Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry

Journal of Cleaner Production 133 (2016) 314e337

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry Mostafa Zohal, Hamed Soleimani* Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University (IAU), Qazvin, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 April 2015 Received in revised form 27 February 2016 Accepted 16 May 2016 Available online 25 May 2016

The forward/reverse logistics network design is an important and strategic issue due to its effects on efficiency and responsiveness of a supply chain. In practice, it is needed to formulate and solve real problems through efficient algorithms in a reasonable time. Hence, this paper tries to cover real case problem with a multi-objective model and an integrated forward/reverse logistics network design. Further, the model is customized and implemented for a case study in gold industry where the reverse logistics play crucial role. A new solution approach is applied for the proposed 7-layer network of the case study and the solutions are achieved in order solve the current difficulties of the investigated supply chain. This paper seeks to address how a multi objective logistics model in the gold industry can be created and solved through an efficient meta-heuristic algorithm. A green approach based on the CO2 emission is considered in the network design approach. The developed model includes four echelons in the forward direction and three echelons in the reverse. First, an integer linear programming model is developed to minimize costs and emissions. Then, in order to solve the model, an algorithm based on ant colony optimization is developed. The performance of the proposed algorithm has been compared with the optimum solutions of the LINGO software through various numerical examples based on the random data and real-world instances. The evaluation studies demonstrate that the proposed model is practical and applicable and the developed algorithm is reliable and efficient. The results prove the managerial implications of the model and the solution approach in terms of presenting appropriate modifications to the mangers of the selected supply chain. Further, a Taguchi-based parameter setting is undertaken to ensure using the appropriate parameters for the algorithm. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Logistics network Closed-loop supply chain Multi-objective Emission Ant colony optimization

1. Introduction Logistics is the process of planning, implementing and controlling the efficient and effective flow and storage of goods, services, and information from the beginning point to the point of consumption in order to comply with customer needs (Hugos, 2011). Logistics network design is a set of long-term decisions and it has a strategic role in effectiveness and efficiency of a supply chain. That's why it needs to be optimized through close-topractice networks and appropriate algorithms. It usually involves multiple and differing objectives or goals, such as profit, cost, quality, customer responsiveness and so on. Green logistics describes all attempts to measure and minimize the ecological impact

* Corresponding author. E-mail addresses: (H. Soleimani).

[email protected],

http://dx.doi.org/10.1016/j.jclepro.2016.05.091 0959-6526/© 2016 Elsevier Ltd. All rights reserved.

[email protected]

of the logistics activities. This includes all activities of the forward and the reverse flows of products, information, and services between the origin point and the consumption point. The final aim is to create a sustainable company which can achieve a balance between economic and environmental factors. Green procurement is defined as an environmental-friendly purchasing activities that include the reduction, reuse and recycling of materials in the process of purchasing. Besides green procurement is a solution for environmentally concerned and economically conservative business, and a concept of acquiring a selection of products and services that minimizes environmental (Salam, 2008). There are various approaches in green network design in CLSC which can be mentioned from Lin et al. (2014) in three different categories: a group of the authors regard fuel consumption optimization, the second group tries to regard gas emissions and the final groups consider the amounts of the waste and the disposals. Here, in this paper, the second approach is selected based on the necessity of the

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

CO2 emissions in the transportation system and in the production of gold industry. In practice, the mining and minerals industry faces some of the most difficult sustainability challenges of any industrial sector (Azapagic, 2004). One of these industries is gold industry. The environmental and social impact of gold mining is particularly acute in both production and transportation (which is in low volume and high frequencies). Closing the loop and reverse logistics is a crucial issue in gold industry since gold is eminently recyclable and is primarily used for ornamentation. Excessive consumption of gold in developing countries has thus created an uncomfortable anomaly for many activists who have blamed modern highconsumption lifestyles for many contemporary social and environmental ills (Saleem, 2006). In this paper, the design problem of an integrated multiobjective, single-product, multi-stage CLSC network is considered. The developed network includes suppliers, manufacturing facilities (factories), distribution centers, collection centers, recycling centers, and disposal centers regarding multi-capacity levels for each entity. This study aims to answer the question that how can a profit-emission based logistic model being efficiently solved through new meta-heuristic algorithm. Besides, what are the issues of implementing CLSC and the related solution algorithms in the real world problems? According to the real world and case base approach, it is tried to find an appropriate case study in order to investigate an industrial problem in green closed-loop supply chain. Indeed, this paper obeys a near-case base approach in order to be useful for both industry and academia. There are many cases that we could choose here but based on the necessity of the gold industry in Iran, the gold industry is considered as our case study. The recent publications in the field of precious metal industries prove the necessity and importance of the selected industry such as Luque-Almagro et al. (2016) and Dobson and Burgess (2007). The supply chain of the selected case study is not optimum and more than that, regarding to new policies and legislations in the environment, it is needed to rearrange its supply chain. The result of the study reveals many shortcomings of the current supply chain of the gold industry. As a result, if the network is optimized in number of vehicles and their travel distances, the pollution will be decreased according to the “Iran-2025 Vision” which explicitly clarifies reducing the amount of industrial pollution (90% reduction).1 The gold industry is highly expanded in all over Iran in all cities (wherever the people live) so despite its low-volume of transportation it has a vast numbers of transportation which leads to a high level of pollution.2 Finally, it is decided to select and completely investigate a gold industry. The aim of this study is to provide a suitable and integrated model for the gold industry that can simultaneously reduce costs and emission and also increase income in the network. The main question which this paper seeks to address is how a multi objective logistics model in the gold industry can be created and solved through efficient meta-heuristic algorithm. Here, efficient implies the quality and reliability of solutions. The research questions can be summarized as follows:
What is the best route in this network in gold logistics network?
How much production should be transferred between facilities in different levels?

1 http://www.vision1404.ir and http://maslahat.ir/DocLib2/Approved% 20Policies/Offered%20General%20Policies/policy%2006-07-1382%20Iran%20Vision% 201404.aspx. 2 http://supply-chain-management.persianblog.ir/page/scm-journal: No. (2), Vol (8).

315


Which facilities should be activated?
How a can multi-objective logistic model (with profit and pollution targets) can be solved through new meta-heuristic algorithms efficiently and reliably?
What are the benefits of green approaches for the gold industry? If the network is optimized the total distances of travel is decreased which result in reducing the pollution. This reduction is along the Iran's-2025 vision which seeks to reduce the amount of industrial pollution. Finally, in order to improve the proposed network minimum amount of emission, cost reduction, and profit maximization are considered and optimized. We try to model the real world with respect to the real variables. It then uses an algorithm to solve the model and the proposed algorithm with both generated and real instances. The rest structure of this paper is as follows: Section 2 presents a literature review involving RL and CLSC modeling and solving approaches. In order to design an integrated logistics network, an integer linear programming formulation is developed in Sections 3. Section 4 discusses an efficient solution approach based on ACO for the small and large-scale instances. The appropriate computational study is presented in Section 5. The discussion of the results is presented in Section 6. The complete explanation and implementation of the model and solution approach in the case study is presented in Section 7. Finally, Section 8 presents conclusions of the paper and offers topics for future research. 2. Literature review The literature of this paper can be divided into three main categories: forward logistics networks, reverse logistics, and ClosedLoop Supply Chain (CLSC). The Reverse Logistics (RL) consists of models that it concentrates on the backward directions. RL addresses the number of collection, recycle and disposal centers and also the related flows. In the real world, when both reverse and forward networks are integrated and considered together, then a closed loop supply chain is created (Ramezani et al., 2013). One of the most important issues in the CLSC is the configuration of the CLSC network that has a significant and long-term effects on the total performance of CLSC. Design of the forward and reverse logistics network should be integrated because designing forward and reverse logistics network leads to the optimal design with respect to the costs, service levels, responsiveness, etc (Pishvaee et al., 2010). Many efforts for modeling and optimizing the supply chain network design problems have been studied that is mostly based on a single-objective such as minimizing cost or maximizing profit (Govindan et al., 2015). However, recently, green objectives such as emissions play an important and impossible-to-ignore role in network design problems. For example Zeballos et al., (2014) represents an objective function that minimizes the expected costs (including facilities, purchasing, storage, transportation, and emissions costs) minus the expected revenue of reselling the return products (collected from repairing and decomposition centers) through the forward network. Network emission is an important matter in a CLSC and it is a desirable choice for the most of the decision makers. Since environmental issues are one of the most effective aspects in supply chain (specially in RL), emission is considered as one of the objectives in this paper. In other words, because of the environmental legislation and the increasing environmental consciousness of the customers, this objective (emission) is added to this model. The importance of the environmental aspects is in a level that no researcher can ignore it in his/her mathematical model (objective or constraint). On the other hand, in term of proposing an appropriate solution methodology and in

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order to present new approaches in this field, an Ant Colony Optimization (ACO) approach is developed and evaluated for the proposed network in order to solve large-scale instances. Many studies can be mentioned in the field of CLSC network design from the modeling and solving points of view. Dullaert et al. (2007) present an overview of supply chain design models. They indicate that the mixed integer planning models are commonly utilized in this area. Ob the other side, cost minimization and profit maximization are two of the most common objectives in this field. Meepetchdee and Shah (2007) try to minimize system costs while the limitations are imposed on guarantee of the minimum level of robustness in the Mixed Integer Linear Programming (MILP) model. Further, Melo et al. (2009) present an overview of the supply chain network models and mention that traditional supply chain network design methods typically focus on deterministic and singleobjective approach in forward logistics. Gen and Syarif (2005) and also Amiri (2006) count total cost of logistics network as an objective function in their works. Recently, many models have been developed for RL/CLSC network design. RL/CLSC issues are recently gone to the main focus of the researchers due to the necessities of reducing the use of raw materials, pollution prevention, recycling management, social responsibility and environmental issues. Many attempts tried to consider deterministic supply chain network design problems in the field of RL and CLSC (Ramezani et al., 2013). Jayaraman et al. (1999) develop an MILP model for RL network design under a pull system and based on customer demands for improved products. The objective of their proposed model is to minimize total cost. Aras et al. (2008) determine the optimal locations of collection centers and maximize the purchase price of the products used in an RL network. Further, they develop a Tabu Search (TS) algorithm to solve the developed nonlinear model. Fleischmann et al. (2001) suggest an integrated forward/reverse network optimization which can present substantial savings in cost compared to the sequential design of both networks. They consider a model of reverse logistics where forward flow is optimized with reverse flow without regard to capacity constraints. Furthermore, Listes and Dekker (2005) propose a stochastic mixed integer programming model based on scenario to maximize the profit. Another research is undertaken in this area is Salema et al. (2007) who develop the Fleischmann's model for networks of multiproducts under uncertain demand. Ko and Evans (2007) propose a mixed integer nonlinear programming model for concurrent design of inverse and forward network. They develop a Genetic Algorithm (GA) to solve their model. Lee and Dong (2008) present an MILP model for integrated logistics network design. They consider a simple network with only a production center and certain number of mixed facilities production-collection, and then they solve this model using TS. Hatefi and Jolai (2013) consider the reliability factors for the design of an integrated forward/reverse logistics network. The proposed model is formulated and then solved based on recent robust optimization method in order to protect the network against uncertainty. Indeed, an MILP model with complete restrictions is proposed to control network reliability among scenarios. Validi et al. (2012) concentrate on the green approaches in the food market supply chain in Ireland through considering CO2 emission. They utilize an integrated multi-objective approach in their location-routing problem. On the other hand and related to the approach of this paper, several studies on multi-objective optimization of supply chain network design problem can be mentioned. Subramanian et al. (2013) consider a single-period, single-product and multi-echelon CLSC and develop a multi-objective integer linear programming using simulated annealing algorithms. Soleimani et al. (2013) develop a multi-echelon, multi-product, and multi-period model

in an MILP structure. Their proposed model is solved by CPLEX optimization software and through a developed GA. Their results demonstrated the acceptable performances of the developed GA. Subramanian et al. (2014) give a two-objective network design problem for the multi-period, multi-product closed supply chain in order to minimize the costs and maximize the efficiency. Their model is a two-objective MILP model to assist in the decision making on: 1) Operational/Location decisions for warehouses, combined facilities and manufacturing facilities, and 2) production and distribution of products between stages in supply chain. Garg et al. (2014) present a bi-objective model in order to exhibit a green closed-loop network design. Their model integrates the environmental issues and the traditional logistic system. FallahTafti et al. (2014) present a multi-objective MILP model and solve it through a well-known STEP method. Their model has three objectives: cost, suppliers' ranks and delivery time. Hasani et al. (2014) propose a multiple products, multiple periods, and multiple echelons model regarding limited warehousing lifetime formulation. They develop an efficient memetic algorithm to solve it. Validi et al. (2014a, 2014b) consider total costs, CO2 emissions, and the traversed distances of the vehicle Validi et al. (2014a, 2014b)s during transportation. Their optimization model for the strategic decision-making is formulated based on an integrating 0e1 mixed-integer programming considering a green constraint and utilizing an analytic hierarchy process approach. Besides, to the best of our knowledge, many algorithms used to solve the closed-loop logistics network including GA, benders decomposition, tabu search algorithm, memetic algorithm, etc. Indeed, in order to have a holistic view of the various papers and to find the gaps in the field of multi-objective green-CLSC network design, Table 1 is constructed to review recent publications. According to Table 1, the CLSC network design can be extended in both multi-objective approaches and solution methodologies. Based on the mentioned table, all of the multi-objective publications consider cost as one of their objective functions which can prove the importance of cost optimization approaches. Therefore, in this paper, cost is also selected as one of the objective functions. Given the importance of the emission in the real world, we can see its impacts on the earlier researches. Based on the vital role of the emissions in greening of the CLSC and also the necessity of them in the Iranian company such as the selected case study of this paper, CO2 emission is considered as one of our objectives. According to the proposed solution methods, despite its excellent performance in other problems, ant algorithm is not used in any of earlier researches of green CLSC network design problems. Based on Table 1, in this paper, three of the major concerns are selected as the objective functions: emission (amount of the output of carbon dioxide), income (multiplying number of demands and the product prices), and finally, the cost function. Cost function includes various supply chain network costs such as production, transportation costs, etc. The green side of the proposed multi objective approach is based on the amount of pollution related to the traveled distance by the vehicles. On the other hand, according to Table 1, the difference between the proposed model and the other models is in the multi objective approaches which are cost, income and emission here. The other point is about the applicability of the proposed model in real cases which we can customize a real-world CLSC network based on the proposed model. Finally, the cost and emission are minimized and profit is maximized, simultaneously. Besides, there are some limitations related to the proposed model which can be mentioned as the vehicles capacity, the capacity of the facilities and so on. In terms of solution methodologies, various types of algorithms are utilized such as exact solvers, GA, Benders decomposition, hybrid scatter search, TS-based heuristic, Fuzzy, r-robust

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317

Table 1 RL/CLSC single/multi objective network design publications. Year

Publication

Network Objective Type of objectives CLSC

Solution method

Multiple

Cost Profit Income Responsiveness Quality Suppliers' Delivery Service Emission ranks time efficiency

Pishvaee * et al. 2013 Ramezani * et al. 2014a Validi et al. 2015 2014b Validi et al. 2015 *

*

*

* *

* *

2014

*

*

*

* *

* *

* *

*

* *

* *

2010

Subramanian et al. 2014 Garg et al. 2014 Fallah-Tafti et al. 2015 Validi et al. 2015 This paper

*

* *

GA *

*

Fuzzy * * * *

*

*

optimization, simulated annealing, goal programming, and memetic algorithm. A detailed review in the literature illustrates a vast number of researches in using metaheuristic algorithms in the field of CLSC network design. Panicker et al. (2013) used ACO for their distribution network. They compared this algorithm with genetic algorithm. At the end of the paper they concluded that ACO is better than genetic algorithm. For the distribution networks Finally, regarding the capabilities of ACO, an algorithm based on this approach is developed in order to solve the model. To the best of our knowledge, it is the first attempt in extending an ant colony for CLSC network design problem. Actually, according to Table 1 and because of the acceptable performance of the ACO for various problems such as route selection and finding the best quantity of transported products, an ACO is developed. Besides, the results of the earlier publications in presenting the abilities of ACO in comparison with other metaheuristics such GA (Panicker et al. (2013)), and the specifications of our model, ACO is selected. However, despite the capabilities of this algorithm, there is no model that is solved with this algorithm which can lead us to a research gap in the solution methodologies. Further, the considered objective functions are making a new investigation package in the literature for the green-CLSC network design problem. 3. Problem definition and formulation The basis models of the proposed model are Pishvaee et al. (2010) and Pazhani et al. (2013). Pazhani et al. (2013) present a bi-objective network design model for a multi-period, multiproduct closed-loop supply chain. Pishvaee et al. (2010) propos a model for an integrated logistics network design in order to avoid the sub-optimality. They developed a bi-objective mixed integer programming formulation to minimize the total costs and maximize the responsiveness of a logistics network. They develop an efficient multi-objective memetic algorithm to find the set of nondominated solution. The proposed CLSC network is a multi-objective multi-echelon single-product model including seven echelons. Today, due to the growing trend of environmental pollution in the world, it is better that the models are designed considering the emissions released from the transportations system and the production processes. The proposed model of the paper wants to minimize the total traveled distance of the vehicles and therefore it can create less pollution. Besides, these vehicles have restriction in the loading space so this factor must be considered in the model. In the basic models of this paper, cost and efficiency was considered as their objective

* * *

Scenario analysis Analytic hierarch process approach Non-preemptive goal programming Exact solver STEP method MOGA-II Ant Colony Optimization

functions, while here, we suggest costs, income and emission. This means that in addition to increasing the number of objectives, a new and necessary objective function is added to the other functions. With this extension, the green approach can play a vital role in the proposed model in comparison with the basic models. The schematic view of the network is presented in Fig. 1. In the forward path, suppliers aim to provide raw materials for manufacturing centers in order to produce the new products. Then, these products are delivered to the customers through distributors. In the backward direction, the returned products are transferred to collection centers by customers. Here, the end of life products are controlled and inspected and if the product can be repaired or restored, they are sent back to the manufacturing facilities, otherwise, they can be sent to the recycling centers. In the recycling centers, the products are disassembled to be reused by suppliers and the remaining parts are sent to the disposal centers to be disposed. Fig. 1 illustrates the structure of the network and the related indices for each entity. Before presenting the formulation of the model, its assumptions should be reviewed. The assumptions of the model can be explained as follows:
The model is single product.
Customer locations are fixed and known.
The potential locations of all entities in the network are identified.
All cost and price parameters are predetermined.
Capacities of vehicles are limited but type and capacity of vehicles at each facility are identical. Further, the capacities of facilities are limited too.
Predefined values have been specified for the rates.
The numbers of facilities that can be opened are limited.
The process of repair or restoration is undertaken at collocation/ repair centers and the process of recycling is accomplished at the recycling centers. These products are placed in the forward network and they are considered to be the same as new products.
The flows are permitted to move between two different echelons and there is no flow between the facilities in the same echelon. The proposed model consists of three objective functions. The first and second functions are cost and income respectively (minimizing cost and maximizing income). These functions are common objectives in the most of supply chain network design problems. The third objective seeks to minimize emission. Emission is the amount of carbon dioxide that comes out of each vehicle. This

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Suppliers

Distribution centers

Manufactures

Customers

Collection centers

Disposal center

Recycle centers

Fig. 1. The proposed CLSC logistics network.

can complete the approach of the model with green aspects. Finally, the main purpose of this paper is to evaluate an integrated logistic system with respect to these objectives in order to determine activated facilities and the flows between them. The formulation of the presented model is presented as follows: Indices i: Set of locations of suppliers, (i ¼ 1,2, …,I). j: Set of locations of manufacturing facilities that make products and receive the repair products from collection/repair centers for remanufacturing, (j ¼ 1,2, …,J). k: Set of distribution centers that sent products to customers, (k ¼ 1,2, …,K). c: Set of locations of customers, (c ¼ 1,2, …,C). o: Set of collection centers that collect end of life products from customers, (o ¼ 1,2, …,O). r: Set of recycling centers that make raw material through returned products, (r ¼ 1,2, …,R). d: Set of disposal centers that try to environmental-friendly dispose the non-recyclable components of the products. Parameters Demand: Demc : Amount of demand of costumer c. Cost of transportation: Transij : Transportation cost per unit of raw material from supplier i to the manufacturer j. Transjk : Transportation cost per unit of products from manufacturer j to the distributor k. Transkc : Transportation cost per unit of products from distributor k to the customer c. Transco : Transportation cost per unit of returned products from customer c to the collection center o. Transoj : Transportation cost per unit of returned products from collection center o to the manufacturer j. Transor : Transportation cost per unit of returned products returned from collection center o to the recycling center r. Transri : Transportation cost per unit of products from recycling center r to the supplier i. Transrd : Transportation cost per unit of products from recycling center r to the disposal center d

Fixed cost: Fixi : Fixed cost for opening supplier i. Fixj : Fixed cost for opening manufacturing facility j. Fixk : Fixed cost for opening distribution center k. Fixo : Fixed cost for opening collection center o. Fixr : Fixed cost for opening recycling center r. Fixd : Fixed cost for opening disposal center d. Capacity of vehicles: Vehiaij : The capacity of existing vehicle a between supplier i and manufacturer j. Vehibjk : The capacity of existing vehicle b between manufacturer j and distributor k. Vehiekc : The capacity of existing vehicle e between distribution center k and customer c. Vehigco : The capacity of existing vehicle g between customer c and collection center o. Vehizor : The capacity of existing vehicle z between collection center o and recycling center r. Vehihoj : The capacity of existing vehicle h between collection center o and manufacturer j. Vehim ri : The capacity of existing vehicle m between recycling center r and supplier i. Vehilrd : The capacity of existing vehicles l between recycling center r and disposal center d. The distance between facilities: Distij : The distance between supplier i and factory j. Distjk : The distance between manufacturer j and distribution center k. Distkc : The distance between distribution center k and customer c. Distco : The distance between customer c and collection center o. Distor : The distance between collection center o and recycling center r. Distoj : The distance between collection center o and manufacturer j. Distri : The distance between recycling center r and supplier i. Distrd : The distance between recycling center r and disposal center d.

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The emission of vehicles: Pollaij : The CO2 output of the vehicle a during transportation between supplier i and manufacturer k. Pollbjk : The CO2 output of the vehicle b during transportation between manufacturer j and distribution center k. Pollekc : The CO2 output of the vehicle e during transportation between distribution center k and customer c. Pollgco : The CO2 output of the vehicle g during transportation between customer c and collection center o. Pollhoj : The CO2 output of the vehicle h during transportation between collection center o and manufacturer j. Pollzor : The CO2 output of the vehicle z during transportation between collection center o and recycling center r. Polllrd : The CO2 output of the vehicle l during transportation between recycling center r and disposal center d. Pollm ri : The CO2 output of the vehicle m during transportation between recycling center r and supplier i. Capacity of the facility: CAPi : Capacity of supplier r for raw material. CAPj : Capacity of manufacturer j. CAPk : Capacity of distribution center k. CAPo : Capacity of collection center o. CAPr : Capacity of recycling center r. CAPd : Capacity of disposal center d.

319

Collo : Collection and inspection costs per unit of product in the collection center o. Repaj : The cost of repair or restoration of each unit in the collection center o. Brokr : Cost of recycling per unit of product at recycling center r. Dispd : Per unit disposal cost of non-recyclable product by the disposal center d. Decision variables Continuous variables (related to the flow of network): Flowij : The amount of material transported from supplier i to the manufacturer j. Flowjk : The amount of product transported from manufacturer j to the distribution center k. Flowkc : The amount of product transported from distribution center k to the customer c. Flowco : The amount of returned product transported from customer c to the collection center o. Flowoj : The amount of returned product transported, that are able to repair and send back to the manufacturing facilities, from collection center o to manufacturing facility (factory) j. Flowor : The amount of returned product transported from collection center o to the recycling center r. Flowri : The amount of returned product transported from recycling center r to the supplier i. Flowrd : The amount of returned product transported from recycling center r to the disposal center d.

Number of facilities: Binary variables (related to the establishment of facilities): Maxs : The maximum number of activated suppliers. Maxx : The maximum number of activated manufacturers. Maxy : The maximum number of activated distributors. Maxz : The maximum number of activated collection centers. Maxm : The maximum number of activated recycling centers. Maxu : The maximum number of activated disposal centers.


Xi ¼




Rates:

Xj ¼ RRco : Rate of returned products from customer c to the collection center o. RXoj : Rate of recovery/repair products from collection center o to manufacturer j. RYor : Rate of recycling products from collection center o to recycling center r. RUri : Rate of recycled products from recycling center r to supplier i. RDrd : Rate of recycled products from recycling center r to disposal center d. RV: Effective loading percentage of a vehicle.

1 0

If the manufacturer j is established Otherwise

1 0

If distribution center k is established Otherwise

1 0

If the collection center o is established Otherwise





Zo ¼


Mr ¼

Other parameters: Purci : Per unit cost of buying raw material from supplier i. Prodj : The cost of producing each unit of product in manufacturing facility j. Disk : Per unit operating cost of product in the distribution center k.

If the supplier i is established Otherwise

Yk ¼

Income: Incori : Per unit price of returned product that bought by recycling center r from supplier i. Pric : The selling price per unit of the product to the customer c.

1 0


Ud ¼

1 0

If the recycling center r is established Otherwise

1 0

If the disposal center d is established Otherwise

The first and second objective functions consist of income (Z1 Þ and cost (Z2 ) respectively. It is possible to integrate these two objective functions as an integrated profit objective function. These objective functions are presented as follows:

320

Z1 ¼

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

X

Demc  Pric

c

2 Z2 ¼ 4

XX i



X

Flowij  Transij þ

j

j

Flowkc  Transkc þ

c



X

Flowor  Transor þ

X

Flowri  Transri þ



Flowij  Purci þ

j

 

X c X



X

Flowkc  Disk þ

X

j

Flowrd  Dispd  Fixi Xi þ

XX i

Fixo Zo þ

Flowoj  Transoj þ

Maximize ½Z 1 

r

3

2

Flowrd  Transrd 5 þ 4

Flowco  Collo þ

X i

X

X

Flowoj  Repaj þ

r

j

2

XX i

Flowri  Incori þ 4 XX i

Fixr Mr þ

Fixk Yk þ

j

XX

j

i

X

X

3

i

i

Fixd Ud 5

j

Where Z1 is the income of the selling process which can be achieved by multiplying total demand and sales price. Besides, Z2 represents the total amount of the costs including transportation and production costs, distribution and collection costs, costs of returning end of life products, disposal costs, and fixed costs of the opening facilities. The third objective function is related to the CO2 emissions as follows:

2 Z3 ¼ 4

XX i



Pollaij Distij

j

X k

Pollbjk Distjk

X Flowij 1 þ a Vehiij RV j

X Flowjk 1 þ b RV Vehi jk



X

X j

Pollekc Distkc

Flowoj Pollhoj Distoj Vehihoj

X 1 þ RV o

X Flowor 1 þ z RV Vehi r r or X X Flowrd 1 l þ  Pollrd Distrd Vehilrd RV r d 3 X Flowri 1 5  Pollm ri Distri RV Vehim ri 

X

Maximize ½Z1  The amount of the penalty function is determined based on the practical taxes for CO2 emissions. Finally, the abovementioned functions are integrated to a profit objective function. The constraints of the formulation (there are in Appendix 1) are demonstrated as follows: Constraint ð1Þ indicates that all customers' demands have to be satisfied. Constraints ð2Þeð11Þ ensure the flow balance at manufacturing facilities, distribution centers, collection centers, recycling centers, and disposal centers respectively. Constraints ð12Þeð18Þ are capacity constraints which prevent the overload flows. Finally, Constraints ð19Þeð24Þ restrict the number of suppliers, manufacturing facilities, distribution centers, collection centers, recycling centers, and disposal centers up to the maximum limitation. 4. Solution approach In order to solve the developed model, a heuristic-based ACO is expanded for solving the multi-objective logistics network problem. The schematic steps (pseudo code) of the developed algorithm are illustrated in Fig. 2. The detail description of the developed algorithm (Fig. 2) is presented as follows: 4.1. Input module

k

X Flowjk 1 þ e RV Vehikc c c X X Flow 1 co þ  Pollgco Distco Vehigco RV o o 

As mentioned before, since the dimensions of the objective functions are different, penalty function is used in order to make one integrated cost function. Penalty function is used as follows:

Minimize ½Z2 ; ðPenalty  Z3 Þ

X o

j

i

Minimize ½Z 2 ; Z 3 

X

k

c o X X

r

X o

Flowjk  Prodj þ

Fixj Xj þ

XX

j

Flowco  Transco þ

k

o

X k

d

XX

Flowor  Brokr þ

j



o

XX

j

d



o

XX

r

X

c

XX

r

i

X

Flowjk  Transjk þ

k

XX

r



XX

dimension of Z3 is completely different from Z1 and Z2 so here, a novel appropriate penalty-based approach is developed in order to integrate three objective functions. The mentioned approach is based on the practical issues of CO2 -based taxes, which will be discussed later. The final formulation of the model can be illustrated as follows:

Pollzor Distor

d

Z3 illustrates the emission function including the amount of pollution, the traveled distance by a vehicle capacity, and the effective capacities of the vehicles. It should be mentioned that the

There are some parameters which should read at the beginning of the algorithm in order to start the solution procedure which is explained as follows:
Potential locations of suppliers, manufacturers, distribution centers, customers, collection centers, recycling centers, and disposal centers.
The demands of the customers (Demc ) and the prices of products.
Transportation cost per unit of raw material (Transij ), transportation cost per unit of products (Transjk and Transkc ), and Transportation cost per unit of returned products (Transco , Transoj , Transor , Transri , and Transrd ).
Fixed costs of opening facilities and the maximum allowable number of entities.
The capacities of various vehicles, the capacities of facilities, and the emission of each vehicle for each possible flow.
The distance between entities for possible flows.
Rate of returned products (RRco ), rate of recovered/repaired products (RXoj ), rate of recycled products (RYor ), rate of

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321

Fig. 2. The schematic steps (pseudo code) of the developed algorithm.

Table 2 Tuning values for various levels of the parameters. Factor

Level 1

Level 2

Level 3

Alpha Q Rho Tau(0) MaxIT nAnt

0.5 10,000 0.1 0.25 50 100

1 100,000 0.45 0.5 75 75

2 500,000 0.85 0.75 100 50

recycled-to-suppliers products (RUri ), rate of disposed products (RDrd ), and effective rate of vehicles' capacity.
The selling prices, costs of raw materials, production costs, operating costs, collection and inspection costs, repairing/ restoration costs, recycling costs, and disposal costs.

4.2. The parameters of the proposed ant colony optimization The parameters of the developed ACO algorithm should be read in the next step. The following parameters are set in this stage:

nAnt: Number of ants; IT: Number of iterations; a: Parameter which controls the magnitude of tfb (the parameter for an ant to delineate the pheromone intensity from the fth partner to the bth partner in the next stage); b: Parameter which controls the magnitude of hfb (the profitability of selecting bth partner from the next stage by the fth partner in the current stage); Q: Parameter which controls the pheromone increment amount (constant); r: Evaporation rate of pheromone. t0 : Initial amount of pheromone in each edge in the graph. These parameters are tuned parameters obtained from experimental results. Taguchi method of robust design is adopted for finding the optimum combination of parameters of the ACO-based heuristic. The parameter values should be set up before the ACO starts. The parameters such as a, b, r, Q, N and IT used in this work are tuned parameters obtained using the Taguchi method of robust design. Through a Taguchi-based method, the above mentioned parameters are assigned to their best values. Table 2 shows the various possible values for each parameter in order to be tuned.

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Fig. 3. Parameters setting based on the values of objective function (the Minitab reports).

Fig. 4. Parameters setting based on the solving time in seconds (the Minitab reports).

Because of the effects of these factors on the performance of the proposed ACO, these factors considered in three level in Table 2. For each of the cells of Table 2, different sizes of instances are run and the mean is reported. Then, the results are achieved through a Taguchi-based design by Minitab software. The results of the mentioned tuning procedure are illustrated in Figs. 3 and 4. According to parameters setting for each of them, appropriate level is selected (according to Figs. 3 and 4). The following results about the parameters are achieved: Alpha: The first level (0.5) is selected because in this level the value of objective function and time of solving are maximized and minimized respectively. Obviously, this is the best case that can found. Q: Here, the value of the objective function is maximized in level 3 (500,000) but the time minimization is occurred in the second level (10,000). Since the slope of the improvement in the objective function is significantly more than in time, the third level (500,000) is selected. Rho: Here, the same situation as parameter “Q” is realized. Again, level 1 (0.1) is selected. In this level, the objective function value has a huge difference in comparison with other levels but the time differences are very low, and ignorable. Tau(0): The second level (0.5) is selected. The value of objective function is maximized in the third level while solving time shows the best performance in the first level. Since the differences

between the values of the objective function in second and third level is low and ignorable and in order to achieve the better solving time, the second level is selected. MaxIT: The third level (100) is selected here. The value of objective function is maximized in this level but the solving time is minimized in the first level (50) which is completely predictable due to the effects of iteration number in solving time. Therefore, an efficient level regarding the value of objective function and time should be selected. As the iteration number is a very effective parameter and in order to achieve the best performance, the third level is selected in order to guarantee finding better objective function values. nAnt: The same as iterations number, if the number of ants are increased, the quality of solutions and the solving time are better and worse respectively. Here again, with the same rational as “MaxIT”, the first level is selected in order to have the chance of finding better solutions. In the process of the performance analysis of the algorithm, six control factors are considered here for the developed ACo. The reason is these are the effective parameters in the ACO performance. The final control factors are presented as follows and it is mentioned in the context of the paper: Alpha (a): Parameter which controls the magnitude of. tfb Q: Parameter which controls the pheromone increment amount (constant). Rho (r): Evaporation rate of pheromone.

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Tau(0) (t0 ): Initial amount of pheromone in each edge in the graph. MaxIT: Maximum number of iterations. nAnt: Number of ants. The abovementioned factors are completely affect the performance of the algorithm so they should be tuned. So for all three levels were considered that were shown in Table 2. Then, according to parameters setting for each of them, appropriate level is selected (according to Figs. 3 and 4). About the measured performance, it should be mentioned that two simultaneous criteria of time and the value of objective function are two measured performance which are recorded from the results and then the analyses are undertaken through these results. Finally, about the noise factor, it is important to be mentioned that in this paper the classic approach of Taguchi without noise factors (Roy, 2010 Chapter 1) are utilized and the dynamic and robust form of Taguchi is not used as in Georgiadis et al. (2006). Strictly speaking, in this paper, no noise factor is identified for the process of parameters setting of the algorithm. Therefore, in the tuning process we work explicitly and directly with the response variables (objective function and time in Figs. 3 and 4) in lieu of S/N ratio or noise factors. Such approach is often used for metaheuristic algorithms such as Keshtzari et al. (2016).

4.3. Probability calculation module Probabilities of ants' choices for selecting in each stage are calculated with probability matrix (PM). Here, in the proposed algorithm, PM must be calculated between any two phases. At each step, an ant (w) compares its random number and the cumulative value of probability matrix to allocate a non-assigned node at the downstream to a node at the upstream. For example, in the first stage, a supplier is assigned to a manufacturer and in the second stage a manufacturer is assigned to a distribution center and so on. w ) is calculated from the Equation (1). Probability matrix (PMor

8 > ½t ðtÞa ½hor ðtÞb > < Xr or w ½t ðtÞa ½hor ðtÞb PMor ðtÞ ¼ r¼1 or > > : 0 ; otherwis

In each step, the allocation procedure of the facilities is undertaken based on the following steps: Step1: Generate random number between 0 and 1, for moving the ant from a facility in a stage to other facility in the next stage. Step2: Using probability matrix and calculate cumulative matrix for all facilities in all stages. Cumulative matrix determines which route (or facility) should be selected by an ant. In other word, the ant using cumulative matrix finds the path that should be traveled. Step3: Based on the generated random number in step 1, find the upstream facility where the value of the cumulative probability facility first exceeds the random number. Step4: Calculate the amount of materials and products transported on routes. Quantity of carrying with respect to the chosen path by an ant and quantity of demand are obtained. Step5: Terminate the allocation procedure if the demands of all the customers are satisfied. 4.5. Compare, find and select best ant solution In any iteration and according to the path and amount of materials and products carried by the ants, objective function values are calculated. Indeed, each ant has a calculated value for its objective function which is an important value in order to evaluate its performance. The best objective function value of any iteration is chosen and then compared (and replaced if better) with the globalbest. 4.6. Update the pheromone levels After completion of any iteration the deposit pheromones by the ants must be updated. For instance, in iteration t, the pheromone levels between supplier i and manufacturer j is updated using Equation (2):

tij ðt þ 1Þ ¼ ð1  rÞtij þ

X w

; if r2Now

(1)

Where, Nw o exhibits the possible neighborhood of ant w when it is in the collection center o. tor shows the pheromone concentration in edge (o,r). hor represents the heuristic information that is usually achieved using greedy heuristic value for guiding the search procedure with some worthy information about the problem. a and b are the parameters related to the search direction which determine the relative importance of pheromone trail and heuristic information respectively. Here, collective knowledge is more important and in this paper, it tries not to act greedily in a way no heuristic information is considered. Indeed, the algorithm should be able to act in a way that the value of h becomes one so that it will be affectless in calculations. In other word, based on the above discussion, the value of b is set to zero here. 4.4. Finding the path and the amount of transported material and product, and generating ant solutions

323

Dtijwij

(2)

Where Dtijw is the amount of pheromone on edge ij (supplier i ij and manufacturer j) which is spilled by the ant w. In other words, each of the ants secreted some amount of pheromone when they pass the routs. Besides, ð1  rÞtij is the pheromone evaporation rate. For the pheromone increment updating rule, an ant-weight strategy is used which is given in Equation (3) (Panicker et al., 2013):

Dt ¼ w

8 > < > :

Q ; global  bestðItÞ 0

;

if allocation is done by ant w

otherwise (3)

Where Q is a constant, and “global-best” represents the total cost of the best allocation made by the ant w in the previous iteration. Besides, decreasing of the pheromone values are associated with the inferior solutions and increasing of the pheromone values are associated with the better solutions. 4.7. Termination condition

In this step, each ant generates a feasible solution which can be found in the form of a matrix in each step. The size of the matrix depends on the number of the facilities in each stage. For instance, if there are 5 suppliers and 4 manufacturers, a 4  5 dimensional matrix is created and the ant can move between the 20 possible elements of the matrix.

In this step of the algorithm, the termination condition is checked. When the algorithm reaches the required number of iterations, then the algorithm stops. It should be mentioned that the required iteration is set to a proper number based on the parameter setting results.

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Table 3 Different weights for four instances. w1

1 2 3 4 5 6 7 Average Error (%)

0.1 0.2 0.3 0.5 0.6 0.55 0.5 0.4

w2

0.3 0.4 0.6 0.3 0.35 0.15 0.4 0.36

w3

0.6 0.4 0.1 0.2 0.05 0.3 0.1 0.25

Instance 1

Instance 2

Instance 3

Lingo

ACO

Lingo

211541.7 484955.0 731056.8 1414441 1701510 1605771 1387130 1076629 0.123%

209774.67 484727.86 728676.14 1414337.86 1698228.31 1605568.11 1385767.84 1075297

202156 202156 472675 472675 713005 713005 1405290 1405290 1690991 1690940 1601078 1600839 1375051 1375051 1065749 1065708 0.004%

4.8. Outputs In this step of the algorithm, the final results and the best solution are reported.

ACO

Step 1: The following data are given as input of the algorithm. Number of suppliers (i ¼ 2), number of manufacturer (j ¼ 2), number of distribution centers (k ¼ 3), number of customersð c ¼ 2), number of collection centers (o ¼ 2), number of recycling center (r ¼ 1), number of disposal centersðd ¼ 3) are read for the algorithm. The rest of the data are presented in Appendix 2. Step 2: ACO parameters. The parameters of the algorithm are predetermined as number of ants (nAnt ¼ 100), number of iterations (MaxIT(IT) ¼ 100), a ¼ 0.2, b ¼ 5, r ¼ 0.10, Q ¼ 500,000, and t0 ¼ 0:5.

ACO

Lingo

ACO

202126 472998 713867 1405623 1691496 1601063 1375620 1066113 0%

202126 472998 713867 1405623 1691496 1601063 1375620 1066113

206002 205940 477660 477437 720229 720229 1408993 1408993 1695196 1695196 1603001 1603001 1379903 1379903 1070141 1070100 0.0038%

Step 3: Probability calculation. For the first iteration, according to the Equation (1), probability matrices are obtained. For instance, probability matrices ij (PMij ) and rd (PMrd ) are calculated as follows:

5. Numerical study In this section, an appropriate example is described in order to illustrate and evaluate the application of the developed ACO algorithm for the presented network. It should be mentioned that all numbers used in this section are generated randomly based on the range of parameters. The results of this section can evaluate the performance of the proposed ACO with the optimum solutions of LINGO software. The selected instances contain 2 suppliers, 2 manufacturers, 3 distribution centers, 2 customers, 2 collection centers, 1 recycling center, and 3 disposal centers. The detail of the instance parameters are presented in Appendix 2. Customers' demands and the selling price of each product are intended to be equal to 5000 and 1000 respectively. For each of the functions, various weights are evaluated which are presented in Table 3. These weights have shown in Table 3. According to Table 3, the performance of the proposed ACO is evaluated in comparison with the global optimum of Lingo in various weights of objective functions. The mean of differences between ACO and Lingo is just 0.03% which is completely acceptable. In other word, the performance of the algorithm does not depend on the weight values so the rest of the evaluations are undertaken with the one of the practically reasonable group of weights values of Table 3. Indeed, in this numerical study, the weights of the functions (Z1,Z2,Z3) have been allocated as 0.5, 0.3 and 0.2 respectively (the bolded line in the Table 3). Based on the importance of income, the more weight is given to this function (Z1 ). Based on the mentioned phases of the algorithm, the following steps should be undertaken:

Instance 4

Lingo

ðt0 Þij ¼



0:5 0:5

 ½0:52 0:5 ¼ 0:5 /PM11 ¼ 0:5 ½0:52 þ ½0:52

The rest of the PMij matrix elements are calculated as above.



0:5 0:5

0:5 0:5

ðt0 Þrd ¼ ½ 0:5

0:5

PMrd ¼



0:5 /PM11 ¼

½0:52 2

2

½0:5 þ ½0:5 þ ½0:5

2

¼

1 3

The rest of matrix arrays PMrd are calculated as above.

 PMij ¼

1 3

1 3

1 3



Similarly, the probability matrices PMjk ,PMkc , PMco , PMor , PMoj , and PMri are calculated. In the next iterations, the probability matrix is calculated from Equation (1). Step 4: Finding the path and the amount of material transported, and generating ant solutions. First, the random numbers are generated and then according to the calculated probability and cumulative probability matrices, all facilities are assigned. Indeed, random numbers are generated (between zero and one) and the results are compared to the cumulative probability matrix (one by one). The first element where random number value is greater than corresponding element in cumulative probability matrix is considered as the selected facility. Afterward, the appropriate amount of the materials and products flows is assigned to the selected facility. At the end of the iteration, there is one solution for each ant so it can be compared with the current solutions based on the objective functions and determined the best. Finally, the best solution of the iteration is compared to the current best solution of all previous iterations and the better will replace in the current global optimum. For instance the following matrix (Table 4) is the final flow matrix between entities during the first iteration by an ant: For instance in Table 4, the highlighted value of 2000 shows the amount of transported products between the manufacturer 1 and the distribution center 2.

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Table 4 Matrix of allocated amount of materials and products between entities.

Step 5: Compare, find and select best ant solution. In this step, all obtained solutions by all ants are calculated, sorted, and compared. Finally, in any iteration, the best solution is selected among all achieved solutions of the ants. If the best solution in an iteration is better than the global-best, then it is replaced as the new global-best value. For the presented instance, the explained matrix in Table 4 is the best solution of the first iteration which is replaced in the “global-best”. Finally, the global-best is 927,541.7 after the first iteration. Step 6: Update the pheromone. The pheromone increment is upgraded as follows:

pheromone increment ¼

trd ¼ ½ 0:989 0:45 0:45  Step 7: termination condition. Since the number of iterations is equal to 100, the algorithm is stopped when the number of iterations reaches to 100. Step 8: Output. After realizing the termination rule, the best objective function for the explained instance is 936,931 and the final flows of the network is illustrated in Table 5(see Table 6).

Q 500000 /pheromone increment ¼ y0:539 global  bestðItÞ 927541:7

Using the pheromone increment, the new pheromone for the routes between activated facilities is calculated as follows:

6. Evaluation of the developed ant colony optimization algorithm

ð0:5  0:9Þ þ 0:539 ¼ 0:989

To evaluate the performance of the ACO-based algorithm for the presented integrated logistics network problem, several instances are solved with small and large sizes and their quality of solutions and related solving time are reported. In order to achieve results, the proposed ACO algorithm is coded in MATLAB version 7.13. Besides, the model is coded in Lingo to achieve the optimum points of the small-size instances. The proposed algorithm is performed on a 2.10 GHz Intel Core 2-Duo processor laptop with 3.00 GB of installed memory (RAM). In order to evaluate the performance of the algorithm, two scales of instances are applied: small and large. The characteristics of the small-sized instances which can be solved by Lingo and other

However, for the routes where there is no activated facility, the amount of pheromone is reduced to 0.45 (0.5  0.9). For instance, the new pheromone matrices tij and trd is as follows: New pheromone matrix between supplier i and manufacturing facility j:

tij ¼



0:45 0:989

0:45 0:45



New pheromone matrix between recycle center r and disposal center d:

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Table 5 Final matrix of allocated amount of materials and products on routes.

Table 6 The characteristics of the network of the small-sized instances. Instance

Suppliers

Manufacturing facilities

Distribution centers

Customers

Collection centers

Recycle centers

Disposal center

Number of decision variable (flows)

Number of decision variable (binary)

Total number of decision variables

1 2 3 4 5 6 7 8 9 10 11 12 13 14

3 3 3 3 3 3 2 4 5 2 4 2 4 1

4 3 4 4 4 4 3 5 4 3 5 2 4 2

2 2 2 3 3 4 3 5 2 2 3 3 3 2

4 3 3 3 3 3 2 3 3 5 5 2 4 2

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

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

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

56 55 52 61 70 98 31 128 66 78 123 31 77 26

18 18 17 19 20 24 14 28 21 21 27 15 21 13

84 73 69 80 90 122 45 156 87 99 150 46 98 39

Table 7 The characteristics of the network of the large-sized instances. Instance

Suppliers

Manufacturing facilities

Distribution centers

Customers

Collection centers

Recycle centers

Disposal center

Number of decision variable (flows)

Number of decision variable (binary)

Total number of decision variables

1 2 3 4 5 6 7 8 9 10

6 7 8 10 15 25 30 40 50 100

5 6 7 11 15 20 27 35 60 110

5 6 7 10 18 22 29 30 55 105

6 5 8 15 20 25 35 45 65 130

4 5 6 14 17 23 28 32 40 100

5 4 5 11 15 20 31 30 30 110

4 5 5 10 16 21 25 31 45 90

199 231 346 1108 2170 3905 6917 9450 18,925 92,100

35 38 46 81 116 156 205 243 345 745

234 269 392 1189 2286 4061 7122 9693 19,270 92,845

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Table 8 Summary of the results for small scales instances. Instance

Maximum iteration

Number of ants

Lingo

ACO-based algorithm

CPU times (second)

Percentage error (Lingo ACO)

1

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100

1864181

1864181 1864181 1405290 1405217 1405623 1405623 1408993 1408993 1406030 1406030 1411423 1410130 936491.9 936491.9 1413499 1413438 1408556 1408267 2345236 2344088 2355647 2353982 936931 936931 1882599 1882376 937557 937557 1508433 1508093

174.38 17.31 132.37 13.99 142.84 14.44 131.41 13.46 146.41 14.43 167.38 16.89 102.32 10.43 181.33 18.58 161.16 16.39 219.03 22.74 279.13 27.80 101.15 10.39 187.20 18.94 106.16 10.83 159.45 16.19

0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0.001% 0.0928% 0% 0% 0.0665% 0.0709% 0.15% 0.17% 0.026% 0.075% 0.032% 0.10% 0% 0% 0.0016% 0.013% 0% 0% 0.0198% 0.0373%

2 3 4 5 6 7 8 9 10 11 12 13 14 Average

1405290 1405623 1408993 1406030 1411440 936491.9 1414441 1410702 2345865 2356398 936931 1882629 937557 1508755

general exact solvers are presented in Table 4. Indeed, in this category, the solutions obtained by the proposed algorithm are compared with the results of Lingo software. The other category is the large-scale instances which are presented in Table 7. Due to the size of the instances, this category cannot be solved by exact solvers in a reasonable time. According to Table 7, ten various networks are considered as real and large-scale instances. The total number of decision variables is from 234 to 92,845 decision variables which cannot be solved by Lingo software. The results of the small-scale instances are reported and evaluated in Table 8. It should be mentioned that the objective function related to the emissions has different dimension to the others so an integrated strategy is undertaken here. For this matter, an appropriate penalty function is determined for the emission function. The penalty function is provided in order to match the scales of all functions into costs. The form of the utility model is often used in multi-objective decision making procedures which consider various weights for objective functions. It should be mentioned that

the proposed penalty-weight approach of this paper converts our multi objective problem into a single-objective function. Then, for each of the functions (Z1 , Z2 and Z3 ), appropriate weights are considered which are 0.5, 0.3 and 0.2 respectively. For the small scale analyses, the proposed instances are solved using LINGO and ACO-based algorithm. The obtained results have been compared with each other. In each instance two cases for ACO-based algorithm is considered (see Table 8). In the first case, the maximum iteration and the number of ants are 100 and 1000 respectively. In next case, the maximum iteration and the number of the ants are 100 and 100 respectively. The second instance is completely based on the tuning results of the algorithm but the first instance is just for ensuring about the reliability of the algorithm. Indeed, if the number of the ants is exaggerated to 1000, the results will be surely better but with losing the time criteria. If the performances of these two types are significantly different, then we cannot rely on the algorithm and the tuning process. The results contain time and the objective function values of Lingo and two types of ACO algorithms. The results show that the

Table 9 Summary of the results for large scale instances. Instance

Total value of the objective function for ACO1

Time ACO(1) (minute)

Total value of the objective function for ACO2

Time ACO(2) (minute)

1 2 3 4 5 6 7 8 9 10 Average

2,830,740 2,360,031 3,789,878 6,915,267 9,467,043 11,553,072 16,083,001 20,855,879 29,731,280 58,737,344 16,232,354

0.66 0.58 1.15 5.74 5.21 26.81 75.21 127.82 325.68 4933.3 550.216

2,838,540 2,363,389 3,798,784 6,962,780 9,469,609 11,660,337 16,168,696 20,939,295 29,952,932 58,767,874 16,292,224

5.34 6.35 11.65 53.64 49.06 272.68 835.67 852.14 2714.1 44,848.2 4964.883



jACOð2Þ ACOð1Þj ACOð2Þ

  100

Objective function

Time

0.27% 0.14% 0.23% 0.68% 0.027% 0.91% 0.53% 0.39% 0.74% 0.37% 0.43%

87% 90% 90% 89% 89% 90% 91% 85% 88% 89% 89%

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(82.2 h) which can be acceptable for such instance in comparison with other choices. It should be considered that such instances cannot be solved by any type of exact solvers. Such results reflect that the performance of the proposed algorithm is acceptable as a new algorithm in the field of CLSC network design. This research attempts to develop a real-world green model with a new solution methodology in closed loop supply chain network design problem. In practice, managers can use the similar approach in promoting their closed loop supply chain and solving real world problems through the green approach of this paper and the proposed solution algorithm. Further, the results of the model have great effects in management decisions for selecting the appropriate facilities and also the flows of materials and products between network entities. On the other hand, the proposed solution methodology of this paper can elevate the capabilities of solving the real and large cases in appropriate time with reliable solutions. This is a vital step in the practical implementation. Finally, the results of this paper present powerful and reliable methods for managers in both modeling and solving issues. This study can help managers to close the loop of their supply chain with green approach while achieving more profit and less emission. To shed more light on the results of this paper, a case study of gold industry in Iran is investigated and the results are analyzed from the managerial points of view. The mentioned case study is also achieve appropriate findings for the selected gold supply chain. According to Table 20, we can see that the proposed model has high precision and it can be used on the real circumstances. The proposed ACO shows acceptable performances in both quality of the solutions and the time of solving. We recommend Fig. 6 as the optimum logistics network to the managers of the supply chain (see Table 19).

differences between the global optimum values of Lingo and the global-best values of the proposed algorithm are very small from 0% up to 0.17%. The mean of results shows just 0.0198% and 0.0373% differences to optimum for two types of ACO respectively. Clearly, the first type of ACO presents better performance. Besides, the performances of two types of ACO are close to each other and the mean difference is just 0.018% which is completely ignorable. However, the time differences between two ACO-based algorithms are significantly high and cannot be ignored (16.19 min in comparison with 159.54 min). The close performances of two ACO-based algorithms and the mentioned time-analyses prove the reliability of the algorithm and the correct process of tuning. Finally, the results of Table 8 can prove the acceptable performances of the developed ACO algorithm and also it is efficient in terms of time and quality of solutions. On the other hand, since the exact solvers are not able to solve large-size instances in a reasonable time, for the second evaluation phase the two mentioned types of the ACO (called ACO1 and ACO2) are compared together. The results are reported in Table 9. In ACO1, the maximum iteration and the number of ants are 100 and 100, respectively and in ACO2, the maximum iteration and the number of ants are 100 and 1000, respectively. As it can be seen in Table 9, the values of the objective functions in both types of the ACO are very close to each other. The maximum differences is 0.91% (less than 1%) and the average of the differences is just 0.43% which can prove the similar performance of two various types of the proposed algorithms. It should be mentioned that there is significant differences when the time criterion is considered. In the proposed model, if the number of the ants is increased, the time of solving increases proportionally. The results show that ACO2 achieves slightly better objective functions but in a significantly more solving time. In other words, whatever the number of the ants is increased, the result of the objective function will be better (the number of ants in ACO2 is ten times more than the number of ants in ACO1). Roughly speaking, although the differences between the responses of the objective functions are very close, the difference between solving times are significantly high. The proposed ACO2 can present better performances but in the enormous and unreasonable time. On average, ACO2 can achieve 0.43% better objective functions through 89% more solving time. Therefore, from the practical point of view, the ACO1 algorithm which is based on the tuning procedure is the more applicable algorithm which can achieve acceptable results in a reasonable time. Finally, in order to solve large-scale instances, the algorithm should be used 100 ants in 100 iterations. Finally, according to the results of Tables 8 and 9, the following conclusions can be achieved: firstly, in small-scale instances, Lingo is able to give the optimum solution and the proposed ACO algorithm can achieve to very-close-to-optimum objective functions. Secondly, the proposed metaheuristic algorithm presents an acceptable performance in real world scale instances so it can be a practical and also reliable algorithm. Thirdly, in 10th instance in Table 7, number of decision variables are 92,845 which is a very large instance and the ACO1 can solve such instance in 4933.3 min

7. Case study analysis Gold is a unique and special product. It may not be a precise date for the history of human interest in gold, but it is known that when the human life began on Earth, the interests of the beautiful objects are created with her/him. Gold has a very important role in the formation of human history as a very precious metal. For this reason and many other reasons, the gold industry is one of the large, high value, and competitive markets in the world which contains a both forward and reverse supply chains. The selected company is a popular and large Iranian company in gold industry with about 50 years of excellent background. The company has both forward and reverse flows of material but it encounters many problems in the integration and in the reverse flow. This study tries to help and elevate the efficiency and profitability of its CLSC network. The process of the mining, extraction, and production of gold is very slow. Therefore, if the reverse logistic is activated and work powerfully, the supply chain can achieve to more profits and higher sustainability together. In the investigated gold supply chain, the gold is extracted from the mine by suppliers and then

Table 10 Transportation cost, pollution, purchase cost, distance and capacity of vehicle matrixes between suppliers and manufacturing facilities. Transportation cost (Rials)

Supplier 1 Supplier 2 Supplier 1 Supplier 2 Supplier 1 Supplier 2

Manufacturing facility 1 1000 900 Manufacturing facility 3 98 100 Manufacturing facility 5 300 250

Pollution

Purchase cost (Rials)

Distance (Km)

Capacity of vehicle

12.59 12.59

215,000 232,000

350 383

e e

12.59 12.59

232,000 215,800

399 380

e e

12.00 11.95

214,000 231,500

94 111

e e

Transportation cost (Rials) Manufacturing facility 2 950 1000 Manufacturing facility 4 300 350 Manufacturing facility 6 50 50

Pollution

Purchase cost (Rials)

Distance (Km)

Capacity of vehicle

12.59 12.59

224,000 209,000

350 396

e e

11.96 12.01

224,000 214,500

108 92

e e

11.47 12.59

205,000 215,800

93 89

e e

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329

Table 11 Transportation cost, pollution, production cost, distance and capacity of vehicle matrixes between manufacturing facilities and distribution centers. Distribution center 1

Manufacturing Manufacturing Manufacturing Manufacturing Manufacturing Manufacturing

facility facility facility facility facility facility

1 2 3 4 5 6

Transportation cost (Rials)

Pollution

Production cost (Rials)

Distance (Km)

Capacity of vehicle

100 110 150 700 700 750

12.59 12.59 12.59 12.59 12.59 12.59

11,000 13,000 13,950 93,000 65,000 69,750

15.1 13.5 13.9 290 270 311

e e e e e e

Table 12 Transportation cost, pollution, distribution cost, distance and capacity of vehicle matrixes between distribution centers and customers. Transportation Pollution Distribution cost (Rials) Distance (Km) Capacity Transportation cost Pollution Distribution Distance (Km) Capacity of of vehicle (Rials) cost (Rials) vehicle cost (Rials) Customer 1 Distribution center 1 100 Customer 3 Distribution center 1 100

12.59

2000

7.1

e

11.95

2000

8.1

e

Customer 2 125 Customer 4 119.5

11.47

200

47

e

11

2000

12.02

e

Customer 5

Distribution center 1

Transportation cost (Rials)

Pollution

Distribution Cost (Rials)

Distance (Km)

Capacity of vehicle

1000

12.59

3000

990

e

Table 13 Transportation cost, pollution, collection/inspection cost, distance and capacity of vehicle matrixes between customers and collection centers. Collection center 1

Collection center 2

Transportation Pollution Collection/inspection Distance (Km) Capacity of Transportation Pollution Collection/inspection Distance (Km) Capacity of vehicle cost (Rials) cost (Rials) vehicle cost (Rials) cost (Rials) Customer Customer Customer Customer Customer

1 2 3 4 5

10,000 15,000 15,000 20,000 50,000

12.59 12.59 12.59 12.59 12.59

93,000 92,500 94,000 90,000 91,500

7.6 6.1 5.9 8.4 990

e e e e e

9000 14,000 17,000 22,000 70,000

12.59 12.59 11.47 12.59 12.59

92,000 92,000 93,500 93,000 89,000

8.2 7.1 12.2 10.1 994

e e e e e

Collection center 3

Customer Customer Customer Customer Customer

1 2 3 4 5

Transportation cost (Rials)

Pollution

Collection/inspection Cost (Rials)

Distance (Km)

Capacity of vehicle

15,000 15,000 15,000 20,000 100,000

11.47 12.59 12.59 11.95 12.59

92,000 95,000 91,000 92,000 93,000

4.5 6.0 7.0 8.1 995

e e e e e

the golds are forwarded to the manufacturing centers. The manufacturing process of the case study of this paper can be summarized as follows:

the mold cavity (It is full of wax and a wax copy of the model is prepared). ➢ Step 4: Branches

➢ Step 1: Modeling Something that is always fix in the casting jewelry, is casting operation with modeling. The model can be created with various materials such as metal, wax, plastic or etc. Modeling is to create or build a prototype of the piece principally that is done in several ways (for example, modeled on traditional methods, using the model CNC machines, using 3-D printing devices, using machinery of fast modeling). ➢ Step 2: The construction of the casting Casting is applied to produce a version of the model. ➢ Step 3: Wax injection At this point, wax injection machine tool, or silicon rubber mold (which are created in the previous step) is injected into

The prepared models of the previous step are glued using a soldering iron to a wire waxy to be a shrub in the bushes, and then put on rubber-soled for casting cylinder. ➢ Step 5: Plaster casting cylinder When the branch wax is finished, wax plugs in a metal cylinder casting with plaster for the casting. Then full it with special plaster until the branches is covered. ➢ Step 6: Removing and curing wax cylinder After the plaster was completely dry, the steam cylinder cast is put in wax stuck. Using indirect heat, the cylinder is heated and then wax has melted and removed from the plaster. After this phase which lasts about 2e3 h, cylinder is ready for baking.

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Table 14 Transportation cost, pollution, repair cost, distance and capacity of vehicle matrixes between collection centers and manufacturing facilities. Transportation cost (Rials) Pollution Repair Distance (Km) Capacity of Transportation cost (Rials) Pollution Repair cost Distance Capacity of cost (Rials) vehicle (Rials) (Km) vehicle Manufacturing facility 1 Collection center 1 15,000 12.59 Collection center 2 22,000 12.59 Collection center 3 15,000 12.59 Manufacturing facility 3 Collection center 1 17,000 12.59 Collection center 2 18,000 11.95 Collection center 3 20,000 12.59 Manufacturing facility 5 Collection center 1 89,000 12.59 Collection center 2 90,000 12.59 Collection center 3 92,000 12.59

92,000 92,000 93,000

8.5 9.1 7.1

e e e

80,000 82,000 85,000

8.8 12.1 15.2

e e e

93,000 92,000 92,000

295 289 292

Manufacturing facility 2 14,000 12.59 15,000 12.59 20,000 12.59 Manufacturing facility 4 75,000 12.59 100,000 12.59 75,000 11.95 Manufacturing facility 6 100,000 12.59 90,000 12.59 90,000 12.59

90,000 92,500 93,000

6.7 8.0 10.1

e e e

90,000 89,000 80,000

290 296 280

e e e

91,000 91,000 91,000

300 296 291

Table 15 Transportation cost, pollution, breakdown cost, distance and capacity of vehicle matrixes between Collection centers and recycling centers. Recycling center 1

Collection center 1 Collection center 2 Collection center 3

Transportation cost (Rials)

Pollution

Broke down cost (Rials)

Distance (Km)

Capacity of vehicle

51,000 52,000 51,000

12.59 12.59 12.59

70,000 62,000 65,000

1 1.2 1.0

e e e

Table 16 Transportation cost, pollution, income (revenue), distance and capacity of vehicle matrixes between Collection centers and recycling centers. Supplier 1

Supplier 2

Transportation cost Pollution Income (revenue) Distance Capacity of vehicle Transportation Pollution Income (revenue) Distance Capacity of cost vehicle Recycling center 1 30,000

12.59

800,000

296

e

30,000

12.59

800,000

e

298

Table 17 Transportation cost, pollution, disposal cost, distance and capacity of vehicle matrixes between recycling centers and disposal centers. Disposal center 1

Recycling center 1

Transportation cost

Pollution

Disposal cost

Distance (Km)

Capacity of vehicle

20,000

12.59

10

0.2

e

Table 18 Fixed costs of suppliers, manufacturer, distribution centers, collection centers, recycling center and disposal centers. Supplier 1

Manufacturing facility 2

1

2

3

Distribution center Collection center 4

5

6

1

Fixed cost 11,415,500 12,411,300 48,000 48,500 51,050 31,750 32,370 40,200 40,000

1

2

Recycling center Disposal center 3

1

28,100 29,800 26,900 12,000

1 10,600

➢ Step 7: Casting

➢ Step 9: Washing

By placing the cylinder in a centrifuge or in a vacuum casting machine, the casting begins. At this point, gold or other alloys used is melted and injected into the plaster mold.

At this stage, the ultrasonic cleaning machines are used to clean pieces of plaster removal of the wear particles in the work piece, such as small holes.

➢ Step 8: Cutting the branches of the casting When these were removed from the casting, it is necessary to cut the in order to branches casting be separated.

➢ Step 10: Polishing Polishing operations, in the machinery for the casting, are undertaken with materials such as ceramic parts, water, soft wood chips etc.

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

331

➢ Step 12: The final step

Table 19 Rates. RRco

RXoj

RYor

RUri

RDrd

RV

0.01

0.90

0.10

0.95

0.05

e

The above parameters are calculated in order to use as the inputs of the model. The model is again run with both LINGO and the developed ACO. The results are presented in Table 20.

After the polishing and washing stage, for final cleaning, the steam engine is used. After the final step of the production, the golds are ready to be forwarded to the customers. The distributors can be wholesalers, shopkeepers, etc. On the other hand, in the reverse logistics, the flow of return products is

Table 20 Final results. Maximum iteration

Number of ants

Lingo

ACO-based algorithm

CPU times (second)

Percentage error (Lingo ACO)

100 100

1000 100

388093908.1

388093908 388093908

227.812 21.25

0% 0%

Fig. 5. Melting the product and return it to the production cycle.

Manufacture 1

Customer 1

Manufacture 2

Supplier 1

Collection center 1

Customer 3

Collection center 3

Customer 4

Collection center 2

Manufacture 3

Distribution center Supplier 2

Customer 2

Manufacture 4

Manufacture 5

Recycle center

Disposal center

Customer 5

Manufacture 6

Fig. 6. The proposed logistics network for the case study.

➢ Step 11: Plating At this step, using an electrolyte, a very delicate layer of precious metals such as rhodium is set in ornaments that it creates special gloss on the surface.

active through the return of impaired products or the ones who want to sell their products. In these states, these products are collected by collection centers, wholesalers, and shopkeepers. When the golds are collected, three possible processes can occur: repairing, recycling, or disposing. The first choice is undertaken

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when the product is repairable so the product is sent to the gold manufacturers and the appropriate step of production is performed (such as polishing, plating and so on). The second and third processes are undertaken for the not-repairable products. These products are sent to the recycling centers. In this phase, the unrecoverable portions of the product are removed and sent to the disposal centers. The other parts of the product are sent to the suppliers in order to melt them and sending them back to the production cycle (see Fig. 5). In the presented case study, there are 2 suppliers (in the city of Esfahan), 6 manufacturers (3 in Esfahan and 3 in Tehran), 1 distribution center, 5 customers (4 in Tehran and 1 in Mashhad), 3 collection center, 1 recycle center and 1 disposal center. Customers demand are 200 g (Mr. Rajabi in Tehran), 200 g (Mr. Abbasi in Tehran), 200 g (Mr. Naraqi in Tehran), 200 g (Mr. Parsa, Tehran) and 200 g (Mr. Rahmani in Mashhad). Cost of sales per gram of gold is equal to 930,000 Rials of Iran.3 According to the analyses of this paper, the data are calculated and rarely estimated which are presented in Tables 10e18 Here, all costs and prices are in Rials of Iran. In addition, it should be pointed out that in this case study due to the low amount and high value of the products, the capacity of existing vehicles and effective loading percentage of a vehicles have been intended to be equal 1. Based on the nature of the gold, usually, the sedan cars are used for transportation so the amount of pollution in each stage is approximately the same. The distance is measured by Google Maps and the amount of demands is for one day. In Table 11, purchasing costs are calculated per grams of products. Because the customer 5 is in another province (Mashhad), so in comparison with others, his related costs are more. In Table 12, production costs are calculated for making a product (such as a gold necklace) from gold bullion. In Table 13, distribution costs are calculated based on various parameters. Since the calculated costs are for one day, the fixed costs are presented in Table 19 for one day based on the assumption of considering the useful life of facilities as 20 years. Finally, the various rates are achieved and illustrated in Table 20. According to the table above (Table 20), we can see that the proposed model has high precision and can be used on a real example. The proposed ACO shows acceptable performances in both quality of the solutions and the time of solving. According to the results, Supplier 1, manufacture facility 1 and 3, distribution center 1, the collection center 1, recycling center 1 and disposed center 1 are selected as optimal sites. For this purpose, it can be the answer for an optimal system in this case study. In other words, we recommend Fig. 6 as the optimum logistics network to the managers of the supply chain. Finally, the proposed model and the related solution approach is successfully implemented in the gold industry and the related recommendations are presented to the supply chain entities. We expected to achieve the acceptable and reasonable solutions at the appropriate time while providing high profits with minimal cost. Further, the paper expected to consider an aspect of green issue in CLSC network design which is successfully achieved. Besides, the practical evaluations through a case study is the most important role of this paper which we could present practical recommendations to the mangers of the selected gold supply chain. Results indicated that the proposed model and algorithm is efficient and reliable in generated instances and real case study.

3 One Dollar is equivalent to 29,960 Rials of Iran (Central Bank of Iran: http:// www.cbi.ir/).

8. Conclusion and future research This paper regards green approach in CLSC network design as an objective function of CO2 emissions. The approach is vital in mining industries such as gold industry so a complete gold supply chain is considered in this paper and the model is customized for the selected supply chain. The model can be successfully applied to the real case study and the green approach is regarded in the real instances. Besides, this paper provides a new solution methodology for the developed multi-stage green closed-loop logistics network model based on the ant colony optimization regarding for random and real instances. The ACO method is implemented for the case of gold company with seven layers. The optimization model explicitly considers green issue through the constraint and objective function. The developed model includes nearly all possible entities and flows in an integrated logistics network. On the other hand, few studies with small and large scale instances can be tracked in the recent literature in this topic. Besides, the performance of the algorithm is evaluated in various types of instances. For this purpose, the model is coded by Lingo 11 to achieve the global optimum and then the ACO-based algorithm is coded by MATLAB 7.13 software. Afterward, 14 instances with small sizes are developed and the performance of the ACO algorithm is compared with the global optimal solutions of Lingo software. The differences of two proposed types of ACO with the optimum points of Lingo are just 0.0198% and 0.0373% which are completely acceptable. Further, 10 different large-scale instances are developed and the mentioned types of ACO (called ACO1 and ACO2) are compared together in terms of time and the quality of solutions. The results demonstrate that these are both presented excellent performance with the mean differences of 0.48% for the objective functions. The results prove the applicability and reliability of the proposed ant colony optimization algorithm in real sizes situations. On the other hand, the green, multi-objective, integrated optimization model has been applied to the case of the gold industry. The optimization model explicitly considers green issues through the constraints and the objective functions. In summary, the proposed model is customized successfully for the case study and it leads to the appropriate modifications in the selected gold supply chain network. The proposed model and the developed solution methodology results in useful suggestions to the supply chain managers for the selected case study. Further, based on the main questions of research, we can say that the findings of the paper clarify the acceptable results in model developing, solution proposing, and real-life application of the model and solution approach. Based on the limitations and assumptions of the current study, some future research can be suggested. In this study, the model is a single product which can be developed to a multi-product network in order to cover more real case studies. Besides, the single-period approach of this paper can be developed to consider more periods. In this article, all parameters are considered deterministic, whereas in the real world some parameters are stochastic such as demand and price. The proposed green supply chain can be extended to a more complex multi-layered model and to other green approaches based on the real needs (such as wastes, petrol consumption, etc.). Performance investigation of the solution method can be further evaluated with other new solution methodologies such as cross entropy or even using simulation-based optimization techniques.

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

X

Acknowledgment The authors would like to thank the editor-in-chief Professor Donald Huisingh and the referees for their comments that significantly improved the earlier version of this paper. We are also grateful to Mr. Mohammad Javad Zohal general manager of the selected gold company for all of his supports and guidance.

k

c

XX i

X

o

Flowor ¼

Flowor ¼

Flowri ¼

o

Flowrd ¼

Flowkc RRc

(4)

X

Flowoj þ

Flowri þ

Flowor ¼

c

XX

Flowco

(5)

o

(14)

Flowor 

X

CAPo Zo

(15)

CAPr Mr

(16)

n

XX c

Flowco

(6)

o

Flowco RXoj

(7)

X

Flowrd 

X n

X

CAPd Ud

(17)

CAPi Xi

(18)

n

Flowri 

r

Flowco RYor

(8)

XX r

Flowrd

(9)

XX

Xj  MaxXj

(20)

Yk  MaxYk

(21)

Zo  MaxZo

(22)

Mr  MaxMr

(23)

Ud  MaxUd

(24)

n

k

n

XX n

XX n

d

Flowor RUri

(19)

n

j

r

d

Xi  MaxSi

n

i

o

o

X n

XX

o

Flowri þ

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d

XX

Flowco RYor ¼

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i

X

i

XX

XX

r

(10)

r

XX o

d

CAPk Yk

(3)

c

XX

X

r

X

XX r

(2)

Flowkc

XX c

Flowjk

k

c

XX c

Flowkc 

r

c

i

XX r

Flowco RXoj þ Flowoj ¼

XX j

XX o

r

XX r

Flowoj þ

Flowoj ¼

XX k

r

XX o

Flowco ¼

j

XX o

k

(13)

(1)

j

XX

CAPj Xj

n

X

o

XX o

Flowjk ¼

j

XX c

o

o

XX

Demc

(12)

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j

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k

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Flowij þ

X

Flowjk 

k

X

c

j

XX j

Flowkc ¼

X

CAPi Xi

n

c

Subject to, Subject to:

XX

X

j

X Appendix 1. Restrictions of proposed model

Flowij 

333

Flowor RDrd

(11)

r

Appendix 2. The parameters of the instance in numerical study

Table 10 Transportation cost, pollution, purchase cost, distance and capacity of vehicle matrixes between suppliers and manufacturing facilities Manufacturing facility 1

Manufacturing facility 2

Transportation cost Pollution Purchase cost Distance Capacity of vehicle Transportation cost Pollution Purchase cost Distance Capacity of vehicle Supplier 1 10 Supplier 2 15

15 10

10 15

12 14

400 400

14 12

10 10

12 14

14 10

600 600

334

Table 11 Transportation cost, pollution, production cost, distance and capacity of vehicle matrixes between manufacturing facilities and distribution centers Distribution center 1

Distribution center 3

Pollution

Production cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Production cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Production cost

Distance

Capacity of vehicle

20

15

20

12

400

20

10

15

20

500

15

13

14

15

450

20

12

20

15

400

22

12

20

15

500

17

14

16

13

450

Table 12 Transportation cost, pollution, distribution cost, distance and capacity of vehicle matrixes between distribution centers and customers Customer 1

Distribution center 1 Distribution center 2 Distribution center 3

Customer 2

Transportation cost

Pollution

Distribution cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Distribution cost

Distance

Capacity of vehicle

15 10 16

20 20 15

10 15 14

20 15 17

400 400 400

10 14 15

12 14 14

14 15 12

20 22 18

500 500 500

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

Manufacturing facility 1 Manufacturing facility 2

Distribution center 2

Transportation cost

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335

Table 13 Transportation cost, pollution, collection/inspection cost, distance and capacity of vehicle matrixes between customers and collection centers Collection center 1

Customer 1 Customer 2

Collection center 2

Transportation cost

Pollution

Collection/ inspection cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Collection/ inspection cost

Distance

Capacity of vehicle

14 13

20 15

10 10

15 14

200 200

13 11

12 11

11 10

14 15

300 300

Table 14 Transportation cost, pollution, repair cost, distance and capacity of vehicle matrixes between collection centers and manufacturing facilities Manufacturing facility 1

Collection center 1 Collection center 2

Manufacturing facility 2

Transportation cost

Pollution

Repair cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Repair cost

Distance

Capacity of vehicle

10

12

5

20

220

12

12

4

21

200

12

10

4

22

220

10

15

3

22

200

Table 15 Transportation cost, pollution, breakdown cost, distance and capacity of vehicle matrixes between Collection centers and recycling centers Recycling center 1

Collection center 1 Collection center 2

Transportation cost

Pollution

Broke down cost

Distance

Capacity of vehicle

20 15

15 17

5 6

18 17

400 400

Table 16 Transportation cost, pollution, income (revenue), distance and capacity of vehicle matrixes between Collection centers and recycling centers Supplier 1

Recycling center 1

Supplier 2

Transportation cost

Pollution

Income (revenue)

Distance

Capacity of vehicle

Transportation cost

Pollution

Income (revenue)

Distance

Capacity of vehicle

30

20

1

30

200

20

20

3

30

200

336

Table 17 Transportation cost, pollution, disposal cost, distance and capacity of vehicle matrixes between recycling centers and disposal centers Disposal center 1

Disposal center 3

Pollution

Disposal cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Purchase cost

Distance

Capacity of vehicle

Transportation cost

Pollution

Disposal cost

Distance

Capacity of vehicle

30

40

20

30

300

35

35

15

50

350

35

30

20

40

300 M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337

Recycling center 1

Disposal center 2

Transportation cost

Table 18 Fixed costs of suppliers, manufacturer, distribution centers, collection centers, recycling center and disposal centers Supplier

Fixed cost

Manufacturing facility

Distribution center

Collection center

Recycling center

Disposal center

1

2

1

2

1

2

3

1

2

1

1

2

3

5000

4500

5500

6000

7000

5000

6000

4000

2000

3500

2000

1000

1500

M. Zohal, H. Soleimani / Journal of Cleaner Production 133 (2016) 314e337 Table 19 Rates RRco

RXoj

RYor

RUri

RDrd

RV

0.20

0.20

0.80

0.80

0.20

0.90

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