# A multi-objective model for closed-loop supply chain optimization and efficient supplier selection in a competitive environment considering quantity discount policy

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## Abstract

Supplier selection and allocation of optimal order quantity are two of the most important processes in closed-loop supply chain (CLSC) and reverse logistic (RL). So that providing high quality raw material is considered as a basic requirement for a manufacturer to produce popular products, as well as achieve more market shares. On the other hand, considering the existence of competitive environment, suppliers have to offer customers incentives like discounts and enhance the quality of their products in a competition with other manufacturers. Therefore, in this study, a model is presented for CLSC optimization, efficient supplier selection, as well as orders allocation considering quantity discount policy. It is modeled using multi-objective programming based on the integrated simultaneous data envelopment analysis–Nash bargaining game. In this study, maximizing profit and efficiency and minimizing defective and functions of delivery delay rate are taken into accounts. Beside supplier selection, the suggested model selects refurbishing sites, as well as determining the number of products and parts in each network’s sector. The suggested model’s solution is carried out using global criteria method. Furthermore, based on related studies, a numerical example is examined to validate it.

## Keywords

Closed-loop supply chain Data envelopment analysis Nash bargaining game Supplier selection Quantity discount policy## Introduction

Production based on the needs and customers’ satisfaction, as well as material and products flow cost control are considered the main goals of manufacturers in different industries. Moreover, for a constant presence in the current competitive markets, it is particularly important to develop the relationships between suppliers and big manufacturers, efficiency control, maximize the value of returned items, and guarantee their systematic disposal, as well as increase environmental and/or legal concerns. Due to the overall mentioned issues, the concept of reverse logistic and closed-loop supply chain (CLSC) is significantly important (Francas and Minner 2009). In fact, the reverse logistic in the CLSC involves the precise transport, on time, and accurate transition of customer’s usable and unusable products to the right unit through the supply chain. This type of supply chain requires an essential concern in environmental issues to enhance the performance of overall supply chain regarding consistency and business operational criteria (Das and Posinasetti 2015). During recent years, researchers have been interested in this process in CLSC optimization. For example, Lee et al. (2009) formulized a mathematical model for a general network of CLSC with a supplier defining optimal amount of process and disassembly centers. Shi et al. (2010) developed a mathematical model for optimizing regeneracy system profit by developing a solution approach based on Lagrangian and Gradient algorithm. Moreover, in another research, Shi et al. (2011) studied a CLSC network in which demand and returned items are uncertain. Roghanian and Pazhoheshfar (2014) suggested a potential model using integer linear programming for designing a multi-product reverse logistic network and estimating demand with the minimum cost in an uncertain environment applied by production and recycle centers. In another study, Kaya and Urek (2016) suggested a mixed integer nonlinear programming model along with innovative solutions for decision making in location, inventory control, and pricing problems in a CLSC. A review of studies on the subject reveals that most researchers were involved with formulization of CLSC networks using facility location while not many of them used supplier selection to configure an integrated CLSC. Accordingly, in their research, Amin and Zhang (2012) suggested a multi-objective integrated model for configuration and supplier selection in the CLSC. Afterwards, Ramezani et al. (2013) presented a stochastic multi-objective model for designing an onward three-level logistic network (including supplier, manufacturer, and distribution centers), as well as a bi-level reverse logistic network (including collector and disposal sites) considering profit optimization, quality level, and responding to customer. Bottani et al. (2015) examined a model with multi-objective optimization of CLSC asset management including a pallet supplier, manufacturer, and seven retails based on Economic Order Quantity (EOQ) policy. Zhang et al. (2015) proposed a dual channel closed-loop supply chain model that improves the sustainability of products. They also used a two-stage optimization technique and Nash bargaining game to evaluate the impact of retail services and the degree of customer loyalty to the retail channel on the pricing of players in the centralized and decentralized dual-channel supply chain.

In general, in a buyer–supplier system, inventory decision making is structured independently. Inventory control problems have been investigated in many studies (Taleizadeh et al. 2009, 2010a; Hsueh 2011). Suppliers sometimes offer special sale prices to decrease inventories of certain items (Kim and Hwang 1989; Taleizadeh et al. 2010b, 2012, 2013a; Duan et al. 2010). Therefore, the supplier sets its favorable policies based on the product’s output and demand while the buyer may set its favorable policies to calculate order from supplier. Besides, in a competitive environment, one policy for suppliers to hold shares in the market is offering customers some incentives like discounts (Dahel 2003; Kokangul and Susuz 2009; Taleizadeh et al. 2013b; Taleizadeh and Pentico 2014). Because a mass purchase buyer would like to buy a larger amount of products with a lower unit price. A supplier offering quantity discounts is a common strategy to entice the buyers to purchase more (Monahan 1984; Taleizadeh et al. 2015). The main assumption underlying this policy is that competition is dynamic and the existing competition features may change after a new competitor arrives. Kamali et al. (2011) developed a multi-objective mixed nonlinear integer programming model for the first time to coordinate the system of single buyer and multi-vendors’ multi-period with certain demand under all-unit quantity discount policy for vendors. In the study, they used quantity discount policy per every unit of products for vendors as an incentive factor against the buyer. Accordingly, Hammami et al. (2014) suggested a stochastic model for supplier selection aiming at optimization of multi-period system’s total cost with diverse buyers and quantity discount.

During last years, considering the increased necessity of availability assurance of an efficient and coordinated supply chain, supplier selection is as a basic component. Because, one of the most important relationships between the supply chain members is the coordination between the focal company and the suppliers (Yousefi et al. 2016). Studies on supplier selection are mostly focused on decision-making methods (Ho et al. 2010). In the CLSC, the relationship between manufacturer and supplier is set in a closed-loop while in reverse logistic, new parts are provided from external suppliers. The point is that, compared to open-loop supply chains (OLSC), criteria related to production performance and parts’ features should be more important in CLSCs and reverse logistics. Because not only parts and supplier criteria should be considered, but also process criteria such as process ability and flexibility are essential. Furthermore, criteria related to environment and environmental protection is among reverse logistic and CLSC goals (Amin and Zhang 2012). Therefore, a close attention should be paid to process elements in supplier selection process of reverse logistic.

Although many researches have been carried out on the supplier selection in the open-loop supply chain, supplier selection in a closed-loop supply chain is a new issue. Govindan et al. (2015) studied 33 articles on green supplier selection examining different criteria and methods up to 2011. In their perspective, popular approaches in green supplier selection include Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), and Data Envelopment Analysis (DEA). Most of these methods have been offered for open-loop supply chain networks. Gradually, regarding the increased existing needs, researchers started either to make use of integrated methods or offer complicated mathematical models. For example, Kannan et al. (2013) used an integrated multi-criteria decision-making and multi-objective programming method for supplier selection and allocation in a certain green supply chain. On the other hand, due to the management focus on the efficiency and previous performance improvement in a competitive market, integrated approaches based on DEA are particularly important. To explain the competitive condition of market, an appropriate option is to use the game theory of cooperation, which has a considerable potential in management applications and supply chain performance improvement. Due to the ability of game theory to be integrated with most sciences, many studies have been executed in the field of designing and coordinating of supply chain’s different levels including effective designing and supply chain management (Talluri and Baker 2002), coordination of single-vendor multi-buyer supply chain (Chan and Kingsman 2007; Leng and Parlar 2010), and optimal supplier selection, pricing and inventory policy making in supply chain (Huang et al. 2012).

Therefore, from the previous studies, it can be concluded that for the first time, using multi-objective programming based on DEA–Nash bargaining game, the present study optimizes the CLSC with quantity discount policy and efficient supplier selection in a competitive environment. In fact, in this study, in addition to the maximization of profit, the concept of efficiency and competition, utilizing integrated DEA and Nash bargaining game approach has been added. In addition to synchronized evaluation and efficient supplier selection for different parts in a competitive environment, the proposed model makes decisions for set-up of refurbishing and disassembly sites. The general structure of the present study is as follows; the second section of the study is devoted to statement of the problem. The third section examines the proposed model. “Solution approach” prepares for an example to be tested in “Analysis of the results” in which computational results are presented and analyzed. Finally, in the last section, conclusion is presented along with suggestions for future more extended researches.

## Statement of the problem

On the other hand, as expressed, one of the most essential relationships between members of the supply chain is coordinating manufacturer (buyer) and suppliers in the supply chain, including the CLSC. So, with coordination among the members can be achieved an efficient supply chain. In the meantime, selecting suppliers based on the perspective of the buyer and allocating orders to their suppliers are one of the main issues to optimize the supply chain in various aspects such as reducing costs in the various policies available on the market that each member considers it. The aim of this study is modeling selection of suppliers in the CLSC considering various dimensions of the real world and using mathematical methods. So in this study, in addition to the maximization of profit and minimization of defective and delivery delay rates (using multi-objective programing), the concept of efficiency and competition, utilizing integrated DEA and Nash bargaining game approach has been added. Also, in this study for consideration the available policies between members of the chain, it is assumed that external suppliers—to increase their sales—perform the quantity discount policy. Also, the buyer to produce final products, to increase customer satisfaction, consider a policy based on controlling the supplier evaluation criteria such as safety and green packaging in the form of efficiency. Likewise, the external suppliers try to achieve the minimum efficiency interested by buyers per each needed part due to the competitive environment. This competition so that suppliers competing with others to sell their parts and improve the supply parts criteria from the perspective of the buyer’s (green supply criteria) and on the other hand, buyer is trying to select a supplier that have necessary efficiency as green choice score and had a higher score in competition with others. Therefore, in this study in addition to purchase price, criteria such as efficiency (according to the CLSC criteria), defective, and delivery delay rates are of great importance in supplier selection and order allocation. Because, coordination and cooperation between the two resources of manufacturer namely refurbishing site and suppliers can affect the production rate and finally change the products cost. Moreover, lack of returned parts and new parts lead to an increase in the inventory maintenance costs. Therefore, another strategic decision is choosing the refurbishing site location. When there are several alternatives for parts refurbishing site, manufacturer prefers to select the one with the lowest cost. In the following, the proposed model based on the problem is presented so the results demonstrate selection of suppliers in the competitive environment, with selecting the refurbishing sites, and determine the number of products and parts in each sector of the CLSC network.

## Proposed model

Assumptions, indexes, parameters, and decision variables of the proposed model

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The proposed model is assumed as a multi-product model | |

The proposed model is a single-period model | |

There’s no inventory shortage | |

The maximum production capacity for part | |

The products demand is certain and defined | |

The manufacturer (buyer) faces limited budget | |

The offered discount by each supplier is applied to whole order volume | |

There are no pre-determined suppliers, and there is a competition between suppliers on the efficiency of the part | |

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As mentioned above, the proposed model is a multi-objective programming model. The objective functions include total profit, defective rate, delivery delay rate, and efficiency in competitive environment that are investigated in the following.

### Total profit

*z*

_{1}mentioned in Eq. (1) maximizes the total profit. The first section of this objective function indicates the profit resulted from product selling. The second section indicates the cost of buying parts from suppliers considering quantity policy. So that, when it falls into a discount interval, the proposed price is exerted to all purchase quantity. The third section indicates cost of disassembly taken place in disassembly site, and it consisted of disassembly cost of each unit multiply the number of parts to be disassembled. The cost of refurbishing and disposal sites is calculated in sections four and five. Furthermore, the sixth and seventh sections indicate the set-up cost of refurbishing and disassembly sites. It is to be noted that refurbishing sites are selected based on the maximum profit.

### Defective rate

*z*

_{2}mentioned in Eq. (2) minimizes the defective rate of parts bought from selected external suppliers. So that, as much as possible, suppliers with less defective rates are selected.

### Delivery delay rate

*z*

_{3}mentioned in Eq. (3) minimizes the delivery delay rate of parts bought from selected external suppliers. So that, as much as possible, suppliers with less delivery delay rates are selected.

### Efficiency in competitive environment

In today’s world, DEA is known as one of the most important methods for efficiency evaluation. In general, the efficiency is defined as the level and quality at which total interested goals are achieved (Färe et al. 1985). In 1957, Farrell (1957) suggested this method by measuring performance of one production unit. In his model, only one input and one output were considered. He failed to develop his model in multi-input/output conditions. Afterwards, other scientists like Lee et al. (2001) developed Farrell model proposing a new model that was able to measure efficiency considering multi-input/multi-output and was then named data envelopment analysis (DEA). This method in various fields such as energy systems (Rezaee et al. 2012a), manufacturing systems (Baghery et al. 2016; Rezaee et al. 2016a), banking systems (Shafiee et al. 2016) and healthcare systems (Rezaee et al. 2016b), have been used. In general, DEA popularity comes from its ability to examine complicated and often unclear relationships between several inputs and outputs. Principally, using mathematical models, efficiency of one unit is optimized over other units; that is, relative efficiency of each Decision Making Unit (DMU) is evaluated based on its inputs and outputs. However, it should be noted that the evaluated units should be quite equal, i.e., with quite similar inputs and outputs. In some cases, due to excess of decision-making units, too many linear programming models are required resulting in a time consuming solution process. In this regard, in their study of integrated locating-DEA models, Klimberg and Ratick (2008) proposed a model named Simultaneous Data Envelopment Analysis (SDEA) to remove the problem in 2008. Accordingly, in the present study, SDEA model is used to simultaneously calculate the efficiency of candidate suppliers.

*u*is attainable from the strategy set

*S*. Also, the resulted utilities should be larger and/or equal to the minimum utility of players

*b*. So in this section, aiming at efficiency optimization, supplier selection is examined using DEA model. This model aims to find states in which buyer who need different parts to produce their final product, seek efficient suppliers. In a competitive environment, it is assumed that the buyer defines a minimum efficiency level of supplier selection per each part. This issue creates a competitive environment for suppliers to build better parts according to buyer’s criteria. Combining SDEA with Nash bargaining game, and considering the minimum required efficiency per each part (

*E*

_{ i }), we have the following objective function for supplier selection in a competitive environment:

Equation (6) guarantees that the amount of part *i* ordered from supplier *k* equals to total part *i* order in discount intervals offered by supplier *k*. Equations (7) and (8) show that the amount part *i* ordered from supplier *k* falls into discount interval offered by supplier *k*. Equation (9) states that in the case of selection supplier *k* for part *i*, order should be accomplished in only one of offered discount intervals. Equation (10) indicates the relationship between *y* _{ ik } and *y* _{ ikd }. Equation (11) guarantees that the number of produced parts equals to the total number of refurbished and purchased parts. Equation (12) indicates that costs of buying different parts for each selected supplier should not exceed the purchase budget available to the buyer. Equation (13) states that the disassembled parts equals to reusable and waste parts. Equation (14) indicates the relationship between parts and products. Equation (15) suggests that the amount of product manufacturing should be less than or equal to maximum production capacity. Equation (16) states that the amount of resources applied in part *i* for disassembly should be less than or equal to maximum capacity of disassembly site of part *i*. Equation (17) indicates that the applied resources for part *i* to be disassembled in set-up site *l* should be less than or equal to maximum capacity of refurbishing site *l* for part *i*. Equation (18) shows that the number of manufactured products should be equal to demand. Equations (19) and (20) indicate the optimal percentage of reusable and waste parts. Equation (21) implies the constraint of maximum percentage of returned parts. Equation (22) shows that the number of set-up refurbishing sites should be less than and/or equal to maximum number of launchable refurbishing sites. Equation (23) guarantees that if there is *j* returned production, disassembly site for production *j* is to be set up. Constraint (24) indicates that per each part those suppliers are selected who have the minimum efficiency required by that part. Equation (25) guarantees that the harmonized total input of each decision-making units (a combination of suppliers and parts) equals to variable zero and one. This equation should be considered in all decision-making units. Equation (26) implies the amount of inefficiency for harmonized total output of each decision-making unit, as well. This equation should be considered in all decision-making units. Equation (27) indicates that the harmonized total output should be less than its correspondent harmonized total input. Equations (28) and (29) indicate that input and output weights should be a non-negative value. Constraint (30) guarantees that the harmonized output for each decision making unit, as well as for each output type is less than and/or equal to 1. Equation (31) indicates the maximum number of selected suppliers per each part. Equations (32) and (33) show the quantity constraints for discount intervals; and Eqs. (34) and (35) indicate the sign limitation of decision-making variables.

## Solution approach

*z*

_{ i }*). This section aims to change a multi-objective function into a single-objective function changing the objective functions of the main model in different intervals. Thus, to avoid the effect of these changes on the results, the global criteria method is used as a normalization method. Consequently, using global criteria method, the final objective function is expressed as Eq. (36):

As shown in Eq. (36), to consider decision maker’s idea, different weights may be given to the objective functions; so that *w* _{ i } is *i*th objective functions’ weight according to decision maker’s idea and equation ∑ _{ i=1} ^{4} *w* _{ i } = 1 is established. Using this approach, if management gave the function a larger weight, in the state of simultaneous optimization, the result would be closer to the interested function’s optimal solution. In Eq. (36), first, the optimal amount of each objective function (*z* _{ i }*) is calculated independently considering all constraints of problem, and a new function is created as expressed in the equation.

## Analysis of the results

Refurbishing sites’ parameters

Parameter | | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

| 1 | 3 | 2 | 3 | 3 | 4 |

2 | 4 | 4 | 3 | 2 | 4 | |

3 | 4 | 3 | 4 | 3 | 4 | |

4 | 4 | 3 | 3 | 4 | 3 | |

5 | 3 | 3 | 4 | 4 | 4 | |

| 1 | 4 | 5 | 4 | 4 | 4 |

2 | 4 | 4 | 4 | 4 | 5 | |

3 | 5 | 5 | 4 | 5 | 5 | |

4 | 4 | 5 | 5 | 5 | 5 | |

5 | 4 | 4 | 4 | 5 | 4 | |

| 1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 1 | 1 | 1 | 1 | |

3 | 1 | 1 | 1 | 1 | 1 | |

4 | 1 | 1 | 1 | 1 | 1 | |

5 | 1 | 1 | 1 | 1 | 1 | |

| 1 | 9000 | 10,000 | 8500 | 10,000 | 9500 |

2 | 10,000 | 9000 | 8500 | 10,000 | 9500 | |

3 | 9000 | 10,000 | 8000 | 9500 | 10,000 | |

4 | 8500 | 9000 | 10,000 | 9500 | 8500 | |

5 | 9000 | 9500 | 10,000 | 9000 | 8500 |

Product’s parameters

| 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

| 150 | 200 | 220 | 230 | 250 |

| 1 | 2 | 2 | 2 | 3 |

| 30 | 35 | 30 | 30 | 35 |

| 1400 | 1500 | 1400 | 1400 | 1500 |

| 5 | 5 | 4 | 5 | 4 |

Amount of part *i* used in each *j* product unit (*q* _{ ij })

| 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

1 | 2 | 1 | 3 | 1 | 3 |

2 | 1 | 3 | 2 | 1 | 2 |

3 | 3 | 2 | 1 | 4 | 1 |

4 | 2 | 1 | 2 | 3 | 4 |

5 | 1 | 3 | 2 | 2 | 3 |

Part’s parameters

| 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

| 9000 | 10,000 | 8500 | 10,000 | 9500 |

| 4 | 5.5 | 2.5 | 3.5 | 3.5 |

| 3 | 4 | 4 | 4 | 3 |

| 1 | 1 | 1 | 1 | 1 |

| 0.50 | 0.55 | 0.60 | 0.55 | 0.50 |

Parameters of suppliers and manufactured parts

Parameter | | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

| 1 | 0.10 | 0.05 | 0.10 | 0.07 | 0.11 |

2 | 0.05 | 0.05 | 0.10 | 0.10 | 0.05 | |

3 | 0.10 | 0.05 | 0.10 | 0.05 | 0.07 | |

4 | 0.05 | 0.10 | 0.07 | 0.10 | 0.60 | |

5 | 0.10 | 0.11 | 0.05 | 0.10 | 0.10 | |

| 1 | 0.10 | 0.08 | 0.06 | 0.10 | 0.11 |

2 | 0.05 | 0.10 | 0.06 | 0.06 | 0.06 | |

3 | 0.09 | 0.07 | 0.10 | 0.10 | 0.10 | |

4 | 0.06 | 0.05 | 0.06 | 0.11 | 0.07 | |

5 | 0.09 | 0.09 | 0.08 | 0.07 | 0.09 |

Quantity discount intervals

| | | | | | | |
---|---|---|---|---|---|---|---|

1 | 1 | 0 < | 14 | 3 | 4 | 0 < | 15 |

2100 ≤ | 13 | 2500 ≤ | 14 | ||||

4200 ≤ | 12 | 5000 ≤ | 13 | ||||

2 | 0 < | 14 | 5 | 0 < | 14 | ||

2300 ≤ | 13 | 2300 ≤ | 13 | ||||

4600 ≤ | 12 | 4600 ≤ | 12 | ||||

3 | 0 < | 18 | 4 | 1 | 0 < | 15 | |

4500 ≤ | 17 | 3600 ≤ | 14 | ||||

9000 ≤ | 16 | 7200 ≤ | 13 | ||||

4 | 0 < | 12 | 2 | 0 < | 14 | ||

1800 ≤ | 11 | 2000 ≤ | 13 | ||||

3600 ≤ | 10 | 4000 ≤ | 12 | ||||

5 | 0 < | 19 | 3 | 0 < | 18 | ||

2800 ≤ | 18 | 4600 ≤ | 17 | ||||

5600 ≤ | 17 | 9200 ≤ | 16 | ||||

2 | 1 | 0 < | 16 | 4 | 0 < | 19 | |

2100 ≤ | 15 | 2600 ≤ | 18 | ||||

4200 ≤ | 14 | 5200 ≤ | 17 | ||||

2 | 0 < | 21 | 5 | 0 < | 14 | ||

4600 ≤ | 20 | 4500 ≤ | 13 | ||||

9200 ≤ | 19 | 9000 ≤ | 12 | ||||

3 | 0 < | 14 | 5 | 1 | 0 < | 18 | |

1800 ≤ | 13 | 3600 ≤ | 17 | ||||

3600 ≤ | 12 | 7200 ≤ | 16 | ||||

4 | 0 < | 16 | 2 | 0 < | 15 | ||

2100 ≤ | 15 | 4500 ≤ | 14 | ||||

4200 ≤ | 14 | 9000 ≤ | 13 | ||||

5 | 0 < | 14 | 3 | 0 < | 14 | ||

4300 ≤ | 13 | 3000 ≤ | 13 | ||||

8600 ≤ | 12 | 6000 ≤ | 12 | ||||

3 | 1 | 0 < | 13 | 4 | 0 < | 13 | |

4800 ≤ | 12 | 4800 ≤ | 12 | ||||

9600 ≤ | 11 | 9600 ≤ | 11 | ||||

2 | 0 < | 23 | 5 | 0 < | 15 | ||

3300 ≤ | 22 | 3800 ≤ | 14 | ||||

6600 ≤ | 21 | 7600 ≤ | 13 | ||||

3 | 0 < | 20 | |||||

4600 ≤ | 19 | ||||||

9200 ≤ | 18 |

*I*

_{ 1ki }(minimum of which is desirable) while product safety and green packaging was defined as outputs

*O*

_{ 1ki }and

*O*

_{ 2ki }(maximum of which is desirable). Values of these criteria are provided in Table 8.

Input and output values for each decision making unit

Evaluation criteria | | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Transportation cost ( | | 90 | 98 | 84 | 84 | 89 |

| 87 | 93 | 96 | 98 | 96 | |

| 157 | 181 | 193 | 186 | 177 | |

| 183 | 174 | 187 | 192 | 193 | |

| 238 | 219 | 232 | 234 | 243 | |

Safety ( | | 336 | 348 | 334 | 335 | 345 |

| 326 | 327 | 324 | 342 | 348 | |

| 365 | 358 | 378 | 398 | 396 | |

| 399 | 352 | 393 | 372 | 353 | |

| 445 | 432 | 421 | 446 | 422 | |

Green packaging ( | | 43 | 49 | 47 | 46 | 48 |

| 43 | 50 | 44 | 48 | 44 | |

| 75 | 64 | 75 | 65 | 71 | |

| 73 | 63 | 73 | 73 | 69 | |

| 99 | 100 | 93 | 98 | 100 |

Independent and simultaneous optimization of objective functions for different weight sets

No. | | | | | |
---|---|---|---|---|---|

S01 | | 368,102.0 | 4297.230 | 4371.480 | 0.04967278 |

S02 | | 249,105.0 | 3114.580 | 4304.020 | 0.03451588 |

S03 | | 257,755.0 | 4972.812 | 3758.375 | 0.05380110 |

S04 | | 257,355.0 | 4768.120 | 4560.873 | 0.09355841 |

S05 | | 336,326.0 | 3394.030 | 4579.220 | 0.03445624 |

S06 | | 368,102.0 | 4297.230 | 4371.480 | 0.04716222 |

S07 | | 357,104.0 | 4497.250 | 4385.500 | 0.06544845 |

S08 | | 315,804.0 | 3206.580 | 4435.270 | 0.03451588 |

S09 | | 256,706.0 | 3114.580 | 4304.020 | 0.03451588 |

S10 | | 257,678.0 | 3288.196 | 4456.389 | 0.06066799 |

S11 | | 294,254.0 | 5066.250 | 3795.750 | 0.05773662 |

S12 | | 253,430.0 | 3200.850 | 4254.993 | 0.01958798 |

S13 | | 261,056.0 | 4886.250 | 3793.010 | 0.06538074 |

S14 | | 282,972.0 | 4776.250 | 4506.050 | 0.09355766 |

S15 | | 250,155.0 | 4464.416 | 4495.820 | 0.09355756 |

S16 | | 246,421.0 | 4667.500 | 4455.830 | 0.09355755 |

S17 | | 330,755.0 | 3316.570 | 4545.260 | 0.02281606 |

S18 | | 360,902.0 | 4456.230 | 4183.980 | 0.04153408 |

S19 | | 325,904.0 | 4705.078 | 4409.531 | 0.08762127 |

S20 | | 257,030.0 | 3114.580 | 4304.020 | 0.02380733 |

S21 | | 257,823.0 | 3393.170 | 4443.520 | 0.06632999 |

S22 | | 261,295.0 | 4667.500 | 4455.830 | 0.09355745 |

S23 | | 330,755.0 | 3316.570 | 4545.260 | 0.03451588 |

S24 | | 336,101.0 | 3977.310 | 4495.510 | 0.06785256 |

S25 | | 349,904.0 | 4556.250 | 4158.000 | 0.07074653 |

S26 | | 315,804.0 | 3206.580 | 4435.270 | 0.03451365 |

S27 | | 291,372.0 | 3400.850 | 4455.530 | 0.06633212 |

S28 | | 257,353.0 | 3364.484 | 4410.701 | 0.06596480 |

S29 | | 317,780.0 | 3286.820 | 4395.510 | 0.02425277 |

S30 | | 349,904.0 | 4556.250 | 4158.000 | 0.07074652 |

S31 | | 259,917.0 | 3896.400 | 4130.730 | 0.06758118 |

S32 | | 277,197.0 | 4487.500 | 4503.800 | 0.09355754 |

S33 | | 279,697.0 | 4676.250 | 4466.050 | 0.09355753 |

S34 | | 249,430.0 | 4464.416 | 4495.820 | 0.09355745 |

S35 | | 314,123.0 | 3917.550 | 4345.760 | 0.07561865 |

The amount of allocated order to suppliers in independent and simultaneous optimization of objective functions

First objective function | Second objective function | Third objective function | Fourth objective function | Multi objective function | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | | | | | | | | | | | | | | | | | | |

1 | 2 | 3 | 5301 | 1 | 2 | 3 | 6999 | 1 | 3 | 3 | 10,800 | 1 | 1 | 3 | 5850 | 1 | 1 | 3 | 4200 |

1 | 4 | 3 | 5499 | 1 | 4 | 3 | 3801 | 2 | 1 | 3 | 6225 | 1 | 2 | 3 | 4950 | 1 | 2 | 3 | 6600 |

2 | 5 | 3 | 9825 | 2 | 5 | 3 | 9825 | 2 | 3 | 3 | 3600 | 2 | 1 | 3 | 5225 | 2 | 5 | 3 | 9825 |

3 | 1 | 3 | 11,775 | 3 | 2 | 2 | 4375 | 3 | 1 | 3 | 9906 | 2 | 2 | 2 | 4600 | 3 | 1 | 3 | 11,775 |

4 | 5 | 3 | 12,975 | 3 | 4 | 3 | 7400 | 3 | 2 | 1 | 1869 | 3 | 1 | 3 | 11,775 | 4 | 1 | 3 | 10,975 |

5 | 4 | 3 | 12,000 | 4 | 1 | 3 | 10,999 | 4 | 1 | 3 | 7200 | 4 | 1 | 2 | 7012 | 4 | 2 | 2 | 2000 |

4 | 5 | 1 | 1976 | 4 | 2 | 3 | 5775 | 4 | 2 | 3 | 5963 | 5 | 1 | 1 | 3001 | ||||

5 | 3 | 3 | 8999 | 5 | 4 | 3 | 12,000 | 5 | 2 | 3 | 12,000 | 5 | 3 | 3 | 8999 | ||||

5 | 4 | 1 | 3001 |

Other results from simultaneous optimization of objective functions

| 1 | 2 | 3 | 4 | 5 | | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|---|---|---|---|---|

Production amounts | 1400 | 1500 | 1400 | 1400 | 1500 | 1 | – | 3600 | – | – | – |

Returned item amounts | 700 | 750 | 700 | 700 | 750 | 2 | – | – | – | 3275 | – |

| 1 | 2 | 3 | 4 | 5 | 3 | – | 3925 | – | – | – |

Disassembly amounts | 7200 | 6550 | 7850 | 8650 | 8000 | 4 | – | 4325 | – | – | – |

Waste amounts | 3600 | 3275 | 3925 | 4325 | 4000 | 5 | 4000 | – | – | – |

Reviewing Tables 10 and 11, it can be claimed that amounts of parts ordered from suppliers, amount of waste and disassembly parts, as well as amounts of production and returned items during decision making period are determined in such a way that the current costs are minimized, while model limitations such as the number of maximum supplier selection per each part, maximum level of suppliers’ discount interval (supplier’s capacity), buyer’s budget, and other constraints are not violated in a competitive environment. Furthermore, Table 11 states that considering the presence of returned items, disassembly sites are settled for all products to maximize chain’s profit. Also, refurbishing sites 1, 2, and 4 are settled for refurbishing products so that part troubleshooting is done with the minimum site number avoiding extra set-up costs.

## Conclusion

During recent years, reverse logistic and CLSC have been taken more serious due to increased environmental concerns, stronger laws, as well as its excessive trading profit. In addition, supplier selection and optimal order allocation are the most important process in a close-looped supply chain. So that in the real world, in the competitive environment, suppliers provide incentives to the buyer such as discount and guarantee of production parts efficiency. The main objective of this study was to develop a model for designing a CLSC considering efficiency in competitive environments, as well as external suppliers’ quantity discount policies. In other words, the aim of this study is adding both efficiency and competition concepts to dimensions of supplier selection problem in the CLSC. Therefore, an integrated model was proposed using multi-objective programming based on DEA–Nash bargaining game to cover the circumstances. This model was consisted four objectives including total profit, defective rate, delivery delay rate, and efficiency that then were put together into one objective using global criteria method. In addition to supplier selection, the proposed model adopts decisions related to refurbishing and disassembly site set-up, as well as part and product amounts in existing in closed-loop network’s ties including manufacturer and sites for disassembly, refurbishing, and disposal. So that, in a CLSC, to produce its productions, the manufacturer purchases its needed parts from external efficient suppliers and/or set-up refurbishing sites. The proposed model can be used in industries such as household electrical appliances, accessories and electronic components, automobile parts and similar cases. The results of simulated example show that increasing efficiency objective function is synonymous with decreasing organization (buyer) profit, because buyer pays more prices for selling parts from efficient suppliers. The results demonstrated that the criteria considered in the evaluation of suppliers’ efficiency are in conflict with the defective rate. It is specified the importance of taking the efficiency objective function. This study is expandable considering uncertainty of other model’s certain parameters or fuzzy demand. More expandable issues resulted from this study including simultaneous competition between manufacturers and suppliers, as well as studying the pricing process between them may be considered in future researches.

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