Design of a green closed-loop location-routing supply ...

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Available online at www.iiec2016.com

International Conference on Industrial Engineering (ICIE 2016) Iran Institute of Industrial Engineering

ICIE (2016) 000–000

Kharazmi University

Design of a green closed-loop location-routing supply chain with spare part consideration M. Zhalechian, R. Tavakkoli-Moghaddam* School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran * Corresponding author: E-mail address: [email protected]

Abstract In this paper, a new green closed-loop location-routing model is proposed. The presented model consists of a bi-objective mathematical model to (i) minimize total establishing costs of facilities and transportation costs (ii) minimize the environmental impacts of greenhouse gas emissions and fuel consumption. The proposed model considers strategic, tactical and operational decisions holistically. Furthermore, a game-based method is utilized to deal with the multiple conflicting objectives of the proposed model. Finally, comprehensive analysis is done to demonstrate the effectiveness of the proposed model. Keywords: Closed-loop supply chain; green supply chain, vehicle routing, game-based method

1. Introduction The traditional definition of supply chain management (SCM) is a process of planning, implementing and controlling the operations from a supplier to a set of customers based on an efficient basis. Despite the forward logistic, a reverse logistic focuses on transferring products from customer to supplier. The integration of forward and reverse logistics results in a closed-loop supply chain (CLSC) which is gained a significant importance recently. In a CLSC, return of damaged product, unsold or end-of-life products through a remanufacturing facility transfer into new products or sold as spare parts or new products to a secondary market [1]. Nowadays, companies have noticed that the spare parts and after-sales service markets could have a huge profit potential for them. After studying more than 80 multi-national companies in different industries in a report, it has been declared that more than 50% of the total revenue of many high tech companies are gained through spare parts and after-sales service [2]. In today’s competitive environment, making tactical/operational decisions alongside the strategic decisions is of crucial importance. There are a limited number of studies in the supply chain network design (SCND) that are entirely incorporated in tactical and operational planning levels of analysis. A vitally important operational decision concerns finding optimal vehicle routes which are used to transfer the products through network [3]. Although finding optimal vehicle routes can lead to a significant reduction in costs and service quality, many of the studies in the area of CLSC did not consider this important operational decision. Distribution network at the end of the chain is significantly important due to the huge flow of small products from retailers to the end-costumers. Hence, using a vehicle routing problem could be a help to save a huge cost resulted in delivering products from the retailers to customers [4]. Regardless of the system’s cost efficiency, sustainability is becoming a growing interest due to the concern about environmental and social impacts (SIs) of business activities [5]. The World Summit of Sustainable Development (WSSD) defines the sustainability as a balance between economic benefits, environmental protection and social developments. Following WSSD, environmental impacts (EIs) are one of a significant pillar of sustainability. There are different environmental metrics such as air emissions, energy use, Greenhouse Gas (GHG) emissions, energy consumption, water consumption and etc. [6]. The proposed study does not focus on the production process of a manufacturing company. Indeed, distribution of products through forward supply chain and collecting and remanufacturing the returned products in the reverse supply chain are the main focus of the proposed study. Transportation of products both in the forward and reverse logistic have an important role in the considered supply chain. Transportation network has a key role in the EIs and affects the environment by GHG emissions and in particular carbon dioxide (CO2). In most of the studies in the literature, measuring CO2 emissions is done through simple and linear mathematical models, in which little attention has been made toward fuel consumption and the

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00 vehicle, road and air physical conditions such as, average acceleration of vehicle, weight of vehicle, air friction and etc. 2. Literature review Routing and location problems is one of the major concerns in logistics, having implications on the complete supply chain [7]. The location routing problem (LRP) is relatively new which considers two key components of a logistics system, namely facility location problem (FLP) and the vehicle routing problem (VRP) [8]. A LRP is defined as a special case of VRP where there is a need to determine optimal number and location of depots simultaneously with finding vehicle routes from depots to customers in order to minimize costs associated with locating depots and distribution customers. There are some review papers dedicated to LRP literature and the interested readers refer to these review papers [9-12]. In the area of supply chain network, there are numerous papers which studied the forward supply chain with different criteria and objective functions. A comprehensive review of this field is done by Farahani, et al. [13]. Similarly, in reverse logistics, various studies have been done including recycling, remanufacturing and etc. Due to the focus of many companies on devising a CLSC, several studies have been done in the field of CLSC. Nowadays, the recent studies regarding closed-loop supply chain network design are discussed in more detail. Lu and Bostel [14] developed a deterministic MILP model for integrating forward/backward flows and designed a supply chain considering remanufacturing activities. They solved it using a solution algorithm based on a Lagrangian heuristic. Kannan, et al. [15] proposed a mathematical model for closed-loop multi-echelon distribution inventory supply chains for build-to-order environments and compared performance of a genetic algorithm and a particle swarm optimisation algorithm for solving the proposed model. In another study, a MILP model for a remanufacturing system was designed by integrating forward and reverse flows, which was solved using CPLEX [16]. El-Sayed, et al. [17] proposed a multiperiod and multi-echelon stochastic MILP model for designing an integrated supply chain with the objective of maximizing the expected supply chain profit. Abdallah, et al. [18] and Diabat, et al. [1] considered a CLSC, in which the remanufacturing centers (RCs) serve as the intermediary between the recovery of the products and their re-entry to the market as spare parts. Although green supply chains are studied in several papers recently, most of the studies in green aspect belong to VRP. Erdoğan and Miller-Hooks [19] proposed a green vehicle routing model which aims to minimize the fuel consumption through minimizing the total traveled distance. They also considered the need for refueling in the route plans in order to avoid the risk of running out of fuel. There are other works in green VRP which considered factors related to the features of vehicle. Suzuki [20] developed an approach in VRP to minimize the distance that a vehicle with heavy payload must travel in a given tour. Bektaş and Laporte [21] considered more parameters related to vehicle features such as vehicle load, speed, total cost and environmental green vehicle routes. They tried to make a trade-off between aforementioned parameters. A robust optimization approach for a green pickup and delivery problem introduced by Tajik, et al. [22]. In their proposed model, the objective function aims to minimize the total costs related to road physical condition, weight of vehicle and the load it carry and the penalty for tardiness and earliness in arrival time of pickup customers. For more precise details, interested readers refer to the review paper of Eskandarpour, et al. [23]. A brief survey on the literature shows that the there is a gap in the integration of strategic, tactical and operational decisions in a CLSC. As discussed before, one of the important tactical/operational decisions in the CLSC is vehicle routing decision. Hence, we consider vehicle routing in the considered CLSC network. In addition, we provide a more comprehensive evaluation of environmental factors including CO2 emissions (i.e., regarding to different factors of vehicles, roads and air condition) and fuel consumption. To address the aforementioned gaps in the literature, we develop a green closed-loop supply chain with vehicle routing model. The presented model can be used to investigate trade-off between cost and EIs including CO2 emissions and fuel consumption.

3. Problem description and mathematical modeling 3.1. Modeling framework Figure 1 shows a schematic view of the structure of proposed closed-loop supply chain network and the interaction between its chain members. In the forward logistic, multiple suppliers ships several types of products through distribution centers (DCs) to different number of retailers. It should be noted that the delivery of products from DCs to

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00 retailers is performed by vehicles through the existing routes. Indeed, a vehicle must leave a DC, visit the retailers on its route and then return to its departing DC. In this network, the responsibility of collecting and sorting the returned products from customers is given to the retailers. Hence, each retailer collects and sorts the returned products and then sends them to a RC. In the RC, the returned products are remanufactured as spare parts and then pushed back to the retailers through the forward supply chain. Following Diabat et al. [1], it is assumed that each product consists of subassemblies, in which one main subassembly is salvaged and M subassembly are shipped from suppliers to RC in order to remanufacture a new product that can be used as a spare part. To eliminate shipping costs from RCs to DCs, an RC can only be opened when a DC is opened at the same site. Notably, the returned products do not influence the demand of the original products. In the reverse logistics, the products that have potential to use as spare parts are transported from retailers to the remanufacturing facilities through vehicles. A normal distribution is a good approximation for sufficiently large demand values [24]. Hence, in our model, the demand of the retailers and the return flows follow a normal distribution of (i.e., ) and (i.e., ), respectively, where . More precisely, it is assumed that a certain share of previous demand quantity will return.

Supplier Open DC Potential DC Open DC & RC Retailer

Figure 1. The structure of the proposed closed-loop supply chain network.

3.2. Mathematical programming Sets: Index of vehicles Aggregate index of retailers and potential DCs Index of DCs, , k, l Index of retailers, , m Index of potential RCs, Index of products , t Index of time periods, Parameters: Distance between node k to node j Fixed cost of using vehicle v Unit cost of shipment product p from supplier to DC j Transportation cost between retailer k and RC m in period t Fixed cost of establishing DC j Fixed cost of establishing RC m Transportation time between node k and node l Environmental impact of fuel consumption Environmental impact of emission Average acceleration of vehicle v Coefficient of rolling resistance Front space of vehicle v Empty weight of vehicle v

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00 Coefficient of air friction Capacity of vehicle v used for transportation between DCs and retailers Capacity of vehicles used for transportation between retailers and RCs | | | | Number of retailers in set K A very large number Decision variables: 1; if DC j is opened; Otherwise, 0 1; if RC m is opened; Otherwise, 0 1; if retailer k is served by DC j, 0; otherwise 1; if returns from retailer k are collected by RC m, 0; otherwise 1; if there is a route of vehicle v between node k and node l in period t; Otherwise, 0 3.2.1. Objective function Following the above notations the objective functions of the proposed model are presented as follows: ∑

∑

∑∑∑(

∑

)

∑ ∑∑(

∑

) (1)

(∑ ∑ ∑ ∑

∑ ∑ ∑∑

)

∑ ∑∑

∑ ∑ ∑∑ ∑ ∑ ∑∑

⁄

(2)

The presented model consists of two objective functions. The first objective function (1) minimizes the total cost, including fixed costs of establishing DCs/RCs and transportation costs. The first and second terms of objective function (1) related to fixed establishing costs of DCs and RCs. The third term is the transportation cost between supplier and DCs. Similarly, the fourth term is the transportation cost between supplier and RCs. The fifth term is the transportation costs between DCs and retailers. The sixth term is the transportation costs between retailers and RCs. The objective function (2) related to EIs of CO 2 emissions and fuel consumption. The three components in the objective function (2) measure the EIs of CO2 emissions regarding to the vehicle, road and air physical conditions (i.e. surface, slope, air fraction, etc.) and weight of vehicles. 3.2.2. Constraints ∑∑ ∑∑

(3) ∑

(4) (5)

∑

∑

∑∑ ∑

(6) (7)

∑

(8) (9) (10) (11)

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00 ∑

(12)

∑

(13) ∑ ∑

(14) (15)

Equation (3) ensures that each retailer is placed on just one vehicle route. Constraint (4) is the capacity constraint associated with vehicles used for transportation between DCs and retailers. Constraint (5) is related to the sub-tour elimination. This constraint guarantees that each route contains one DC and some retailers. Equation (6) is related to flow conservation. It ensures that the routes remain circular and whenever a vehicle visits a DC or retailer in a time period; it should leave the visited DC or retailer in that time period. Constraint (7) makes sure that only one DC is existed in each route. Constraint (8) links the routing and allocation decision variables; if vehicle v starts its trip from DC j and serves retailer k during its trip, then retailer k will be assigned to DC j. Equation (9) implies that there is not any route between DCs. Constraint (10) states that assignment to a DC j is not possible unless a DC is opened at j. Similarly, constraint (11) states that assignment to a RC m is not possible unless a RC is opened at m. Equation (12) ensure that each retailer is assigned to one DC. Equation (13) indicates that each retailer must be assigned to exactly one RC. Constraint (14) implies that a RC can be opened when a DC has been opened at the same site. Constraint (15) calculates the number of vehicles needed to transfer return products form retailer k to RC m at period t. 4. Proposed approach In this section, at first, we briefly explain the modified game theory approach. Afterward, we introduce the steps of the game-based approach to deal with the conflicting objective functions. 4.1. Modified game theory approach In the literature, various approaches have been introduced to solve the multi-objective programming model. Among them, we have utilized a negotiation base solving approach which is proposed by Annamdas and Rao [25]. There are two major groups of games in the game theory: non-co-operative and co-operative games. In the non-cooperative games, players make decision independently. On the contrary, in the co-operative games, they may enforce co-operative behaviors. Indeed, this type of games is a competition between coalition players rather than individual players. For the purpose of understanding game-based optimization approach, consider three objective functions and , in which the value of them related to decision variables and . In the game-based optimization approach, each objective function associated with a player. Hence, each player desires to minimize his/her own objective function. Figure 2 shows the schematic view of a multi-objective optimization problem. In this Figure, the contours of and are depicted. By assuming that the players do not co-operate with each other, nodes , and (i.e., called the Nash equilibrium solutions) are the candidate for three-objective minimization problem. Despite the non-cooperative game in which players can not deviate unilaterally form their Nash equilibrium point, in the co-operate game, players can improve their situation unilaterally. Subsequently, any player, can forces the other players to play at the equilibrium of his/her own choice by choosing a proper value of his/her decision variable [25]. In this way, any point in the shaded region of Figure 2 will provide a better solution rather than their Nash equilibrium solutions for all of the objective functions. Since there is more than one solution in the shaded region, the concept of Pareto optimal solutions can be helpful to choose a compromise solution that is acceptable to all of the players in the game. In Figure 2, the Pareto optimal solutions are shown as the nodes between boundaries of red region.

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00

Increasing f3

O3 N3

Increasing f2

N2 O2

N1

O1

Increasing f1

Figure 2. Co-operative and non-co-operative game theory.

4.2. The main steps of the game-based approach The steps of the game-based approach are presented as follows: Step1: Determine the positive ideal solution and negative ideal solution for each objective function. Step2: Normalize each objective function in order to change its magnitude and scale it between zero and as Eq. (16). (16)

Step3: The Pareto optimal solution set can be calculated as the following formulation: (17) where

should be minimized under the stated constraints for all combination of weights vector (∑

).

In order to make sure that each of the normalized objective functions will be as far away as possible from its worst possible value, a super-criteria is introduced as Eq. (18). (18)

∏

Therefore, Eq. (18) can be replaced by Eq. (19) to find Pareto optimal solution which represents a compromise solution as: (19)

∏ where Step4: Minimize

to find

which yields the best compromise solution of multi-objective problem.

5. Computational results In this Section, the validity of the proposed model is evaluated among several medium-sized test problems. The proposed CLSC model was coded in GAMS 22.9 software using BARON solver. It should be noted that the source of randomly generated samples follows Table 1. The instances were solved on a Laptop with 2.6 GHz CPU and 4 GB RAM. Table 2 shows the computational results obtained from different test problems. Afterward, a sensitivity analysis is done on the effect of total available number of vehicles between DCs and retailers on the second objective function.

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00

Table 1. Source of randomly generated parameters. values parameters values Uniform(50,100) Uniform(25,50) 1500+ Uniform(0.3,0.6) Uniform(15,20) Uniform(3.5,5) Uniform(6,12) Uniform(0.8,2.8) Uniform(0.05,0.2) Uniform(1,3) Uniform(400,800) Uniform(0,1)

Parameters

∑ ∑ ∑

Uniform(50,100)

Test Problem 1 2 3 4 5 6 7 8 9 10

Uniform([

| |

]

Table 2. Computational results for different test problems Problem Size Objective function | | | | | | | | | | OFV1 OFV2 2124.64 989.89 2378.08 807.13 2844.76 1202.15 3187.72 1170.54 3563.92 1434.74 3808.12 1366.59 4371.64 1110.34 4961.80 1004.30 5305.36 1255.85 5952.04 1001.21

∑ ∑ ∑

[

| |

])

GT 1.04 0.9 0.83 0.96 0.86 1.04 0.97 1.01 0.92 0.98

Hundreds

Figure 3 illustrates the changes in OFV2 vs. changes of the total available number of vehicles between DCs and retailers. The increase in the value of | | between the intervals of [ ] will significantly decrease the value of OFV2, because the increase in the number of vehicles let the model to choose routes which are shorter than the previous routes through creating more tours. But, increasing the value of | | more than four could not provide a better solution for the designed network due to the additional fixed usage cost of vehicles incurred in OFV 1. In this way, the model decided not to use the all available vehicles and used three vehicles out of total number of vehicles. Alternatively, the value of OFV2 will not significantly decrease in the intervals of [ ]. 16 15 14

OFV2

13 12 11 10 9 8 2

3

4

V

5

6

7

Figure 3. OFV2 vs. number of vehicles.

6. Conclusions and future work Considering green factors of supply chains has become more important in recent years due to increasing concerns about the EIs of business processes. Public demand and governmental forces also intensify the need for green networks in today’s business environment. To move forward the literature in this area, this paper proposes a biobjective non-linear mathematical programming model for a closed-loop supply chain network in which the decisions have been made in a multi-period and multi-product system. The main contributions of this paper to the literature are twofold: (i) proposing a new bi-objective mathematical programming model for a green CLCS network to address strategic, tactical and operational supply chain planning decisions. The proposed model considers location-routing,

M. Zhalechian, R. Tavakkoli-Moghaddam / IIEC 00 (2016) 000–00 and green factors (ii) utilizing an efficient game-based approach to deal with the multiple conflicting objectives of the proposed model. Some extensions on the presented work could be aimed for the future research. Since the proposed model is a NP-hard, developing efficient meta-heuristic algorithms or using an efficient exact method such as Lagrangian relaxation algorithm to solve the large-sized problems is a good direction for future research. Furthermore, considering another pillar of sustainability (i.e., social impacts of a designed network) can be another interesting topic for future research. References [

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