijp

+Xj

Xk

Xp

expjkUtjkp

+Xi

Xk

Xp

(eypki + ecqkp) �M tkip; (23)

max S+t =� ws0@X

i

Xj

Xp

Xtijpraij

+Xj

Xk

Xp

U tkqrtjk

+Xi

Xk

Xp

M tkiprcki

!

� wc0@X

i

Xj

Xp

Xtijpfl

qp

1A ; (24)

s.t.:Xp

�qpi �Xj

Xtijp � Kq

ip � U tiq 8 q:i; (25)

Xp

"qpk �Xi

M tkip � KCqkp � UCtkq 8 q:k; (26)

Xi

Xtijp � DP tjp 8 j:p; (27)

Xk

M tkip(1�MFp)�X

j

Xtijp�

Xk

M tkip(1�DFp)

8 i:p; (28)

Xtijp:M

tkip � 0 8 i:j:p:k: (29)

OF (22) is used to maximize revenue of collectioncenters and recycling centers in period t as well asmultiple revenues of SCN in the target ROI in order toconsider ROI of the earned revenue in future periods.EI is minimized by OF (23) and OF (24) is appliedto maximizing SI of shipment decisions. Constraints(25) and (26) are related to capacity constraints ofrecycling centers and collection centers, respectively.

Surplus supply to retailers is prevented by Constraint(27). The amount of ow of materials between col-lection centers and recycling centers is balanced byInequality (28) considering downfall rate of collectedmaterials at recycling centers. The non-negativityrestrictions on shipment decision variables are enforcedby Constraint (29).

Beginning of period TThe beginning of this period is formulated similarly tothat of the previous periods:

max Q�T =X!T

P (T =!T )�Q+T (UT :UCT :DPT );(30)

min N�T =Xi

Xq

uTiqesqi +

Xi

Xq

ucTkqetqk; (31)

max S�T=wj

Xi

Xq

uTiqjoqiuni

+Xk

Xq

ucTkqjpqkupk

!

+we

Xi

Xq

uTiqrdi+Xk

Xq

ucTkqrvk

!

�ws X

i

Xq

uTiqlwqi +Xk

Xq

ucTkqlmqk

!;

(32)

s.t.:

BDT�Xi

Xq

CTiqUTiq �

Xk

Xq

QTkqUCTkq �

Xm

RTm

+Xb

LTb +T�1Xt=1

Xm

�T�1m �Rtm�

Xb

�T�1b �Ltb

!�0;

(33)

UTiq :UCTkq 2 f0; 1g 8 i:k:q; (34)

LTb :RTm � 0 8 b:m:t: (35)

Here, the structure of sub-problems is still the same.The expected pro�t and SI of the decisions that shouldbe made at the beginning of period T are maximizedby OFs (30) and (32), respectively, and the total EIof these decisions is minimized through OF (31). InConstraint (33) the revenue of the previous periodsis added to the available budget and the amountof loans that should be paid back in period t issubtracted from the available budget. Non-negativeand binary nature of decision variables at the beginningof period T are presented by Constraints (34) and (35),respectively.


DR � 1�

Xt

Xm

�Tm:RTm �

Xb

�Tb :LTb

!+Xi

Xj

Xp

Xp

((Rtijp � V tijp) �Xtijp + (Ztkip � V rtkip

�(U tjkp:V ctjkp)):M

tkip)

!� (1 +ROI)T�t�X

i

Xq

(~iq) � UTiq � CTiq �Xk

Xq

( kq):UCTkq:QTkqP

tBGt:(1 +ROI)T�t+1 : (43)

Box I

End of period TThe following problem is formulated for the end of theplanning horizon:

max Q+T =Xi

Xj

Xp

Xk

��RTijp � V Tijp�XT

ijp

+(ZTkip�V rTkip�(UTjkp�V cTjkp))MTkip�

+Xj

�j � SLj � &DR

+TXt=1

Xm

�Tm �RTm �Xb

�Tb � LTb!

�Xi

Xq

(~iq) � UTiq � CTiq

�Xk

Xq

( qk) � UCTkq �QTkq; (36)

min N+T =Xi

Xj

Xq

(enqp + empij)X

Tijp

+Xj

Xk

Xp

expjkUTjkp

+Xi

Xk

Xp

(eypki+ ecqkp)�MTkip; (37)

max S+T =� ws0@X

i

Xj

Xp

XTijpraij

+Xj

Xk

Xp

UTkqrtjk

+Xi

Xk

Xp

MTkiprcki

!

� wc0@X

i

Xj

Xp

XTijpfl

qp

1A ; (38)

s.t.:Xp

�qpi �Xj

XTijp � Kq

ip � UTiq 8 q:i; (39)

Xp

"qpk �Xi

MTkip � KCqkp � UCTkq 8 q:k; (40)

Xi

XTijp � DPTjp 8 j:p; (41)

Xk

MTkip(1�MFp)�X

j

XTijp�

Xk

MTkip(1�DFp)

8 i:p; (42)

Eq. (43) is shown in Box I.Xi

Xt

Xp

Xtijp � SLj �

Xt

Xp

DP tjp

8 j; (44)

SLj 2 [0; 1] 8 j; (45)

DR � 0: (46)

In OF (36), the following extra terms are consideredin comparison with the end of the previous periods.For this purpose, �rst, the depreciation rates of theproduction and collection centers are subtracted fromtotal revenue; second, the service level is maximized;third, the downside risk is minimized; and forth, thetotal loans payback and total investment revenue areconsidered. The EI and SI of OFs are similar tothose in the previous periods. Inequalities (39){(42)represent the production centers capacity, collectioncenters capacity, demand, and downfall constraints,respectively. The downside risk of the target ROI,which is minimized in OF (36), is calculated throughInequality (43). Finally, the service level for each cus-tomer, which is maximized in OF (36), is determinedby Constraint (44).


4. Solution approach

The above-mentioned formulation of SSCND with �-nancial decisions problem explicitly pertains to theconcept and multi-stage structure of the problem.Analysis of the interactions among variables provesthat the decisions made on locations, investments,loans, and shipments are connected to each other anda�ect service level and downside risk at the end of thetime horizon.

The problem was simpli�ed in the model in theprevious section. However, for solving and implement-ing the problem, a more compact model compatiblewith the general solver is needed. The path formulationmethod for solving a multi-stage SCND problem wasintroduced by Nickel et al. [15], in which the sequenceof events was de�ned as a scenario; then, the pathand sub-paths for each scenario were determined. Thefollowing new notation is introduced before presentingthe path formulation model:

Scenario path formula- St = 1 � 2 � � � � � t: The set for the potential

sequence of events up to period t;

- st 2 St = (!0 � !1 � � � � � !t): Path of events fromthe root node to one particular node in period t;

- s0: Root node;

- sT : Path of the events oriented from the root nodeto a leaf node (a scenario);

- pathst = fs0:s1 � � � stg: Set of all sub-paths contain-ing parts of path st;

- P (St = st) =tQt=1

p(t = !t): The probability that

the sequence of the events passes through path st.

The problem is reformulated as follows:

max Q =Xt

Xst2St

P (St = st)

�"X

i

Xj

Xp

Xk

((Rtijp

� V tijp)Xtijp(s

t)) + (Ztkip � V rtkip

� (U tjkp(st) � V ctjkp)) �M t

kip(st))

#+X

sT2STP (ST = sT ) �

"Xj

�j

� SLj(sT )� & �DR(sT )

+Xt

Xst�12pathsT

Xm

�tm(sT )

�Rtm(st�1)�Xb

�tb(sT ) � Ltb(st�1)

!�X

i

Xq

(~iq) � UTiq(st�1) � CTiq

�Xk

Xq

( kq) � UCTkq(st�1) �QTkq�: (47)

min N =Xt

Xst2St

P (St = st)

� hXq

Xp

Xi

Xj

(enqp � empij)X

tijp(s

t)

+Xj

Xk

Xp

enpjk � U tjkp(st)

+Xq

Xp

Xk

Xi

(eypki+ecqkp)�M t

kip(st)

#+Xt

Xst2St

P (St = st)

�"X

i

Xq

UTiq � esqi

+Xk

Xq

UCTkq � etqk#; (48)

max S =Xt

Xst2St

P (St = st)

�24�ws0@X

i

Xj

Xp

Xtijp(s

t) � raij

+Xj

Xk

Xp

U tjkp(st) � rtjk

+Xk

Xi

Xp

M tkip(s

t) � rcki!

�wc0@X

i

Xj

Xp

Xq

Xtijp(s

t) � flqp1A35

+Xt

Xst2St

P (St = st)


�"wj

Xi

Xq

U tiq(st�1) � joqi � uni

+Xk

Xq

UCtkq(st�1) � jpqk � upk

!

+ we

Xi

Xq

U tiq(st�1) � rdi

+Xk

Xq

UCtkq(st�1) � rvk

!

� ws X

i

Xq

U tiq(st�1) � lwqi

+Xk

Xq

UCtkq(st�1) � lmq

k

!#; (49)

s.t.:

BD1 �Xi

Xq

C1iqU

1iq(s

0)�Xk

Xq

Q1kqUC

1kq(s

0)

�Xm

R1M (s0) +

Xb

L1b(s

0) � 0; (50)

BDt �Xi

Xq

CtiqUtiq(s

t�1)�Xk

Xq

QtkqUCtkq(s

t�1)

�Xm

RtM (st�1) +Xb

Ltb(st�1)

+t�1Xt=1

Xm

�tm �Rtm(st�1)�Xb

�tb � Ltb(st�1)

!� 0; (51)X

p

�qpi�Xi

Xtijp(s

t)�Kqi �U tiq(st�1) 8 q:j; (52)

Xp

"qpk �Xi

M tkip(s

t) � KCqk � UCtkq(st�1)

8 q:k; (53)

Xi

Xtijp(s

t) � DP tjp(st) 8 j:p; (54)

Xk

M tkip(1�MFp)�X

j

Xtijp�

Xk

M tkip(1�DFp)

8 i:p; (55)

Eq. (56) is shown in Box II.Xi

Xt

Xp

Xtijp(s

t) � SLj �Xt

Xp

DP tjp(st)

8 j:st; (57)

U1iq:UC

1kq 2 f0; 1g; (58)

Xtijp(s

t):M tkip(s

t):DP tjp(st):Rtm(st�1):Ltb(s

t�1)

:DR(sT ) � 0 8 i:j:p:k:m:b; (59)

SLj(sT ) 2 [0; 1] 8 j: (60)

The concept of the above path formulation model iscompletely based on the multi-period, multi-productCL SSCND problem explained in Section 3, in whichevery combination of events is considered as a scenario.Here, every scenario consists of di�erent sequences ofevents (paths). Probability of each path in a scenariois calculated by multiplying probability of the eventsin a path. Finally, the OFs are computed based on theprobabilities of scenarios (Eqs. (44){(46)). An exampleof the scenario trees with 3 periods and 2 possibleevents in each period is depicted in Figure 2. Thespeci�ed lines in red color demonstrate a scenario whichencompasses event 2 in period 1, event 1 in period 2,and event 1 in period 3.

The SSCND problem is multi-objective in nature.To solve the multi-objective programming models,there exist many methods. In this article, "-constraintmethod is adopted to deal with the multi-objectivenature of the SSCND problem. Several versions ofthe "-constraint method have been proposed in thebody of literature. Here, the augmented "-constraint(AUGMECON) method proposed by Mavrotas [41] isadopted. In comparison with other versions of the "-constraint method, AUGMECON is able to:

DR � 1 �

XsT

Xt

�Xm�Tm(sT ) � RTm(st�1) �X

b�Tb (sT ) � LTb (st�1)

�+Xi

Xj

Xp

Xp

(�Rtijp � V tijp

� �Xtijp(st) +�Ztkip � V rtkip

��Utjkp:V c

tjkp

��Mtkip(st))

!:(1 + ROI)T�t �X

i

Xq

(~iq) � UTiq(st�1) � CTiq �Xk

Xq

( kq) � UCTkq(st�1) � QTkqPtBGt � (1 + ROI)T�t+1

: (56)

Box II


Figure 2. An example of the scenario trees.

1. Guarantee e�ciency of the obtained solution;

2. Calculate the range of the OFs over the e�cient set;

3. O�er acceptable solution time in the cases withseveral objectives [41].

In order to solve the problem by the above-mentioned method, �rst, the economic objective pre-sented in OF (47) is considered as the main objectiveand OFs (48) and (49) are expressed in the form ofinequality constraints. Then, environmental OF isoptimized by adding economic OF = Q� as an equalityconstraint and OF (49) as an inequality constraint.Subsequently, the social OF is optimized by consideringeconomic OF = Q� and environmental OF = N�as constraints. Consequently, payo� matrix of theproblem is employed as a tool for calculating the rangesof OFs. In the next step, economic OF is taken as theone to be optimized and the ranges of environmentaland social OFs are separated into the same intervals.Based on the de�ned intervals, constraints related toenvironmental and social OFs are taken into accountfor de�ning some sub-problems. Therefore, the Paretoset is obtained by solving each sub-problem. In orderto avoid ine�ciency of the "-constraint method, slackvariable technique is deployed based on augmented "-constraint method [41]. Finally, the decision makerselects the most desired solution among all the derivednon-dominated solutions.

5. Implementation and evaluation

The validity of developed model and the functionalityof the solution method are assessed through the datafor the considered case study. The subject �rm here has20 customers and 10 candidate locations are consideredfor production and collection centers. This �rm canproduce two products with two di�erent technologies

Figure 3. Comparison between service levels in themodels with and without �nancial decisions.

and each technology has a di�erent depreciation rate.The �rm has 6 investment alternatives with di�erentrates of return and di�erent variances. Besides theavailable exogenous budget, the manager of the �rmhas the opportunity to give 5 di�erent loans withdi�erent payback times and payback types.

The proposed model is coded and solved throughIBM ILOG CPLEX 12.1. A time limit of 3600 secondsis considered in this process. The results are tabulatedin Table 3.

In order to evaluate e�ectiveness of considering�nancial decisions in the SSCND problem, the pro-posed model is solved without considering �nancialdecisions. The results for the problem solved withouttaking �nancial decisions are tabulated in Table 4.

Tables 3 and 4 con�rm that by solving the modelwith �nancial decisions, both the customer servicelevel and OF value increase, indicating that �nancialleveraging with loans and considering other investmentalternatives besides investment in SCN can improvethe physical and �nancial performance of SCN. Con-sidering �nancial decision in the studied �rm increasesservice level by 6/531% and OF value by 12/56%. Thecomparison between the amounts of service level in the�nancial and non-�nancial models is given in Figure 3.

The above-mentioned results have been achievedby considering �ve loan alternatives, which can beadded to the available budget of investors. A sensitivityanalysis has been run on the number of available loans.Decreasing the number of available loans reduces the�nancial leveraging power of investors. The fact thatmore �nancial leverage increases the economic value ofthis model is illustrated in Figure 4.

By taking advantage of the available loans, in-


Table 3. Result for the problem solved by �nancial decisions.

Number andregion ofcustomers

Service level ofcustomer during thewhole time horizon

Weighted average ofthe service level

of the whole system

Value of the economicOFa at the end ofthe �nal period

Downside riskrelated to the

value of the OF1=Isfahan 0.87

0.7487 465868 0.15

2=Isfahan 0.893=Isfahan 0.704=Isfahan 0.665=Isfahan 1.006=Isfahan 0.707=Isfahan 1.008=Tehran 1.009=Hormozgan 0.1010=Azerbaijan 0.5011=Isfahan 0.6512=Tehran 1.0013=Isfahan 0.9014=Isfahan 0.7015=Markazi 0.6316=Khoozestan 0.9017=Isfahan 0.7618=Fars 0.5019=Khorasan 0.6020=Yazd 0.63

aOF: Objective Function.

Table 4. Result for the problem solved without �nancial decisions.

Number andregion ofcustomers

Service level ofcustomer during thewhole time horizon

Weighted average ofthe service level ofthe whole system

Value of the economicOFa at the end ofthe �nal period

Downside riskrelated to the

value of the OF1=Isfahan 0.70

0.7028 413879 0.12

2=Isfahan 0.753=Isfahan 0.634=Isfahan 0.635=Isfahan 0.956=Isfahan 0.707=Isfahan 0.978=Tehran 0.999=Hormozgan 0.0910=Azerbaijan 0.5011=Isfahan 0.6012=Tehran 1.0013=Isfahan 0.8914=Isfahan 0.6515=Markazi 0.5916=Khoozestan 0.8517=Isfahan 0.7018=Fars 0.4519=Khorasan 0.5820=Yazd 0.59



Table 5. Sensitivity analysis of the number of available loans.

Number ofavailable loans

Weighted average of the servicelevel of the whole system

Value of the economic OFa atthe end of the �nal period

0 0.7197 4425751 0.7285 4493152 0.7359 4547733 0.7419 4593674 0.7464 4635395 0.7487 465868


Figure 4. E�ect of available loans on economic ObjectiveFunction (OF).

vestors can increase the number of facilities, henceraising the amounts of production and sale. In theproposed model, the advantage of taking loans isimproving the economic value as far as the pro�tgenerated by the sale rises and is su�cient to pay backthe loans and their interest. The fact that consideringall the available �ve loans improves the economic OFby 5.26% and service level of the whole system by 4%is tabulated in Table 5.

In general, the above-mentioned tables and �guresapprove e�ectiveness of considering �nancial decisionsin SSCND problem. Considering other investmentalternatives in addition to SSCN investments providesinvestors with an overall view to expand their choices.Moreover, the possibility of �nancial leveraging bygetting loans empowers the �rms with respect to their�nancial status. As a result, investors become able toincrease pro�tability of their decisions regarding theSSCND problem.

6. The relevance of applying a stochasticapproach

When uncertainty is considered in an optimizationmodel, the important issue is to assess its superiorityover deterministic methods. Relative Value of Multi-stage Stochastic Approach (RVMSA) is a measurethat calculates this relevance. RVMSA examinesthe importance of achieving perfect information onstochastic parameters [42] through measuring the dis-

tance between stochastic and deterministic values ofthe problem and dividing the yield distance into thedeterministic value of the problem. The result of thisdivision examines the e�ectiveness of applying multi-stage stochastic approach.

In order to compute RVMSA, the value of thedeterministic problem should be calculated, which isobtained through substituting all random variableswith their expected values [15]. To accomplishing this,�tm(sT ) is substituted with E[�tm(sT )] and DP tjp(sT ) issubstituted with E[DP tjp(sT )].

To analyze the performance of this multi-stagestochastic approach in the context of the introducedproblem, the deterministic problem value (QDET ) iscomputed for the subject �rm. Here, the RVMSA ismeasured as follows:

RVMSA =QSTO �QDET

QDET=

465868� 441163441163

= 0:056:

The result of RVMSA measurement indicates thatsolving the problem through this multi-stage stochasticapproach can improve supply chain performance in theproblem time horizon by 5.6% in terms of the OF value.This con�rms e�ectiveness of implementing the multi-stage stochastic approach in the SSCND problem with�nancial decisions.

7. Conclusions

In this study, integration of physical and �nancialdecisions in Sustainable Supply Chain Network De-sign (SSCND) problem with uncertainty issue wasfacilitated by implementing a multi-stage stochasticapproach. The main objectives of the proposed multi-objective model consisted of:

1. Maximizing total revenue, maximizing service levelto customers, and minimizing deviation from targetReturn On Investment (ROI);

2. Minimizing Environmental Impact (EI);


3. Maximizing social bene�ts.

In addition to general decisions made on locationand allocation, �nancial decisions were of concern.Uncertainty was considered in demand and investmentrate of return and in order to cope with the uncertainty,a mixed-integer multi-stage stochastic programmingformulation was implemented. The applicability of themodel was tested by the case study of a real plasticrecycling company located in Iran. "-constraint andpath-formulation methods were adopted for handlingmulti-objectiveness and stochastic nature of the prob-lem. Computational results indicated that consider-ing the �nancial decisions improved service level andOF value. Moreover, sensitivity analysis proved thebene�ts of considering loan alternatives in such prob-lems. Loan consideration assists managers to leveragetheir �nancial power. Furthermore, Relative Valueof Multi-stage Stochastic Approach (RVMSA) indexwas used to assess the value of implementing multi-stage stochastic approach and the results indicated thatstochastic approach outperformed the deterministicapproach.

The results of this paper can be applied to otherindustries with closed-loop SC structure, such as petro-chemical, electrical, etc. The proposed model can beextended in future studies by making improvement inits di�erent aspects. For example, future research canbe aimed at implementing other policies for coping withuncertainty and analyzing performance of di�erentpolicies. Also, it is necessary to evaluate the value ofthe stochastic approach for social and environmentalOFs.

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Biographies

Amir Salar Mohammadi accomplished his BSc inIndustrial Engineering at Azad University of NajafAbad, Isfahan, Iran, in 2009 and MSc in IndustrialManagement at Shahid Beheshti University, Tehran,Iran in 2011. Now, he is working as a PhD candidate atShahid Beheshti University, Tehran, Iran. His researchinterests are supply chain management, optimizationunder uncertainty, and �nancial engineering.


Akbar Alemtabriz is a Professor in the Managementand Accounting Faculty at Shahid Beheshti University,Tehran, Iran. He received his PhD in Managementfrom Gazi University, Ankara, Turkey, in 1989. Mostof his recent studies have focused on decision making,multi-objective optimization under uncertainty, andsupply chain management.

Mir Saman Pishvaee received his PhD in IndustrialEngineering from University of Tehran and now, he isAssistant Professor at Iran University of Science andTechnology (IUST). He has published many papersin various journals such as Omega, TransportationResearch: Part E (TR-E), Computers & OperationsResearch (COR), and Computers & Industrial Engi-neering (CAIE) as well as several book chapters underSpringer-Verlag in the area of supply chain manage-

ment. His research areas are supply chain management,robust optimization, and system dynamics.

Mostafa Zandieh accomplished his BSc in IndustrialEngineering at Amirkabir University of Technology,Tehran, Iran, in 1998 and MSc in the same �eldat Sharif University of Technology, Tehran, Iran, in2000. He also obtained his PhD in Industrial En-gineering from Amirkabir University of Technology,Tehran, Iran, in 2006. Currently, he is an Asso-ciate Professor in the Industrial Management Depart-ment of Shahid Beheshti University, Tehran, Iran.His research interests are production planning andscheduling, �nancial engineering, quality engineering,applied operations research, simulation, and arti�cialintelligence techniques in the areas of manufacturingsystems design.

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