Sustainable Supply Chain Design using Two-stage Stochastic ...ieomsociety.org/dc2018/papers/220.pdf · Sustainable Supply Chain Design using Two-stage Stochastic Modeling under Demand

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Sustainable Supply Chain Design using Two-stage Stochastic Modeling under Demand Uncertainty

Vahab Vahdat, Amir T. Namin, Rana Azghandi Department of Mechanical and Industrial Engineering

Northeastern University Boston, MA 02114, USA

[email protected], [email protected], [email protected]

Abstract

Sustainability in the supply chains (SCs) has become an essential and intrinsic element in the design of new and remodeling the current SC networks. One of the best practices of sustainability is design and operation of closed-loop supply chains where malfunctioned products can be collected and re-used. If a product requires a minor service, the required repair is provided in the collection centers and the product is returned into the market as refurbished. If the product requires a major service, the product would be either remanufactured or recycled and used as raw material. In the case that the product is out of the order, it will be disposed safely with regard to environment regulations. In this paper, a mixed integer linear programming (MILP) model is proposed for a closed-loop supply chain network design under uncertainty. The model is a multi-stage, single commodity, single period, and capacitated where demand for new and refurbished products and the amount of returned products are stochastic. In the manufacturing stage, the possibility to build on-site remanufacturing plant, called hybrid manufacturing/remanufacturing site is examined. In the distribution center stage, risk pooling is considered as an effective inventory policy for new and refurbished products.

Keywords Closed-loop supply chain network design, Reverse logistics, Mixed Integer Programming, Risk Pooling, Sustainable supply chain

1. Introduction

In the past decade, sustainability and the concept of circular economy (CE) have been widely discussed. Efficient consumption of resources has become a principal element in sustainability due to the scarcity and finiteness of natural resources(Dornfeld, 2014). After the industrial revolution, consumption of resources has increased exponentially and reached to the alarming rate over the last decades; therefore, we are unable to continue to deplete and misuse the resources for our endless needs over extraction, manufacturing, use phase, and end of life products en route to landfills(I. S. Jawahir & Bradley, 2016). Expanding social awareness, product stewardship and responsibility, and infrastructure capability can play important roles in advancing circular economy. CE is based on reducing waste of resources towards 6R methodology including more efficient strategies for Redesigning, Reducing, Remanufacturing, Recovering, Reusing, and Recycling of products. The 6R approach offers a closed-loop multiple product life cycle system as a substructure for sustainable manufacturing(I. Jawahir et al., 2006). Supply Chain Management (SCM) and Reverse Logistics (RL) can play a substantial role in supporting circular economy and sustainability in manufacturing.

SCM is intended to integrate independent but interdependent entities including suppliers, manufacturers, distribution centers, and retailers to produce and distribute products to customers in an efficient way. These entities constitute a network that should be designed appropriately (Simchi-Levi, Simchi-Levi, & Kaminsky, 1999). The network design of SC comprises the decision regarding the number, location, and capacity of production facilities, the assignment of each market region to one or more locations, and supplier selection for sub-assemblies components and

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Proceedings of the International Conference on Industrial Engineering and Operations Management Washington DC, USA, September 27-29, 2018


materials(Chopra & Meindl, 2007). Supply chain network design (SCND) including design, planning, and operations of supply chain networks has shown a strong impact not only on overall profitability of the system but also on 6R approach (Vahab Vahdat & Vahdatzad, 2017). SCND is a very complex planning problem in which multi-level classified decisions such as long-term, mid-term and short-term should be made. Long-term decisions (strategic level) mostly include crucial elements such as the number of locations, and the capacity of facilities; mid-term decisions (tactical level) contain the transportation quantity and the volume of transportation between entities; short-term decisions (operational level) include scheduling all material flows based on the decisions made in the two other levels (Amiri, 2006).

In recent years, supply chain classical problems extended into Reverse Logistics (RL). The Importance of RL had increased due to strict environmental regulations and diminishing resources at the alarming rate. RL with effective management not only leads to higher profitability by reducing transportation, inventory, and warehousing costs but also improves circular economy by decreasing resource consumption. RL involves the entire activities associated with used products. These activities consist of recovery, remanufacturing, reusing, and recycling of used and defected products(Ilgin & Gupta, 2010). Recovery contains a broad set of activities designed to return economic and ecological values from used materials, parts, and products. It refers to the process of product collection at the end of the use stage, disassembling, sorting and cleaning for utilization in subsequent life cycles of the product(I. Jawahir et al., 2006). Reprocessing of used products in such a way to restore their initial or comparable to the new form state by using as many parts as possible without loss of functionality is called remanufacturing or refurbishing. Some specific examples of remanufacturing apply to single-use cameras where for instance, kodak has designed a remanufacturing process ) that recovers and reuses 90% of their cameras (by weight) (Doppelt & Nelson, 2001). Reusing mainly includes demanufacturing operations. Demanufacturing primarily focuses on reclaiming materials and parts to avoid disposal by reusing them wherever possible. Examples of successful demanufacturing have been implemented in steel, paper, and tires industry. As an illustration HP use demanufacturing in plastic water bottles of inject cartridge("HP “Closed Loop” Inkjet Cartridge Recycling Program," 2008). The process of converting materials that are not being used in any steps mentioned above into new materials is considered as recycling. In this paper, to improve circular economy and sustainable manufacturing, we proposed a mathematical model for a closed-loop multi product supply chain network considering single period stochastic demand for recovery, remanufacturing, and recycling. The rest of the paper is structured as follows: Section 2 literature review on SCM and RL; Section 3 contains problem definition; Section 4 presents the proposed mathematical formulation; and Section 5 outlines the final remarks and potential future research. 2. Literature Review

Managing forward supply chain to manufacture a final product from the time the raw materials are acquired from suppliers to the time that the product is sold to the customers is complicated. When considering process of product return into account, the complexity of the network and the number of decisions need to be made become uncountable. Recover centers, inspection centers, recycling, disposal centers, and remanufacturing are only few examples of centers associated with return of products. Melo, Nickel, and Saldanha-Da-Gama (2009)divided the literature of supply chains with reverse flows into two groups: (1) supply chains that decisions pertaining to forward and reverse network are made simultaneously. These networks are generally called Closed-Loop Supply Chain (CLSC) network design; (2) supply chains that fully concentrate on reverse activities that is called reverse logistic (RL). In the RL it is assumed that the supply chains focus is the process of returning and recovering the product without assessment of production plans.

Since CLSC networks integrates networks of reverse and forward flows, managing and making decisions in these networks are very complex and these networks have become a feasible alternative for the cost-effectiveness RL operations. Recently, different surveys have been published on effectiveness and modeling of supply chain network design (SCND). Klibi, Martel, and Guitouni (2010) present a critical review on SCND problem under uncertainty, and discuss the optimization models proposed in the literature. Akçalı, Çetinkaya, and Üster (2009) has done a bibliographic network design review on reverse logistic and closed loop models and solutions. Tozanli, Duman, Kongar, and Gupta (2017) conducted a survey on environmentally concerned logistics operations. Kasarda (2017) discussed advantages of incorporating customer value in supply chain management process. Govindan, Fattahi, and Keyvanshokooh (2017) and Wieland, Handfield, and Durach (2016) reviewed supply chain network design under uncertainty and framework the future research in SCM. Snyder et al. (2016) conducted a review on operations research and management science for supply chain disruptions. In order to extend the surveys in the literature, we explored

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several papers in SCND, shown in Table 1 that used mathematical modelling for closed-loop supply chain network design problems with further characterizing the models regarding to objective function, decision variable sets, mathematical modelling approaches, and solution procedures.

The first distinction between the models, presented in Table 1, is objective function. While most of the papers deal with minimizing the cost of SC in transportation, facility locations, and inventory costs, there are some research focusing on maximizing profit (Lieckens & Vandaele, 2007). In recent years, multi objective models have been broadly adopted in various decision methodologies to provide insights on decision tradeoffs such as energy use, occupational safety control, waste management, risk measures and profit maximization(Ayvaz, Bolat, & Aydın, 2015; Duta, Zamfirescu, & Filip, 2014; Erbis, Kamarthi, Namin, Hakimian, & Isaacs, 2016; Hatefi & Jolai, 2014; Ramezani, Bashiri, & Tavakkoli-Moghaddam, 2013) or more detail-oriented other objective functions such as minimizing total delivery tardiness (Pishvaee & Torabi, 2010).

Several articles are based on single period where only one-time decisions are made. An example of these one-time decisions can be opening a new facility for distribution centers(Sahyouni, Savaskan, & Daskin, 2007). Multi-period models have more complexities since some characteristics of the model changeover each period, the information of the current period should be transited to the next period and the decisions should be made accordingly. Examples of multi-period models is change of demand of product, inventory level in manufacturing and distribution centers, and raw material acquisition quantity(Nickel, Saldanha-da-Gama, & Ziegler, 2012; Pishvaee & Torabi, 2010).

In the SC literature, a collection of centers that serves a similar purpose such as suppliers, plants, and distribution centers is referred as a level and the set of arcs between two successive levels is referred to a stage. Some early models, only consider one stage of the SC (Sahyouni et al., 2007), but previous studies signify the importance of interdependencies among activities of a system while the sub-systems are interconnected(V. Vahdat, 2017). Therefore, many recent studies focused on multi-stage problems focusing on decisions for suppliers, manufacturers, and distribution centers in one platform(Batarfi, Jaber, & Aljazzar, 2017; Bidhandi, Yusuff, Ahmad, & Bakar, 2009).

Table 1. Review of supply chain network design literature (MILP=Mixed Integer Linear Programming, MOMILP= Multi-objective Mixed Integer Linear Programming, MINLP= Mixed Integer Non-Linear Programming)

Article Objectives

Period Stage Demand Capacity

Solution method

Sing

le

Mul

tiple

Sing

le

Mul

tiple

Det

erm

inis

tic

Stoc

hast

ic

Cap

acita

ted

Unc

apac

itate

d

Mod

el

Exac

t

Heu

ristic

Hyb

rid

(Bidhandi et al., 2009) Total costs MILP

(Sahyouni et al., 2007) Total costs MILP

(Üster, Easwaran, Akçali, & Çetinkaya, 2007)

Total costs MILP

(Pishvaee & Torabi, 2010)

Total costs, Total delivery tardiness MOPMI

LP

(Lu & Bostel, 2007) Total costs MILP

(Ko & Evans, 2007) Total costs MINLP

(Pishvaee & Rabbani, 2011) Total costs MILP

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(Wang, Lai, & Shi, 2011)

Total costs, Total CO2 emission MILP

(Du & Evans, 2008)

Total costs, Total tardiness of cycle time

MILP

(Lee & Dong, 2008) Total costs MILP

(Lieckens & Vandaele, 2007)

Profit maximization MINLP

(Nickel et al., 2012) Financial benefit MIP

(Yu & Solvang, 2017)

Government subsidies, Global warming, Profit maximization

MILP

(Fattahi & Govindan, 2017)

Maximize the net income MILP

(Soleimani & Govindan, 2014)

Profit maximization, Conditional value at risk

MILP

Majority of existing models of the SCND are restricted to deterministic environments where the value of parameters does not change over time. Few papers proposes a stochastic programming model and solution algorithm for solving supply chain network with realistic inputs (Fattahi & Govindan, 2017; Fattahi, Govindan, & Keyvanshokooh, 2017; Keyvanshokooh, Ryan, & Kabir, 2016; Santoso, Ahmed, Goetschalckx, & Shapiro, 2005; Soleimani & Govindan, 2014). A stochastic optimization for single period multi product multi stage reverse logistics system has been designed considering government subsidies and green house global warming potentials to maximize the network profit (Yu & Solvang, 2017). Another stochastic MILP has been used for a multi-period multi stage forward-reverse logistics network to maximize the total expected profit(El Ashhab, Afia, & El-Kharbotly, 2010). Demand of new product is one of the key parameters of the supply chains where it is mainly considered deterministic(Bidhandi et al., 2009; Pishvaee & Rabbani, 2011). A robust deterministic MILP has been developed for designing a closed-loop supply chain network(Pishvaee, Rabbani, & Torabi, 2011).

Features reported in Table 1 are concluded with capacity constraints in the design of supply chains. Capacity of the arcs or the nodes in SC can be unlimited(Lu & Bostel, 2007) or limited(Nickel et al., 2012). For instance capacity of distribution centers as a node or transporting vehicle as an arc may or may not have capacity restrictions. These decisions are mainly derived from the type and the mission statement of a supply chain.

In term of modeling approaches, problems are classified to MILP (Mixed Integer Linear Programming), MIP (Mixed Integer Programming), and MINLP (Mixed Integer Non-Linear Programming). As an example, Pishvaee and Torabi (2010)propose MOPMILP model (Multi-Objective Possibilistic Mixed Integer Linear Programming) for closed-loop supply chain network design.

Finally, solution methods are explored and classified into Exact, Heuristic, and Hybrid methods. Exact methods are widely used for small and medium-scale problems. Benders’ Decomposition (BD), Branch and Bound (B&B), and Branch and Cut are some exact method used in the supply chain network design. Vahab Vahdat and Vahdatzad (2017) extended the use of exact methods into solving large-scale problems by incorporating valid inequalities to accelerate general benders’ decomposition method for solving a closed-loop supply chain network design problems. In general solving large-scale problems with exact methods require excessive time and memory. One solution for solving these problems is utilizing the heuristic and meta-heuristics methods that provide near to optimal solution. Evolutionary Algorithms (EA) like Genetic Algorithm (GA), Simulated Annealing (SA), Particle Swarm Optimization (PSO,) and

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Ant Clooney Optimization (ACO) are most popular metaheuristic methods used in solving large-scale linear and non-linear mathematical modelling. Hybrid methods use both exact and heuristic algorithms to achieve benefits of both methods. For instance(Du & Evans, 2008)solve their MILP model by a combination of scatter search, dual simplex method, and constraint method, while (Lee & Dong, 2008)solved a MILP model by a two-stage heuristic method, a simplex algorithm and Taboo search.

3. Problem definition As Shown in Figure 1, we propose a closed-loop supply chain network considering distribution centers, collection centers, recovery and remanufacturing centers and finally disposal and recycling centers.

Figure 1. Proposed model for closed-loop supply chain. Black arrows represent forward logistics where products are moved from

remanufacturing centers to the customers. Red arrows indicate the reverse logistic where products are returned from customers and transferred into the associated center based on the quality of the product.

In this model, it is assumed that the location of manufacturers are previously determined and the recovery/remanufacturing centers can only be located in manufacturing sites. In fact, this is a common decision in design of supply chains since the regulations, limitations, and requirements are similar in both remanufacturing and manufacturing centers and the flow of goods between the centers are high. Consequently, some locations will become a hybrid manufacturing/remanufacturing centers producing new and refurbished/recovered products. The new and refurbished products are shipped to the distribution centers. Distribution centers are assumed to have finite capacity that need to be assigned to both type of products. For this purpose, the distribution centers will utilize risk pooling concept to reduce that demand variability. If one aggregates demand across locations, it becomes more likely that high demand from one customer will be offset by low demand from another. This reduction in variability allows a reduction in safety stock and therefore decrease average inventory. As a result, in the centralized distribution system, each warehouse serves all customers, which leads to a reduction in variability measured by either the standard deviation or the coefficient of variation. For example, when demands from customers are negatively correlated, the higher the coefficient of variation, the greater the benefit obtained from centralized systems.

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In the proposed model, three sets of customers with different demand needs are defined. First set of customers have stochastic demand for buying new products, while second set of customers buy refurbished products. Finally, third set of customer return used products to collection centers due to several incentives such as guarantee policies and environmental regulations. In the collection centers, returned products are inspected and classified based on the quality and cost of recovering. A proportion of returned products are scrapped and shipped to safety disposal centers, while remained proportion shipped to recovery centers for refurbishment or remanufacturing processes. Before presenting the mathematical formulation, several features of the proposed model and underlying assumptions are summarized as follows: A multi-stage, single commodity, single period, and capacitated closed-loop supply chain network design model with stochastic demand for new and refurbished products is proposed. More specifically, the network consists of sets of remanufacturing, distribution, collection, and disposal centers. The uncertainty on the model happens for demand of refurbished products as well as return products of customers shipments to collection centers. The model assumes that there is a finite sets of facilities (i.e. recovery and collection centers) need to be opened. It also assumes that transportation cost is linearly dependent on the distance between stages. 4. Model formulation The following notations are used for the mixed integer linear programming (MILP), as a two stage stochastic programming formulation:

Sets:

I Set of potential recovery center locations Ii∈

J Set of potential distribution center locations Jj∈

K Set of potential collection center locations Kk ∈

L Set of potential disposal locations l L∈

nCu Set of customers with demand of new product n ncu Cu∈

fCu Set of customers with demand of refurbished product f fcu Cu∈

rCu Set of customers that returns a used product r rcu Cu∈

S Set of scenarios Ss∈

Parameters: Rc

if Fixed cost of locating recovery center at location i Dc

jf

Fixed cost of locating distribution center at location j Cc

kf Fixed cost of locating collection center at location k Rc

ic Cost for capacity of recovery center i per unit of recoverable products Dc

jc Cost for capacity of distribution center j per unit of refurbished products

Cckc Cost for capacity of collection center k per unit of returned products

DcPijtc −

Cost of transporting per unit of product between plant i and distribution center j

,n

n

Dc Cuj cuTc − Cost of transporting per unit of new product between distribution center j and customer ncu

,f

f

Dc Cuj cutc −

Cost of transporting per unit of refurbished product between distribution center j and customer

fcu

,r

r

Cu Dccu ktc − Cost of transporting per unit of returned product between customer rcu and collection center k

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RcCc

iktc −,

Cost of transporting per unit of recoverable product between collection center k and recovery center i

DisCcdktc −

, Cost of transporting per unit of unrecoverable product for safe disposal between collection center k and disposal center l

MaxRc

icap Max capacity of recovery center i MazDc

jcap Max capacity of distribution center j

MaxCc

kcap Max capacity of collection center k MiW Capacity of manufacture i

,n

NewPcu sd New product demand of customer ncu in scenario s Re

,f

cPcu sd Refurbished product demand of customer fcu in scenario s

,rcu sr Returns of used products from customer rcu in scenario s

spr Probability of scenario s α Average disposal fraction M A large number Decision variables:

Z DcMsji−

,, Quantity of new products shipped from recovery center i to distribution center j in scenario s

, ,n

n

Dc cu

j cu sZ − Quantity of new products shipped from distribution center j to customer ncu in scenario s

, ,f

f

Dc cu

j cu sZ − Quantity of refurbished products shipped from distribution center j to customer fcu in scenario s

, ,r

r

cu Cc

cu cc sZ − Quantity of returned products shipped from customer rcu to collection center k in scenario s

Z RcCcsik−

,, Quantity of recoverable products shipped from collection center k dc recovery center i in scenario s

Z DisCcsdk

−

,, Quantity of unrecoverable products shipped from collection center k to disposal center d in scenario s

Z DcRcsji−

,, Quantity of refurbished products shipped from recovery center i to distribution center j in scenario s

fcu ,sNS Quantity of non-satisfied demand of customer fcu in scenario s RciW Capacity of recovery center i DcjW Capacity of distribution center j CckW Capacity of collection center k

=01

xi

Binary variable equals to 1 if a recovery center is located at location i

Binary variable equals to 0 if a recovery center is located at location i

=01y j

Binary variable equals to 1 if a distribution center is located at location j Binary variable equals to 0 if a distribution center is located at location j

=01

kq

Binary variable equals to 1 if a collection center is located at location k Binary variable equals to 0 if a collection center is located at location k

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The objective function of the proposed model is shown in relation (1). The model minimizes capital cost of locating/opening the recovery centers, distribution centers, and collection centers. It also minimizes the cost of capacity based on the capacity decisions for each center. It is assumed that the cost of capacity increases linearly by the capacity of the center. Since the transportation quantity changes based on the stochastic demand, the cost of transportation among different levels of proposed model are minimized for each scenario. While the model is designed to satisfy the demand for new products and also have enough capacity to receive all returns of used products, there is a chance that the demand for refurbished products are not completely satisfied. For this purpose, ( )2

Pr 2cuNS Ms cu ss

∑ ×∑

minimizes the quantity of non-satisfied demand of refurbished products.

_ _, , ,, , , , , ,

1

,, , , ,2

Pr

n n

nn

f rf

ff r

Rc Dc Cc Rc Rc Dc Dc Cc Cci i j j k k i i j j k k

i j k i j k

M Dc Rc Dc Dc Cu Dc CuP Dc P Dci j i j j cui j s i j s j cu s

i j i j j cu

Dc Cu CuDc Cus j cuj cu s cu k s

s cu

Min v x f y f q f W c W c W c

Tc Tc Tc

Tc

Z Z Z

Z

− − − −

− −−

= + + + + +

× + × + ×

+ + × +

∑ ∑ ∑ ∑ ∑ ∑

∑∑ ∑∑ ∑∑

∑ ∑ ,, , ,3

, ,, ,2

r

r

f

Cc Cc RcCu Cc Cc Rck icu k k i s

j cu k k i

Cc Dis Cc Disk d cu sk d s

k d cu

Tc Tc

Tc Ns M

Z Z

Z

−− −

− −

× + × + × + ×

∑ ∑∑ ∑∑

∑∑ ∑

(1)

Subject to:

ReMaxii

Rci capxW ×≤

i∀ (2)

MaxDcjj

Dcj capyW ×≤

j∀ (3)

MazCckk

Cck capqW ×≤

k∀ (4)

Constraints (2), (3), and (4) ensure that the capacity restrictions for each recovery, distribution, and collection center to be less than the maximum allowable capacity, respectively.

Mi,, W≤∑ −

j

DcMsjiZ si ∀∀ , (5)

Rci,, W≤∑ −

j

DcRcsjiZ

si ∀∀ , (6)

Dcj,,,, W≤+∑∑ −−

i

DcRcsji

i

DcMsji ZZ

sj ∀∀ , (7)

Cck, ,

Wr

rr

Cu Cc

cu k scu

Z −≤∑ sk ∀∀ , (8)

Constraints (5-8) are also capacity constraints with regard to the flow of products between the stages of the supply chain. More specifically, Constraint (5) assures that products are not produced more than manufacturers’ capacities in each scenario. Constraint (6) shows that in each scenario the quantity of refurbished products shipped from each recovery center to distribution centers cannot exceed its capacity. Constraint (7) ensures that quantity of products (new and refurbished) shipped from manufacture i to distribution center j is lower than the capacity of distribution centers. The capacity of collection centers should be greater than customers’ product returns in each scenario, as guaranteed by constraint (8).

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, , , ,n

nn

M Dc Dc Cu

i j s j cu si cu

Z Z− −=∑ ∑ sj ∀∀ , (9)

, , , ,f

ff

Rc Dc Dc Cu

i j s j cu si cuZ Z− −

=∑ ∑ sj ∀∀ , (10)

Dc-C Re,, , ,sNsf

ff f

u cPcu sj cu s cu

j

dZ + =∑ scu ∀∀ ,2 (11)

,, ,r

rr

Cu Cccu scu k s

k

rZ −=∑ scu ∀∀ ,3 (12)

, , , ,( )r

rr

Cu Cc Cc Dis

cu k s k d scu d

Z Zα− −

=∑ ∑ sk ∀∀ , (13)

, , , ,(1 )( )r

rr

Cu Cc Cc Rc

cu k s k i scu i

Z Zα− −

− =∑ ∑ sk ∀∀ , (14)

∑∑ −− =j

DcRcsji

k

RcCcsik ZZ ,,,,

si ∀∀ , (15)

,, ,n

nn

Dc Cu NewPcu sj cu s

j

dZ −=∑ scu ∀∀ ,1 (16)

Relation (9) ensures that the total amount of new products shipped from manufacture to distribution center is equal to the total amount of products shipped to customers CUf from distribution center. Relation (10) presents a flow conservation constraint that assures the outflow of refurbished products from recovery center to each distribution center is equal to the inflow of products from each distribution center to the targeted customers in each scenario. Relation (12) ensure that all returned products of customer CUr are received and inspected in collection center K. The returned products are then classified into scrapped and recoverable products, so a portion of returned products are sent from collection center K to disposal centers D (i.e. constraint (13)) and the rest are shipped to the recovery centers I as described in relations (14). Relation (15) assures that the outflow of recoverable products in a collection center is equal to the inflow of refurbished products in that distribution center at each scenario. Finally, relation (16) ensures that all new products demand of customers are equal to outflow of new products from all distribution centers at each scenario. 5. Conclusions and guidelines for future research The need for strategic network design for reverse logistics which is constituent of returned products is more apparent than ever. Aside from national and international regulations for collecting and processing used products with the focus on environmental concerns, product stewardship and customers’ awareness of global warming and other environment issues have changed the consumption behavior towards more sustainable products. The importance of systematic thinking for reverse logistics supply chain can be shown by economic impacts of various decisions that should be made for returned products. Specifically, returned products can be refurbished and sold to the customers in a lower price, remanufactured so that some parts can be reused in the manufacturing processes of new products, dispatched to raw materials when the raw material acquisition is costly or the natural supply of the raw material is limited and finally disposed safely with least harm to environment. In this paper, a stochastic Mixed Integer Linear Programming Model (MILP) has been proposed for closed-loop supply chain network design problems under uncertainty. The closed-loop supply chain model considers the flow of both new and remanufactured products. The model is designed to make decisions about the number and location of collection centers to collect used products, recovery centers to remanufacture the used products, and finally distribution centers to receive the recovered products from manufacturers and sell it to the customers. It is assumed that the quantity and quality of returned products are stochastic and may change in each scenario. The model proposes a hybrid manufacturing/remanufacturing site when the location of remanufacturer is beneficial to be the same as manufacturer. Furthermore, the risk pooling concept is considered in distribution centers where new and refurbished products are aggregated. While the proposed MILP model provides a generic platform for building closed loop supply chains, the limitations, processes, costs, regulations, and value stream of handling used products differ based on the industry. A remarkable

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next step is to utilize this model for different industries and tailor the model based on industry features accordingly. Finally, in order to solve the model, Benders' decomposition approach is an appropriate exact method candidate since the model is structured as a two-stage stochastic model. The first stage of the problem decides around strategic decisions (i.e. the number and the locations of reverse logistic centers), while in the second stage, decisions pertaining the transportation costs are minimized. However, since the problem is NP-hard, therefore, achieving optimal solution in real-world problems could be intricate. Heuristics and Metaheuristic methods that provide a near optimal solutions for large scale problems are an appropriate replacement for exact methods in solving the proposed model. References Akçalı, E., Çetinkaya, S., & Üster, H. (2009). Network design for reverse and closed‐loop supply chains: An annotated

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Biographies Vahab Vahdat is a PhD Candidate of Industrial Engineering at Northeastern University, Boston, USA. Vahab has received his BS of Computer Engineering from Yazd University, Iran, and MS of Industrial Engineering at Northeastern. He is recipient of Alfred. J. Ferretti award for excellence in research and he formerly served as vice president of INFORMS student chapter at Northeastern University. Vahab has actively published several papers in highly acclaimed journals and peer-reviewed conference proceedings related to supply chains and healthcare process improvement. Vahab’s current research is applied operations research in healthcare industry. His projects with leading healthcare institutes and universities such as Brigham and Women Hospital, Boston Children Hospital, Harvard Medical School, Dartmouth College, and MIT explored patient flow optimization, outpatient clinic layout design, resource allocation policies, real-time location systems in hospitals, and dynamics of new technology adoption in healthcare. Amir T. Namin is a PhD Candidate of Industrial Engineering at Northeastern University, Boston, USA. Amir has received his Bachelor's degree in Electrical Engineering from Purdue University. He subsequently completed his Engineering Management Master’s degree at Northeastern University in 2013 and later began his PhD in Industrial Engineering at Northeastern University. The focus of his research has been on sustainability in smart manufacturing, cost benefit analysis of Nano and additive manufacturing, dynamic simulation, optimization, 3D printing and its applications in the medical field, and modeling the adoption and diffusion of new technologies. Amir has actively published several papers and attended several conferences related to sustainable manufacturing and green design supply chain. He is a recipient of the Additive Manufacturing Fundamental Certification from SME. Rana Azghandi is a PhD Candidate at the Department of Mechanical and Industrial Engineering at the Northeastern University, Boston, MA. Her research focuses on supply chain management, operations research, system dynamics, and agent-based simulation, with applications in public health policy, service systems, emergency transportation, and humanitarian logistics. Her e-mail address is [email protected].

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Sustainable Supply Chain Design using Two-stage Stochastic ...ieomsociety.org/dc2018/papers/220.pdf · Sustainable Supply Chain Design using Two-stage Stochastic Modeling under Demand