Supplier selection and order allocation in closed-loop ...

International Journal of Production Research, 2015 Vol. 53, No. 20, 6320–6338, http://dx.doi.org/10.1080/00207543.2015.1054452

Supplier selection and order allocation in closed-loop supply chain systems using hybrid Monte Carlo simulation and goal programming Kamran S. Moghaddam* Department of Information Systems and Decision Sciences, Craig School of Business, California State University-Fresno, Fresno, CA, USA

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(Received 2 December 2014; accepted 16 May 2015) Supplier selection is an important strategic design decision in closed-loop supply chain systems. In addition, and after identifying the candidate suppliers, optimal order allocations are also considered as crucial tactical decisions. This research presents a multi-objective optimisation model to select the best suppliers and configure manufacturing and refurbishing facilities with the optimal number of parts and products in a closed-loop supply chain network. The objective functions in this research are formulated as total profit, total defective parts, total late delivered parts and economic risk factors of the candidate suppliers. The proposed multi-objective model is solved by hybrid Monte Carlo simulation integrated with three different variants of goal programming method. The effectiveness of the mathematical model and the proposed solution algorithms in obtaining Pareto-optimal solutions is demonstrated in a numerical example adopted from a real case study. Keywords: supplier selection; order allocation; closed-loop supply chain systems; multi-objective optimisation; Monte Carlo simulation; goal programming

1. Introduction With the globalisation and the emergence of large-scale enterprise of interdependent organisations in the twenty-first century, there has been an increasing trend in outsourcing of raw materials, parts and services (Aissaoui, Haouari, and Hassini 2007). This trend has forced companies to give more attention to purchasing operations and their associated decisions. Under the pressure of global competition, companies strive to achieve excellence in delivering high-quality and low-cost products and services to their customers on time and rely on the efficiency of their supply chain to gain competitive advantage. Supply chain management involves suppliers, manufacturers, distribution centres and retailers to ensure the efficient flow of raw materials, work-in-process inventory, finished products, information and funds among different facilities. Effective supply chain management involves managing supply chain assets and products, information and fund flows to maximise total supply chain surplus (Chopra and Meindl 2013). A growth in supply chain surplus increases the size of the total share and allows contributing members of the supply chain to benefit. One of the important decisions that influences the entire company’s performance and competitiveness is the supplier selection and order allocation to the selected suppliers. A closed-loop supply chain system is defined as the process of planning, implementing and controlling the inbound flow and storage of secondary goods and related information opposite to the traditional supply chain directions for the purpose of recovering value and proper disposal operations (Fleischmann et al. 1997). In addition to selecting the best candidate suppliers and allocating optimal orders to them, closed-loop supply chain systems consist of reuse, resale, repair, refurbishing, remanufacturing and recycling operations. In the remanufacturing process, used/returned products are disassembled in disassembly sites and then usable parts are cleaned, refurbished and transmitted to part inventory. In the next stage, the new products are manufactured from the refurbished and new parts (Kim, Song, and Jeong 2006). In closed-loop supply chains, the new parts are purchased from external suppliers and the used parts are obtained from used or returned products. Not only the cost of purchase is important but also other criteria of suppliers play a prominent role. For instance, late delivery can affect the production schedule and increases the final costs tremendously. As a result, suppliers should be evaluated based on several criteria and purchasing cost is only one of them. Supplier selection problem is a multi-criteria decision-making problem that includes both quantitative and qualitative factors such as

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total cost, on-time delivery, quality, customer satisfaction level, etc. The problem can be viewed as two interrelated sub-problems (Weber and Current 1993):


(1) Which supplier(s) should be selected? (2) How much/many should be purchased from each selected supplier? In addition to cost-related factors, in supplier selection when consolidating and reducing the number of suppliers, companies run the risk of not having sufficient raw materials to meet the fluctuating demand. These risks may be caused by natural disasters or man-made actions (Li and Zabinsky 2011). Environmental factors are another group of characteristics that should be emphasised in closed-loop configurations. Recycling, clean technology, pollution reduction capacity and environmental costs are examples of environmental factors. It is noticeable that conservation of environment is one of the designated goals of closed-loop supply chain systems (Amin and Zhang 2012). Two major areas of current research in supply chain management are relevant to our work; make or buy, and vendor selection. The first area deals with the management and quantification of closed-loop supply chain systems. The second topic involves supplier selection methods which are being practiced by researchers and managers to enhance effectiveness in outsourcing decisions to achieve and maintain higher levels of competitiveness. In this research, we develop a general closed-loop supply chain network that includes multiple suppliers, manufacturing/refurbishing sites and disassembly facilities. The manufacturer uses new parts purchased from selected suppliers and refurbished parts obtained from returned products to produce new products demanded by the customers. The main decisions of the system are to determine the optimal set of candidate suppliers and refurbishing strategies along with the optimal number of products and parts in each section of the system. The problem is then formulated as a multi-objective optimisation model in which the objective functions are total profit to be maximised, total number of defective parts purchased from suppliers to be minimised, total number of late delivered parts to be minimised and economic risk factors of the candidate suppliers to be minimised. The proposed model can be used by decision-makers for supplier and refurbishing sites selection (strategic decisions) and also for determining the optimal number of products and parts in each stage of the network (tactical decisions). We also propose three Monte Carlo simulation algorithms integrated with non-preemptive goal programming, compromise programming and fuzzy goal programming to find Pareto-optimal solutions (aka non-dominated solutions) of the proposed model. This paper is organised as follows: Section 2 reviews the current literature on network configuration in closedloop supply chains and also different decision models used in supplier evaluation and order allocation. Section 3 presents the structure of the closed-loop supply chain system and the mathematical formulation of the problem. Section 4 develops the solution methodology in which Monte Carlo simulation is combined with three different versions of goal programming in order to find the non-dominated solutions of the proposed multi-objective model. Section 5 presents computational results obtained from a sample problem and provides guidelines for sourcing and refurbishing decisions. Section 6 summarises the paper by highlighting the importance of inclusion of multiple objectives into the modelling approach and the advantage of using hybrid algorithms in solving supplier selection decisions.

2. Literature review 2.1. Network configuration in closed-loop supply chains Fleischmann et al. (1997) reviewed and categorised the closed-loop supply chains literature into three main categories: distribution planning, inventory planning and production planning. Melo, Nickel, and Saldanha-da-Gama (2009) examined the application of facility location models in supply chain management and segmented the literature of reverse logistics to closed-loop and recovery networks. Kim, Song, and Jeong (2006) developed a mathematical model to determine the quantity of parts and products processed in the remanufacturing facilities and the number of parts to be purchased from a single supplier while maximising manufacturing cost savings. A mixed integer non-linear programming model was formulated by Ko and Evans (2007) in order to model multi-period, two-echelon, multi-commodity and capacitated network design problems with simultaneous forward and reverse flows of parts and products. PATI, VRAT, and KUMAR (2008) proposed a goal programming model to determine the facility location, route and flow of different types of recyclable wastepaper in the multi-product, multi-echelon and multi-facility system. Lee, Gen, and Rhee (2009) formulated a mathematical model for a general closed-loop supply chain network and used genetic algorithm to solve the model. An optimisation model to maximise the profit of a remanufacturing system was presented by Shi, Zhang, and Sha (2011) in which they developed a solution approach based on Lagrangian relaxation method and sub-gradient algorithm. Amin and Zhang (2012) examined a

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general closed-loop supply chain network containing manufacturer, disassembly, refurbishing and disposal sites and proposed a two-phase integrated model to select suppliers and refurbishing sites and to allocate number of parts and products to the network. In an another study, Amin and Zhang (2013) expanded their previous work by developing a three-stage model that included evaluation, network configuration and order allocation using fuzzy set theory. A multi-objective linear programming model was developed by Arikan (2013) to solve multiple sourcing supplier selection problems. The author defined the three objective functions as minimisation of costs, maximisation of quality and maximisation of on-time delivery.


2.2. Decision models for supplier evaluation and selection Since the proposed modelling approach in this research is based on multi-objective mathematical programming along with inputs from subjective pair-wise comparisons evaluated by analytic hierarchy process (AHP) method, the related literature employing these methods will be surveyed in the following subsections. In addition, because one of the proposed algorithms incorporates application of fuzzy set theory to determine the Pareto-optimal solutions of the developed model, we briefly review the relevant literature that employs fuzzy sets in supplier evaluations and selection problem. The following survey focuses on modelling approaches dealing with multiple sourcing supplier selection and it is useful to mention that the vast majority of the supplier selection literature focuses only on single-sourcing supplier selection problems which will not be considered in this research.

2.2.1. Mathematical programming models and algorithms Narasimhan, Talluri, and Mahapatra (2006) formulated a mathematical model that effectively incorporated different types of products with different ranges of life cycles and contributed to the sourcing literature by demonstrating an approach for optimally selecting suppliers and supplier bids. Ravindran et al. (2010) modelled the risk-adjusted supplier selection problem as a multi-criteria optimisation model and solved it in two phases. In their multi-objective formulation, price, lead-time, risk of disruption due to natural event and risk of quality were explicitly considered as four conflicting objectives to be minimised simultaneously. Li and Zabinsky (2011) developed a two-stage stochastic programming (SP) model and a chance-constrained programming model to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Two multi-objective mixed integer non-linear models were developed by Rezaei and Davoodi (2011) for multi-period lot-sizing problems involving multiple products and multiple suppliers. The first model represented a lot-sizing problem with supplier selection in situations where shortage is not allowed, while in the second model, all the demand during the stock-out period is allowed to be backordered. Wu, Chien, and Gen (2012) formulated a strategic outsourcing decision problem as a bi-objective combinatorial optimisation problem and developed a genetic algorithm to determine the outsourcing order allocation with non-linear cost structure while minimising both the total alignment gap and the total allocation cost. Esfandiari and Seifbarghy (2013) presented a multi-objective model in which purchasing cost, rejected orders and late delivered orders were minimised while the total scores from the supplier evaluation process were maximised. In another study, Talluri and DeCampos (2013) developed a novel approach in data envelopment analysis efficiency assessment to measure performance diversity on strategic sourcing and supply base rationalisation. They applied this method to a supplier data-set of a large multinational telecommunication company in categorising their supply base into groups for effective supplier rationalisation.

2.2.2. Analytic hierarchy process (AHP) In one of the earlier studies, Ghodsypour and O’Brien (1998) proposed an integration of an analytic hierarchy process (AHP) and linear programming to consider both qualitative and quantitative factors in choosing the best suppliers with capacity constraints and placing the optimum order quantities among them such that the total value of purchasing is maximised. Since the work of Ghodsypour and O’Brien (1998), many researchers have employed AHP and in its extension analytic network process (ANP) integrated with mathematical programming methods to model and solve multi-criteria supplier selection problems (Ghodsypour and O’Brien 2001; Bhutta and Huq 2002; Handfield et al. 2002; Korpela et al. 2002; Gencer and Gürpinar 2007; Wang and Yang 2007; Demirtas and Ustun 2008, 2009; Kokangul and Susuz 2009; Wu et al. 2009; Ravindran et al. 2010; Parthiban and Abdul Zubar 2013). In all


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these studies, a two-stage approach to evaluate and rank the candidate suppliers and then to determine the optimal amount of purchase from each supplier is proposed. The priorities are calculated for each supplier using AHP/ANP and then these priorities are used as the objective function weights in a multi-objective mathematical programming model. 2.2.3. Fuzzy set theory Fuzzy set theory is widely used to formulate problems with insufficient and sometimes inaccurate information related to different criteria encountered in real-world decision-making. Amid, Ghodsypour, and O’Brien (2006) developed a weighted additive fuzzy model for a supplier selection problem to deal with imprecise inputs and to overcome the problem of determining the weights of quantitative and qualitative criteria under conditions of multiple sourcing and capacity constraints. Kumar, Vrat, and Shankar (2006) employed a fuzzy goal programming approach to solve the vendor selection problem with multiple objectives of minimising total cost, total rejections and total late deliveries subject to constraints for buyer’s demand, vendors’ capacity, vendors’ quota flexibility, purchase value of items and budget allocation to individual vendor. Özgen et al. (2008) proposed an integration of fuzzy set theory with multi-objective possibilistic linear programming to model the uncertainties encountered in integrated supplier evaluation and order allocation. Crispim and Pinho de Sousa (2009) proposed an exploratory process to help the decision-maker in gaining knowledge about the network in order to identify the criteria and the companies that best suit the needs of each particular project. Their process involved a multi-objective Tabu Search to find a good approximation of the Pareto front and a fuzzy TOPSIS algorithm to rank the alternative for virtual enterprises configurations. Faez, Ghodsypour, and O’Brien (2009) proposed a case-based reasoning approach which is a recently recommended method for solving the vendor selection problem by making use of previous similar situations. More recent studies on application of fuzzy set theory in supplier selection problem can be found in (Wang et al. 2010; Wu et al. 2010; Amid, Ghodsypour, and O’Brien 2011; Ozkok and Tiryaki 2011; Yücel and Güneri 2011; Shaw et al. 2012).

2.3. Contributions of this research This research develops a novel multi-objective optimisation model in order to optimally determine the best set of candidate suppliers and optimal order allocation in a closed-loop supply chain system. The traditional methods to solve multi-objective optimisation problems are based on preference-based approach in which a relative predetermined vector of weights is used to combine multiple objectives into a single objective function. Other methods, such as ε-constraint method, reformulate the multi-objective optimisation problems by just keeping one of the objectives while placing the others into the set of constraints and then restricting them by user-specified values. Goal programming methods seek Pareto-optimal solutions that attain a predefined target value for one or more objectives by minimising deviations from these target values. All these methods employ a point-by-point deterministic optimisation approach by finding singlePareto-optimal solution at each trial. Since multi-objective optimisation problems have equally important Pareto-optimal solutions, an ideal approach would be finding multiple trade-off optimal solutions at once and let the decision-maker choose the desired solution based on other higher level information. The optimal solutions obtained by the ideal approach will be then independent from the user’s predefined parameters. An effective multi-objective solution procedure should successfully perform three following conflicting tasks as suggested by Zitzler, Deb, and Thiele (2000) and Deb (2001): (1) The obtained non-dominated solutions should be close enough to the true Pareto front. Ideally, the non-dominated solutions should be a subset of the Pareto-optimal set. (2) The obtained non-dominated solutions should be uniformly distributed over of the Pareto front in order to provide the decision-maker a true insight of existing trade-offs. (3) The obtained non-dominated solutions should capture the whole spectrum of the Pareto front. This requires investigating non-dominated solutions at the extreme ends of the objective functions space. In the past three decades, numerous multi-objective evolutionary algorithms have been developed and tested as trustable and efficient solution methods to solve multi-objective models. However, these algorithms are best known to their capability of obtaining good or near optimal solutions and the attainment of the exact optimal solution(s) is never guaranteed.

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In this research, non-preemptive goal programming, compromise programming and fuzzy goal programming are considered as subroutines of a simulation solution approach. The major drawback of these standard goal programming methods is that they can obtain only one non-dominated solution which is highly dependent to the decision-maker’s choice of the goals and the weights of deviation from the predefined goals. The goal programming formulation requires the decision-maker to specify an acceptable level of achievement for each objective function and to provide a weight to be associated with the deviation between each objective function and its goal. As such, goal programming is considered under the category of methods that use completely pre-specified preferences from the decision-maker in solving the multi-criteria decision-making problem. A detailed description of these goal programming methods can be found in (Masud and Ravindran 2008). In order to avoid the subjective weighting from decision-makers when solving the multi-objective model, we integrate Monte Carlo simulation method with non-preemptive goal programming, compromise programming and fuzzy goal programming to develop three algorithms to find Pareto-optimal solutions of the proposed model. These hybrid algorithms can reveal the Pareto-optimal front and the trade-off aspects of the objectives to decision-makers without requesting their original preferences.


3. System specifications and problem formulation In this research, a closed-loop supply chain system with manufacturing/refurbishing, disassembly and disposal facilities is considered in which the manufacturer controls the flow of parts, products and information in the network and produces final products according to the customers’ demand. After selling the products to customers, some of them may be returned back to the supply chain system. The returned products are collected and disassembled at a disassembly facility and the parts then are categorised into reusable and unusable parts from which the unusable parts will be transported to the disposal facilities outside of the network. The reusable parts are then sent to manufacturing/refurbishing facilities to be tested and refurbished. These parts are finally added to part inventory along with new parts. The structure of this closed-loop supply chain is illustrated in Figure 1.

Figure 1. Structure of the closed-loop supply chain system in this study.

According to the demand and availability of refurbished parts in the inventory, the manufacturer purchases new parts from external suppliers to be able to meet the demanded products. Not only the purchase price and other associated costs such as transportation and inventory costs of new parts are important to manufacturer but also other criteria such as quality, delivery and risk factors of economic environment of suppliers should be considered. The manufacturer encounters two types of decisions. First, suppliers’ evaluation and selection have to be considered as strategic decisions. Second, the optimal number of products and parts at each stage of the network should be determined as tactical decisions. Determination and setting up the refurbishing and disassembly facilities are the other types of strategic decisions to be included in the decision-making context. When there are some alternatives for refurbishing facilities, the manufacturer prefers to select the site which has the lowest overall cost (including first, fixed and variable costs). Table 1 lists the notations for sets, indices, decision variables and parameters used to develop and express the multi-objective optimisation model.


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Table 1. List and description of notations. Sets

Description

I J M N K

set set set set set

Indices i j m n k

index index index index index

Decision variables xijm yjn rn om dm refjm si bdn

number of part m purchased from supplier i by plant j, i ∈ I, j ∈ J and m ∈ M number of product n produced at plant j, j ∈ J and n ∈ N number of returned product n to be disassembled at disassembly site, n ∈ N number of part m obtained at disassembly site, m ∈ M number of part m to be disposed from disassembly site, m ∈ M number of part m to be refurbished at plant j, j ∈ J and m ∈ M binary variable, has value of 1 if supplier i is chosen, 0 otherwise, i ∈ I binary variable for setup of disassembly site for product n, n ∈ N

Parameters selln costjn priceim shipij invj setdisn disam dispm refcostjm qualityim deliveryim econriski demn reqmn supmaxim supminim reusem returnn

unit selling price of product n, n ∈ N unit production cost of product n at plant j, j ∈ J and n ∈ N unit price of part m purchased from supplier i, i ∈ I and m ∈ M transportation cost from supplier i to plant j, i ∈ I and j ∈ J inventory holding cost at plant j, j ∈ J setup cost of disassembly site for product n, n ∈ N unit disassembly cost for part m, m ∈ M unit disposing cost for part m, m ∈ M unit refurbishing cost for part m at plant j, j ∈ J and m ∈ M fraction of poor quality parts of type m purchased from supplier i, i ∈ I and m ∈ M fraction of late delivered parts of type m purchased from supplier i, i ∈ , and m ∈ M risk factors of economic environment associated with supplier i, i ∈ I demand for product n, n ∈ N unit requirements for part m to produce one unit of product n, m ∈ M and n ∈ N maximum capacity available of part m provided of supplier i, i ∈ I and m ∈ M minimum purchase quantity of part m from supplier i, i ∈ I and m ∈ M maximum percent of reusable part m, m ∈ M maximum percent of returned product n, n ∈ N

of of of of of

suppliers manufacturing/refurbishing plants parts final products objective functions of of of of of

suppliers, i = 1, …, I manufacturing/refurbishing plants, j = 1, …, J parts, m = 1, …, M final products, n = 1, …, N objective functions, k = 1, …, K

3.1. Multi-objective optimisation model The proposed multi-objective optimisation model for supplier selection and order allocation in the above closed-loop supply chain setting is presented using the following Equations (1)–(15). XX XX X X Max f1 ¼ ðselln costjn Þyjn ðpriceim þ shipij þ invj Þxijm setdisn bdn j2JX n2N i2IX j2J X m2M n2N ðdisam om þ dispm dm Þ refcostjm refjm (1) m2M

j2J m2M

Min f2 ¼

XX X

qualityim xijm

(2)

deliveryim xijm

(3)

i2I j2J m2M

Min f3 ¼

XX X i2I j2J m2M

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Min f4 ¼

X

econriski xijm

(4)

i2I

Subject to : X

yjn ¼ demn

8n 2 N

(5)

j2J

X

reqmn yjn ¼

n2N

X

xijm þ refjm

8j 2 J ; m 2 M

(6)

i2I

X

refjm þ dm ¼ om

8m 2 M

(7)

j2J

om ¼

X

8m 2 M

reqmn rn

(8)

n2N


X

xijm supmaxim si

8i 2 I; m 2 M

(9)

xijm supminim si

8i 2 I; m 2 M

(10)

j2J

X j2J

X

refjm reusem om

8m 2 M

(11)

dm ð1 reusem Þom

8m 2 M

(12)

j2J

X

returnn yjn rn

8n 2 N

(13)

j2J

rn B bdn

8n 2 N

si ; bdn 2 f0,1g 8i 2 I; n 2 N xijm ; yjn ; rn ; om ; dm ; refjm 0 8i 2 I; j 2 J ; m 2 M ; n 2 N

(14) (15)

3.2. Objective functions The objective function (1) maximises the total profit which is the net profit gained from selling of final products minus parts purchasing costs from external suppliers, transportation cost, inventory holding cost of parts, set-up cost of products at disassembly sites, disassembly cost of obtained parts, disposal cost of unusable parts and refurbishing cost of parts at manufacturing/refurbishing facilities. The objective function (2) minimises the total number defective parts which is also equivalent to maximising the total quality of parts purchased from the suppliers. The objective function (3) minimises the total number of late delivered parts purchased from the suppliers, and finally, the objective function (4) minimises the total risk factors of economic environment associated with each supplier.

3.3. Functional and operational constraints Constraint (5) ensures the total number of manufactured products from each type is equal to the demand for each type of products. Constraint (6) expresses the number of parts used to manufacture final products at each plant to be equal to the total number of refurbished parts from refurbishing sites and purchased parts from the suppliers. Constraint (7) shows that the number of disassembled parts is equal to the number of refurbished parts and disposed parts, whereas


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constraint (8) demonstrates the relationship between the number of parts that can be obtained from returned products. Constraints (9) and (10) represent the maximum supplier capacity and the minimum purchase quantity requirement of each part from suppliers. Constraints (11) and (12) limit the percentage of reusable and disposed parts that can be obtained from returned products at the disassembly facility. Constraint (13) enforces the limitation on returned products and constraint (14) is for imposing set-up initiation of disassembly sites. Constraint (15) limits the decision variables of supplier selection and set-up of disassembly sites for each type of products to be binary variables and all the other decision variables to be non-negative. Complexity of the optimisation model can be expressed as a function of problem size as it has M(I·J + J + 2) + N(J + 2) decision variables of which N + I are binary and M(2I + J + 4)+3N functional and operational constraints.


4. Solution methodology To rectify the dependability to subjective weighting from decision-makers when solving the multi-objective model, the following hybrid Monte Carlo simulation procedures are proposed in which randomly generated objective goals and deviation weights are used in goal programming sub-models in each simulation replication. In the following hybrid algorithm 1 that employs non-preemptive goal programming method as the optimisation sub-model, the goals for each objective function and weights of the deviations are randomly generated by the Monte Carlo simulation procedure and they are not asked from the decision-maker. Algorithm 1. Hybrid Monte Carlo Simulation and non-preemptive goal programming

Begin Step 1: Calculate the best and the worst solutions (also known as ideal and nadir solutions) of the objective function k, fkmin and fkmax , by incorporating only one of the objectives while ignoring all other objectives subject of the set of functional constraints (5)–(15); Step 2: Current replication = 1; While (current replication
kmax fkmin

:

(22)

(Continued)


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Step 2.3: Generate random observations for the membership functions;

wk ¼ randð0; 1Þ 8k 2 K w0k ¼ Pwkw 8k 2 K

(23)

k

k2K

Step 2.4: Solve the Fuzzy Goal Programming sub-model (24);

Max

P k2K

w0k kk

subject to : kk lk ðfk Þ 8k 2 K set of functional constraints (5)–(15)

(24)


Step 2.5: Current replication = Current replication + 1; End while End

5. Computational results 5.1. Data setting In reality, decision-makers usually have intangible information related to decision criteria and constraints, rather than exact and complete information. Qualitative parameters such as the economic environment evaluated by customers are typically unclear in nature. For example, it is easy to say that the economic environment is good or not, but hard to give a specific value for it. In this study, 10 suppliers are identified as the potential candidate suppliers from 21 available and qualified suppliers under multiple conflicting criteria for a global manufacturing company. We defined 14 supplier performance measurement attributes under 7 major criteria to evaluate 21 potential suppliers. We distributed survey forms to the decision-makers and asked them to compare each criterion and each attribute against one and other. The decision-makers also compared these 21 suppliers under different attributes. We applied AHP method to analyse the survey data to be able to identify top candidate suppliers. Finally, the ranking of the decision-makers was aggregated by assigning weights to each decision-maker based on their positions, knowledge and skills. In addition to 10 candidate suppliers, we considered 4 manufacturing plants to be used as manufacturing and/or refurbishing facilities to produce 5 different types of product from 25 different available parts in the market that can be either purchased from the candidate suppliers or be refurbished from the returned products. The demand function used in this research was assumed to be deterministic under certain assumptions as shown in Table 2. The detailed data-sets are available upon request in an electronic format. Visual Basic.Net programming environment is used to develop the simulation model in which LINGO optimisation software is utilised to solve the goal programming sub-models in the algorithms all to be run on a laptop computer with Intel® Core™ i7-3520M CPU @ 2.9 GHz with 8.00-GB RAM.

5.2. Ideal solutions of the objective functions Tables 3–6 show the ideal solutions with respect to each objective function (1)–(4) independently subject to the functional and operational constraints (5)–(15). It is observed that through the ideal solution for objective function (1), total profit is the highest but this comes with large number of defective and late delivered parts purchased from the suppliers.

Table 2. Total number of product n demanded by the customers (demn).

Demand

Product 1

Product 2

Product 3

Product 4

Product 5

2154

2406

2764

2079

1765

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Table 3. Ideal solution of the optimisation model with only the total profit as the objective function. (a) Objective function values and computational time Objective

Total profit

Defective parts

Late delivery

Economic risk

CPU time (s)

Value

$6,207,719

7553

6740

16,046

2.75

(b) Selected suppliers (si) Supplier

S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

Selected

–

–

–

Yes

Yes

–

–

Yes

Yes

Yes

(c) Number of product n produced at plant j (yjn)


Plant Plant Plant Plant

Product 1

Product 2

Product 3

Product 4

Product 5

679 0 66 1409

353 1608 0 445

875 550 1153 185

1088 0 0 991

0 504 1261 0

1 2 3 4

(d) Number of returned product n to be disassembled (rn) and set-up of disassembly site for product n (bdn) Product 1

Product 2

Product 3

Product 4

Product 5

0 –

0 –

0 –

0 –

0 –

Returned Setup

(e) Number of part m obtained (om) and disposed at disassembly site (dm) Part

Obtained Disposed

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

(f) Number of part m to be refurbished at plant j (refjm) Part


1 2 3 4

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Under this scenario, suppliers 4, 5, 8, 9 and 10 are selected as the only providers of new parts and the system does not use any refurbished parts from returned products as all the used/returned products are salvaged before coming back to the system. The four manufacturing plants almost have very similar contribution in total number of manufactured products as 27, 24, 22 and 27%, respectively. The second ideal solution demonstrated in Table 4 is completely in contrast with the first one. This ideal solution for the objective function (2) minimises the total number of defective parts purchased from the selected suppliers 1, 2, 6 and 7. This case recommends another policy in which not all the required parts are to be purchased from the suppliers, but some can be used as refurbished parts obtained from the used/returned products back to the system. In this scenario, all the manufacturing plants are determined to disassemble the returned products and then reuse the refurbished useable parts and dispose the unused ones. The contribution of the plants is found to be 33, 25, 14 and 27%. The third ideal solution illustrated in Table 5 determines a similar refurbishing strategy under different set of selected suppliers and different group of products to be manufactured at the production facilities. As can be seen in the third scenario, only suppliers 2, 3, 6 and 8 are selected. Plants 1 and 4 contribute 46 and 38% of the total


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Table 4. Ideal solution of the optimisation model with only the total defective parts as the objective function. (a) Objective function values and computational time Objective

Total profit

Defective parts

Late delivery

Economic risk

CPU time (s)

Value

$3,399,549

4767

6226

10,652

1.53


S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

Selected

Yes

Yes

–

–

–

Yes

Yes

–

–

–




Product 1

Product 2

Product 3

Product 4

Product 5

1429 463 262 0

971 1192 243 0

0 256 0 2508

665 628 786 0

669 218 326 552

1 2 3 4


Product 2

Product 3

Product 4

Product 5

215 Yes

120 Yes

138 Yes

62 Yes

106 Yes

Returned Setup

(e) Number of part m obtained (om) and disposed at disassembly site (dm) Part 1

2

3

4

5

6

7

8

9

10

11

12

13

14 15 16

17

18

19

20

21

22

23

24

25

Obtained 106 168 289 504 120 354 384 106 226 321 215 580 168 336 0 259 226 459 259 442 536 459 168 215 427 Disposed 93 128 251 408 103 283 269 89 161 225 177 504 145 302 0 212 195 358 186 349 429 377 146 183 371 (f) Number of part m to be refurbished at plant j (refjm) Part


1 2 3 4

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

0 0 0 13

0 0 0 40

38 0 0 0

0 0 96 0

0 17 0 0

0 0 0 71

115 0 0 0

0 0 17 0

0 0 66 0

0 0 0 96

0 0 39 0

0 75 0 0

0 0 24 0

0 34 0 0

0 0 0 0

0 0 47 0

0 0 0 32

0 0 101 0

0 72 0 0

93 0 0 0

0 0 0 107

83 0 0 0

0 22 0 0

0 0 32 0

55 0 0 0

production, respectively, while plants 2 and 3 only manufacture 8 and 9% of the total manufactured products. The last ideal solution, presented in Table 6, tends to minimise the total economic risk factors associated with the selected suppliers 1, 3, 5 and 6. The refurbishing strategy is again similar to the ideal solutions 2 and 3, but the contribution of production plant 1 is 44%, while production facilities 2, 3 and 4 only contribute to 19, 32 and 6% of the total number of manufactured products. Examining these ideal solutions reveals an existing trade-off between the objective functions that results in different sets of selected suppliers, different production contribution of facilities and different plans of disassembly, refurbishing and disposal of the returned products. More detailed computational results of optimal order allocation to the selected suppliers are available as an online supplementary appendix.

5.3. Distribution of Pareto-optimal solutions Figures 2–4 illustrate the Pareto-optimal solutions obtained by hybrid algorithms containing non-preemptive goal programming, compromise programming and fuzzy goal programming sub-models (18), (20) and (24). It is observed that

6332

K.S. Moghaddam

Table 5. Ideal solution of the optimisation model with only the total late deliveries as the objective function. (a) Objective function values and computational time Objective

Total profit

Defective parts

Late delivery

Economic risk

CPU time (s)

Value

$3,806,141

6504

4389

12,052

1.56


S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

Selected

–

Yes

Yes

–

–

Yes

–

Yes

–

–




Product 1

Product 2

Product 3

Product 4

Product 5

750 0 204 1200

1327 0 177 902

2014 107 0 642

0 0 631 1448

1017 748 0 0

1 2 3 4


Product 2

Product 3

Product 4

Product 5

215 Yes

120 Yes

138 Yes

62 Yes

106 Yes

Returned Setup


2

3

4

5

6

7

8

9

10

11

12

13

14 15 16

17

18

19

20

21

22

23

24

25



1 2 3 4

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

0 13 0 0

40 0 0 0

0 38 0 0

96 0 0 0

17 0 0 0

71 0 0 0

0 0 0 115

0 17 0 0

0 66 0 0

96 0 0 0

39 0 0 0

0 75 0 0

0 0 0 24

0 0 34 0

0 0 0 0

47 0 0 0

0 32 0 0

101 0 0 0

0 72 0 0

0 0 93 0

0 107 0 0

0 0 0 83

0 0 22 0

32 0 0 0

55 0 0 0

all these algorithms perform well in finding the non-dominated solutions close enough to the ideal solutions and far enough from nadir solutions that make them more likely to be close enough to the true Pareto front (task 1) and also in capturing non-dominated solutions at the extreme ends of the objective functions space (task 3). On the other hand and with respect to the second task in solving multi-objective optimisation, compromise programming seems to be more capable in finding uniformly distributed non-dominated solutions over of the Pareto region in comparison with non-preemptive goal programming and fuzzy goal programming. This observation is based on the distribution of non-dominated solutions depicted in diagonal graphs of Figures 2–4.

5.4. Performance evaluation of the proposed algorithms In order to evaluate the performance of each proposed algorithm, we ran the algorithms over 500 simulation runs. We then collected the computational results and calculated the average and standard deviation of objective functions’ values, CPU time and simulated weights on yielding probabilities of selected suppliers by each method as presented in Tables


6333

Table 6. Ideal solution of the optimisation model with only the economic risk as the objective function. (a) Objective function values and computational time Objective

Total profit

Defective parts

Late delivery

Economic risk

CPU time (s)

Value

$3,804,657

7217

6365

4222

0.83


S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

Selected

Yes

–

Yes

–

Yes

Yes

–

–

–

–




Product 1

Product 2

Product 3

Product 4

Product 5

244 0 1910 0

1120 0 781 505

813 1611 339 0

1962 0 2 115

724 496 544 0

1 2 3 4


Product 2

Product 3

Product 4

Product 5

215 Yes

120 Yes

138 Yes

62 Yes

106 Yes

Returned Setup


2

3

4

5

6

7

8

9

10

11

12

13

14 15 16

17

18

19

20

21

22

23

24

25



1 2 3 4

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

13 0 0 0

0 0 40 0

0 0 38 0

96 0 0 0

17 0 0 0

71 0 0 0

0 0 0 115

0 17 0 0

34 13 0 18

0 90 7 0

0 0 39 0

75 0 0 0

0 24 0 0

0 0 34 0

0 0 0 0

0 0 47 0

30 1 0 0

101 0 0 0

0 0 0 72

0 0 0 93

38 0 0 69

0 0 83 0

0 0 0 22

32 0 0 0

0 0 0 55

7–9. Non-preemptive goal programming and compromise programming sub-models are able to reach to a slightly better total profit, total number of defective parts and late delivery objective functions than the fuzzy goal programming method. But fuzzy goal programming outperforms the other two in obtaining lower economic risk factors. Fuzzy goal programming is also the fastest and the most stable method in this research in terms of both average and standard deviation of CPU time. Table 8 gives the yielding probabilities of each selected supplier in 500 simulation runs and Table 9 demonstrates the final rank for each supplier using the proposed hybrid algorithms. It is observed that suppliers 1, 6, 3 and 8 are the most likely suppliers to be selected and suppliers 2 and 5 have been preferred with the probability of about 10%. Suppliers 9, 4, 7 and 10 are identified as not preferred candidates by the manufacturing/refurbishing plants due to their undesired features in terms of four criteria of total profit, total defective parts, late deliveries and economic risk factors.

6334

K.S. Moghaddam x 106 10

Profit

5 0 8000

Defective 7000 Parts 6000 5000 4000 8000 7000

Late Delivery 6000 5000 4000 x 10 4


2 1.5

Economic Risk

1 0.5 0 0

5

Profit

10 x 10

4000

6000

8000 4000

Defective Parts

6

6000

8000

0

Late Delivery

1

2

Economic Risk

x 104

Figure 2. Non-dominated (Pareto-optimal) solutions obtained using non-preemptive goal programming.

x 106 10

Profit

5 0 8000

Defective 7000 Parts 6000 5000 4000 8000 7000

Late 6000 Delivery 5000 4000 x 10 4 2 1.5

Economic Risk

1 0.5 0 0

5

10

Profit

x 106

4000

6000

Defective Parts

8000 4000

6000

8000

Late Delivery

Figure 3. Non-dominated (Pareto-optimal) solutions obtained using compromise programming.

0

1

Economic Risk

2 x 104


6335

x 106 10

Profit

5 0 8000

Defective 7000 Parts 6000 5000 4000 8000 7000

Late 6000 Delivery 5000 4000


2 1.5

Economic Risk

1 0.5 0 0

5

10

Profit

4000

6000

8000 4000

Defective Parts

6

x 10

6000

8000

0

Late Delivery

1

Economic Risk

2 x 104

Figure 4. Non-dominated (Pareto-optimal) solutions obtained using fuzzy goal programming.

Table 7. Average and standard deviation objective functions’ values and computational time. Objective function Algorithm

Total profit

Defective parts

Late delivery

Economic risk

CPU time (s)

Non-preemptive GP

$5,082,207 $528,925 $5,087,375 $531,851 $5,068,581 $524,466

6184 632 6231 650 6283 667

5456 570 5508 588 5541 606

9388 3134 9140 2988 8866 3010

2.66 1.55 2.62 1.28 2.27 1.14

Compromise programming Fuzzy GP

Table 8. Probability of selected suppliers. Supplier Algorithm Non-preemptive GP Compromise programming Fuzzy GP

S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

0.212 0.217 0.222

0.109 0.102 0.092

0.162 0.168 0.177

0.010 0.007 0.009

0.079 0.083 0.092

0.216 0.213 0.203

0.002 0.004 0.004

0.158 0.150 0.144

0.050 0.054 0.056

0.002 0.001 0.001

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K.S. Moghaddam

Table 9. Final suppliers’ rank. Suppliers Algorithm Non-preemptive GP Compromise programming Fuzzy GP

S1

S2

S3

S4

S5

S6

S7

S8

S9

S 10

2 1 1

5 5 6

3 3 3

8 8 8

6 6 5

1 2 2

10 9 9

4 4 4

7 7 7

9 10 10


6. Conclusions and future research In this paper, a multi-objective mathematical model for supplier selection and order allocation in the closed-loop supply chain system is developed. We defined the problem over a set of potential suppliers, manufacturing, disassembly and refurbishing facilities in which parts are to be purchased from the suppliers or recycled from the returned products. Under this setting, a multi-objective optimisation problem was formulated to determine the best set of suppliers and refurbishing sites (strategic decisions) and to find optimal number of parts and products in the system (tactical decisions). In order to solve the mathematical model and find the non-dominated optimal solutions, we developed Monte Carlo simulation procedures integrated with three different variants of goal programming technique: non-preemptive goal programming, compromise programming and fuzzy goal programming sub-models. A numerical example is adopted to demonstrate the effectiveness of the proposed model and also to analyze the efficiency of the solution method in ranking the candidate suppliers and allocating the optimal order quantities in a closed-loop supply chain setting. It needs to be emphasised that one significant applied contribution of this research beneficial to practitioners is to develop three novel algorithms to avoid the subjective weighting from decision-makers in multi-criteria decision-making problems. These algorithms independently or alongside with each other can be used in other applications requiring multi-objective decision-making. Since this research is one of the early attempts that integrates supplier selection and order allocation in the closedloop supply chain systems, there are many opportunities for future research and expansion. For example, interested researchers can investigate the application of different supplier selection methods in the closed-loop supply chain systems. However, it should be noted that in general, the complexity of closed networks is higher than open supply chains and because of that computational time is expected to increase. In such situations, metaheuristic algorithms such as Genetic Algorithm and Simulated Annealing may be useful. The remanufacturing capacity of plants is limited and some of the returned products should be sent to the remanufacturer/subcontractor for further investigation. In our research, we assumed that the parameters of the optimisation model are deterministic, but in the real world they are usually not. For instance, some parameters like demand and number of returned products are associated with some kind of randomness. SP and chance constraint programming methods can be useful frameworks to take these probabilistic aspects into consideration. Acknowledgements The author is grateful to the reviewers and the editor whose valuable comments and suggestions significantly improved the overall content and presentation clarity of the paper.

Supplemental data Supplemental data for this article can be accessed here. [http://dx.doi.org/10.1080/00207543.2015.1054452]

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