Paper

International Journal of Supply and Operations Management

IJSOM May 2017, Volume 4, Issue 2, pp. 115- 132 ISSN-Print: 2383-1359

ISSN-Online: 2383-2525

www.ijsom.com

Design of a Forward/Reverse Logistics Network with Environmental Considerations

Masoud Rabbani *, a, Niloufar Akbarian Saravi a, Hamed Farrokhi-Asl b

a School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran b School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

An increase in environmental issues has encouraged the consideration of various factors that influence the environment.

In this regard, the green supply chain has attracted the attention of researchers because of its considerable impacts on the

environment. This study, therefore, was an attempt to design a forward/revers logistics network by putting emphasis on

some environmental issues like the quantity of CO2 emission in its model. In this logistics network, three objective

functions including minimizing the total cost and quantity of CO2 emission as well as maximizing the satisfaction of

customers are considered simultaneously. This persuaded the researchers to adopt multi-objective optimization methods.

Thus, Non-dominated sorting genetic algorithms (NSGA-ӀӀ) and Multi-objective particle swarm optimization (MOPSO)

are proposed to cope with the problem. Finally, the results of the experiments on several test problems are verified by

GAMS software. They confirm the superiority of NSGA-ӀӀ over MOPSO in terms of all comparison metrics.

Keywords: Green supply chain; CO2 emission; Forward/reverse logistics; Environmental issues; Multi-objective optimization.

1. Introduction

Nowadays, global warming and fluctuation in oil prices make protection of the environment a primary concern. Various

factors including greenhouse gases increase the temperature of the earth and in turn lead to global warming. Greenhouse

gases (GHGs), as one of the most important factors, are produced by human activities and industrial activities in both

developed and developing countries. Since there has been a rise in the amount of these gases, global warming has become

a major issue all over the world. It leads to an increase in the number of hurricanes and floods, accelerates the ice melt

at the poles, and causes other environmental problems. Therefore, it is important to consider environmental factors

besides social and economic factors to design a logistics network and to determine an appropriate allocation of facilities

in order to decrease the greenhouse gases emitted from factories and vehicles.

Recently, many researchers have focused on the concept of supply chain management (SCM), which dates back to the

early 1990, as well as increasing profitability and staying competitive in firms as the most significant role of the supply

chain (Choon Tan et al., 2002; Li et al., 2006; Pasandideh et al., 2015). Forward/reverse logistics is one of the sub-

branches of the field of supply chain management which has captured the attention of researchers regarding

environmental, social, and economic factors (Govindan et al., 2015). Resource restrictions along with the increasing

costs of logistics networks, and tendency towards using new products instead of consumed products in the environment

promote designing logistic networks with considering both forward and reverse flows (Saffari et al., 2015).

Passengers and freight transport generate a number of activities which impact on sustainability and international

economy. Also, these activities have their own consequences, especially those related to the environment (Wang et al.,

2011). As such, governmental and environmental regulations and the increasing demands of customers for products and

services force companies to reconsider how they can administer their supply chains with regard to environmental issues.

Thus, in order to reduce environmental effects and achieve environmental efficiency, an increasing emphasis is being

placed on green aspects (Kumar et al., 2017)

*Corresponding author email address: [email protected] 115

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Green supply chain has gained in popularity among firms and research companies due to the importance of industrial

ecology (Graedel et al., 1995). Industrial ecology is described as a systematic organizing framework associated with

aspects of environmental management (Lowe, 1993). Carbon dioxide (CO2), one of the most important greenhouse

gases, is produced from human activities. An increase in the CO2 emission, for a considerable portion of which human

activities are responsible, has a negative impact upon the natural cycle. On the other hand, supply chain comprises

different activities including production, transportation, recovery, and so forth. Thus, considering environmental factors

has significant effects on designing supply chain networks (Saffar and Razmi, 2014). Designing facilities in logistics

networks and designing suitable forward/reverse logistics have a profound impact on the profitability of systems which

depend on many factors with social, economic, and environmental aspects.

In this regard, taking economic factors into consideration influences determining an appropriate allocation and designing

suitable logistics networks. The establishment cost of each center as well as the transmission cost of each unit among

each center affect the design of logistics networks.

It is also necessary to take social factors into account due to the increasing requirements of customers. Customer

responsiveness, an important factor related to the quality of products and delivery time, is increased by both enhancing

products' quality and timely delivery of products.The rest of this paper is organized as follows: A brief literature review

is provided in Section 2. It is followed by the problem and the methodology to tackle it in Section 3. Section 4 is devoted

to the parameters tuning for NSGA-ӀӀ and MOPSO algorithms. Experimental results and sensitivity analyses are given

in section 5. Finally, conclusions and future research directions are provided in Section 6.

2. Literature Review

In recent years, researchers have studied various topics related to supply chain. As a result, a mixed-integer linear

programming for designing reverse logistics network models is presented. In addition to considering demand as a

deterministic parameter, the economic aspects which influence logistics networks are studied (El Saadany and El-

Kharbotly). A memetic algorithm is introduced by Pishvaee et al. (2010) in order to design an integrated forward/reverse

logistics network. In this study the objective functions are related to customer responsiveness and total cost which are

maximized and minimized respectively. An impressive memetic algorithm is fostered to discover a set of non-dominated

solutions. Moreover, a mixed integer linear programming model is presented by Pishvaee et al. (2011) to design a closed-

loop supply chain network. Because of the growing concern for transformation in the business environments like

demands of customers and transportation cost, the robust optimization model is considered for supply chain. The model

utilizes the intrinsic uncertainty of input data in closed-loop supply chain network design problems. A mixed integer

linear optimization is presented to select appropriate sources, CO2 storage sites, and the optimal total minimum cost in

supply chain management frameworks (Pishvaee and Razmi, 2012). Diabat et al. (2013) also introduced a multi-echelon

multi-commodity facility location problem dealing with the cost of carbon emission and cost of preparation.

In another study, Mousazadeh et al. (2014) considered the green supply chain and reverse logistics simultaneously to

reduce the environmental pollution. Fuzzy environment through analyses of the previous literature and systematic review

is used to design and plan reverse and green logistics. Choudhary et al. (2015) presented a quantitative optimization

model for the forward/reverse logistics which consider CO2 emission in order to facilitate layout decision. The aim of

the proposed model was to minimize carbon footprint and total cost by a genetic algorithm (Kumar et al.). In the same

vein, Soysal et al. (2015) introduced a multi-period model for inventory routing which includes the evaluation of CO2

emission and fuel consumption. The model showed that when the requirement of service level is satisfied and a better

support system is proposed, a considerable saving in the overall cost is achieved. Kalyanarengan et al. (2016) also

proposed a multi-objective fuzzy mathematical model to design a supply chain by considering environmental factors of

different alternatives for supply chain network. In addition to the traditional cost, the life cycle method was applied to

evaluate and quantify the environmental factors. In fact, optimization of the network design is a key factor in improving

economic, environmental, and social efficiency (Ghaderi et al., 2016). Soleimani et al. (2016) designed a closed-loop

multi-period, multi-product supply chain network. They assumed demand and price to be stochastic by using mixed

integer linear programming, studied forward/reverse logistics models which include multi-period, multi-echelon and

vehicle routing, and considered particle swarm optimization and artificial immune system algorithms. The aim was to

maximize the total expected profit and to obtain an appropriate route for the vehicle corresponding to an optimal solution

(Kumar et al., 2017). Significant features of the mentioned studies and this study about different environmental,

economic, and social aspects are listed in Table 1.

The main contribution of this study which distinguishes it from the existing relevant research can be presented as follows:

To have satisfactory and favorable environmental conditions, it is necessary to consider the amount of CO2 emitted

through vehicles and factories in the forward/reverse logistics networks and we did so. To the best of authors' knowledge,

this study is the first study which considers environmental, social, and economic aspects simultaneously. In addition,

two applicable algorithms are used in the study in order to obtain the best approach to solve the proposed problem.

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Table 1. Significant features of this study and different relevant aspects of other studies

Study Solution methods Type of

network a

Factors b Objective c

F L RL EV EC SC C QC RS

Pishvaee et al. (2010) Memetic algorithm      

Pishvaee et al. (2011) MILP     

Pishvaee and Razmi (2012) LCA    

Diabat et al. (2013) MILP      

Mousazadeh et al. (2014) Fuzzy mathematical

programming

   

Choudhary et al. (2015) GA    

Soysal et al. (2015) MILP      

Soleimani et al. (2016) MILP    

Kalyanarengan et al.

(2016)

MILP   

Kumar et al. (2017) PSO, AIS     

This study NSGA-ӀӀ,MOPSO        

aFL : forward logistics, RL: reverse logistics bEV : environmental, EC: economic, SC: social cC: cost, QC: quantity of CO2 emission, RS: responsiveness

3. Problem definition

In this paper, the integrated forward/reverse logistics network (IFRLN) is a multi-category logistics network containing

production, distribution, customer zones, collection/inspection, recovery and disposal centers with multi-level capacities.

First, in the forward flow, new products are shipped from production centers to customer zones through distribution

centers to meet the demand of each customer. Then, in the reverse flow, returned products are collected in collection/

inspection centers. Our strategy in this model is to minimize the total costs and maximize the responsiveness of the

logistics network. The returned products can be transported directly to the suitable facilities. Because the recoverable

products are sent to recovery facilities and scrapped products are sent to disposal centers after testing, the total cost will

be minimized. Furthermore, considering hybrid processing facilities with both distribution and collection centers

established at the same location decreases the total cost. In addition to minimizing the total cost, maximization of the

responsiveness is considered in the study. It is important to save the resulting cost with regard to separate distribution

and collection centers. Also, in response to the increase in global warming, a crucial strategy is to consider and control

the quantity of greenhouse gases such as CO2 emitted through vehicles and factories. To this end, shipping of products

through various centers is accomplished by three types of vehicles, namely CNG, gasoline, hybrid. Using these vehicles

influences the release of greenhouse gases. Therefore, the model intends to consider the quantity of CO2 emission per

units shipped from different centers. Using hybrid-collection facilities is a decision variable, and as mentioned before,

we considered a three-transport system between the centers. This study aims to design a model between these transport

systems to recognize which system is better in terms of pollution and environmental issues besides traditional costs and

customer responsiveness. The resulting network of supply chain is shown in Figure 1. Forward and revers flows are

demonstrated by dark and dotted arrows, respectively. It should be pointed out that customer zones are assumed to be

predetermined and constant in this network. Other assumptions are as follows:

 Emission from transportation is assumed to be proportional to the type of vehicle.

 It is assumed that emission from facilities is relevant to production centers and it is not considered for other

centers.

 Emission from transportation is assumed to be proportional to the distance of both centers between which

products are shipped.

 All of the parameters are assumed to be deterministic.

 The total amount of products carried by a vehicle does not exceed its capacity.

 Shortage is not allowed and all demands of customers and centers should be satisfied.

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Production Distribution

Collection/

inspection

customer

Disposal

Figure 1. A generic form of forward/reverse logistics

The following notations are used in the formulation of the integrated forward/reverse logistics model according to the

schematic form of logistics:

Sets:

B potential number of distribution centers b∈ 𝐵 P potential number of production/recovery centers p∈ 𝑃 C potential number of customer zones c∈ 𝐶 I potential number of collection/inspection centers 𝑖 ∈ 𝐼 G potential number of disposal centers 𝑔 ∈ 𝐺 F set of capacity level available for facilities 𝑓, 𝑓′ ∈ 𝐹 K set of vehicle types, namely CNG, hybrid, gasoline, k ∈ {1,2,3}

J set of joint potential sites between collection/inspection centers and distribution centers 𝑗 ∈ 𝐽 𝐽 ∈ 𝐵 𝐽 ∈ 𝐼

Parameters:

𝑑𝑐 Demand of customer zone c 𝑟𝑐 Rate of the return of used products from customer zone c 𝑤 Average disposal fraction

𝑓𝑖𝑓𝑝 fixed cost of opening production/recovery center p with capacity level f

𝑜𝑐𝑓𝑏 fixed cost of opening distribution center b with capacity level f

ℎ𝑓𝑖 fixed cost of opening collection/inspection center i with capacity level f

𝑎𝑓𝑔 fixed cost of opening disposal center g with capacity level f

𝑓𝑐𝑓𝑓′𝑗 fixed saving cost associated with opening distribution center with capacity level f and collection/inspection center at joint potential site j with capacity level 𝑓′

𝑐𝑥𝑝𝑏𝑘 shipping cost per unit of products from production/ recovery center p to distribution center b by vehicle k

𝑐𝑢𝑏𝑐𝑘 shipping cost per unit of products from distribution center b to customer zone c by vehicle k 𝑐𝑞𝑐𝑖𝑘 shipping cost per unit of returned products from customer zone c to collection/inspection center I by

vehicle k

𝑐𝑝𝑖𝑝𝑘 shipping cost per unit of recoverable products from collection/inspection center i to production/recovery center p by vehicle k

𝑐𝑠𝑖𝑔𝑘 shipping cost per unit of scrapped products from collection/inspection center i to disposal center g by vehicle k

𝜕𝑓𝑝 capacity of production with level f for production/ recovery center p

𝜑𝑓𝑏 capacity with level f for distribution center b

𝜔𝑓𝑖 capacity with level f for collection/inspection center i

𝛾𝑓𝑔 capacity with level f for disposal center g

𝜏𝑘 capacity for each transportation vehicle k 𝑒𝑝𝑏𝑘 quantity of CO2 emission from production center p to distribution center b by transportation vehicle k

𝑒𝑏𝑐𝑘 quantity of CO2 emission from distribution center b to customer zone c by transportation vehicle k 𝑒𝑐𝑖𝑘 quantity of CO2 emission from customer zone c to inspection/collection center i by transportation vehicle k 𝑒𝑖𝑝𝑘 quantity of CO2 emission from inspection/collection center i to production center p by transportation

vehicle k

𝑒𝑖𝑔𝑘 quantity of CO2 emission from customer zone c to inspection/collection center i by transportation vehicle k

𝑒′𝑝 quantity of CO2 emission per unit of product from center p

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𝑡𝑓𝑏𝑐 delivery time from distribution center b to customer zone c 𝑡𝑟𝑐𝑖 collection time from customer zone c to collection/ inspection center i 𝑑𝑒𝑙𝑓 expected delivery time in the forward network

𝑑𝑒𝑙𝑟 expected delivery time in the reverse network 𝐷𝐿𝑓𝑐 = {b|𝑡𝑓𝑏𝑐 ≤ 𝑑𝑒𝑙𝑓 }

𝐷𝐿𝑟𝑐 ={i|𝑡𝑟𝑐𝑖 ≤ 𝑑𝑒𝑙𝑟 } α a sufficient large number (α≥w∗ ∑ 𝑟𝑐𝜖𝐶 cdc) 𝜆 weighting factor (importance) for the forward responsiveness in second objective function; (1-𝜆)denotes

the weight of the reverse responsiveness

Variables:

𝑥𝑝𝑏𝑘 quantity of products shipped from production/recovery center p to distribution center b by transportation vehicle k

𝑢𝑏𝑐𝑘 quantity of products shipped from distribution center b to customer zone c by transportation vehicle k 𝑞𝑐𝑖𝑘 quantity of returned products shipped from customer zone c to collection/inspection center i by transportation

vehicle k

𝑐𝑙𝑖𝑝𝑘 quantity of recoverable products shipped from collection/inspection center i to production/recovery center p by transportation vehicle k

𝑦𝑖𝑔𝑘 quantity of scrapped products shipped from collection/ inspection center i to disposal center g by transportation vehicle k

𝑍𝑓𝑝:{ 1 𝑖𝑓 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑟𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝑐𝑒𝑛𝑡𝑒𝑟

𝑤𝑖𝑡ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑓 𝑖𝑠 𝑜𝑝𝑒𝑛𝑒𝑑 𝑎𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑝 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑂𝑓𝑏 :{ 1 𝑖𝑓 𝑎 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑐𝑒𝑛𝑡𝑒𝑟 𝑤𝑖𝑡ℎ

𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑓 𝑖𝑠 𝑜𝑝𝑒𝑛𝑒𝑑 𝑎𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑑 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑀𝑓𝑖 :{

1 𝑖𝑓 𝑎 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛𝑠𝑝𝑒𝑐𝑡𝑖𝑜𝑛 𝑐𝑒𝑛𝑡𝑒𝑟 𝑤𝑖𝑡ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦

𝑙𝑒𝑣𝑒𝑙 𝑓 𝑖𝑠 𝑜𝑝𝑒𝑛𝑒𝑑 𝑎𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑖 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑁𝑓𝑔:{ 1 𝑖𝑓 𝑎 𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 𝑐𝑒𝑛𝑡𝑒𝑟 𝑤𝑖𝑡ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦

𝑙𝑒𝑣𝑒𝑙 𝑓 𝑖𝑠 𝑜𝑝𝑒𝑛𝑒𝑑 𝑎𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑔 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑡𝑓𝑓′𝑗:{ 1 𝑖𝑓 𝑎 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑐𝑒𝑛𝑡𝑒𝑟𝑠

𝑎𝑟𝑒 𝑙𝑜𝑐𝑎𝑡𝑒𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Min 𝑊1= ∑ ∑ 𝑓𝑖𝑓𝑝𝑍𝑓𝑝

𝑓∈𝐹𝑝∈𝑃

+ ∑ ∑ 𝑜𝑐𝑓𝑏 𝑂𝑓𝑏 𝑏∈𝐵𝑓∈𝐹

+ + ∑ ∑ ℎ𝑓𝑖 𝑀𝑓𝑖 𝑖∈𝐼𝑓∈𝐹

+ ∑ ∑ 𝑎𝑓𝑔 𝑁𝑓𝑔 + ∑ ∑ ∑ 𝑐𝑥𝑝𝑏𝑘 𝑥𝑝𝑏𝑘 𝑘∈𝐾𝑏∈𝐵𝑝∈𝑃𝑔∈𝐺𝑓∈𝐹

+ ∑ ∑ ∑ 𝑐𝑢𝑏𝑐𝑘 𝑢𝑏𝑐𝑘 𝑘∈𝐾𝑏∈𝐵𝑐∈𝐶

+ ∑ ∑ ∑ 𝑐𝑞𝑐𝑖𝑘 𝑞𝑐𝑖𝑘 +

𝑘∈𝐾𝑖∈𝐼𝑐∈𝐶

∑ ∑ ∑ 𝑐𝑠𝑖𝑔𝑘 𝑦𝑖𝑔𝑘 𝑘∈𝐾𝑔∈𝐺𝑖∈𝐼

+ ∑ ∑ ∑ 𝑐𝑝𝑖𝑝𝑘 𝑐𝑙𝑖𝑔𝑘 −

𝑘∈𝐾𝑔∈𝐺𝑖∈𝐼

∑ ∑ ∑ 𝑐𝑓𝑖𝑓𝑓′𝑗 𝑇𝑓𝑓′𝑗 𝑗∈𝐽𝑓′∈𝐹𝑓∈𝐹

(1)

Max𝑊2 =

𝜆 (∑ ∑ ∑ 𝑢𝑏𝑐𝑘 𝑘∈𝐾𝑐∈𝐶𝑏∈𝐵

) / ( ∑ 𝑑𝑐 𝐶∈𝐷𝐿𝑓𝑐

) + (1 − 𝜆) (∑ ∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾𝑖∈𝐼𝑐∈𝐶

) / ( ∑ 𝑟𝑐 𝑑𝑐 𝐶∈𝐷𝐿𝑟𝑐

)

(2)

Min𝑊3 = ∑ ∑ ∑ 𝑥𝑝𝑏𝑘 𝑘∈𝑘𝑏∈𝐵𝑝∈𝑃

. 𝑒𝑝𝑏𝑘 + ∑ ∑ ∑ 𝑢𝑏𝑐𝑘 . 𝑒𝑏𝑐𝑘 𝑘∈𝐾𝑐∈𝐶𝑏∈𝐵

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+ ∑ ∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾𝑖∈𝐼𝑐∈𝐶

. 𝑒𝑐𝑖𝑘 + ∑ ∑ ∑ 𝑐𝑙𝑖𝑝𝑘 . 𝑒𝑖𝑝𝑘 𝑘∈𝐾𝑝∈𝑃

𝑖∈𝐼

+ ∑ ∑ ∑ 𝑦𝑖𝑔𝑘 . 𝑒𝑖𝑔𝑘 𝑘∈𝐾𝑔∈𝐺𝑖∈𝐼

+ ∑ ∑ 𝑥𝑝𝑏𝑘 .

𝑘∈𝐾

𝑒′𝑝 𝑏∈𝐵

(3)

∑ ∑ 𝑢𝑏𝑐𝑘 𝑘∈𝐾𝑏∈𝐵

= 𝑑𝑐 ∀𝑐 ∈ 𝐶 (4)

∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾𝑖∈𝐼

= 𝑟𝑐 𝑑𝑐 ∀𝑐 ∈ 𝐶 (5)

∑ ∑ 𝑥𝑝𝑏𝑘 𝑘∈𝐾𝑝∈𝑃

= ∑ ∑ 𝑢𝑏𝑐𝑘 𝑐∈𝐶

𝑘∈𝐾

∀𝑏 ∈ 𝐵 (6)

∑ ∑ 𝑦𝑖𝑔𝑘 𝑔∈𝐺𝑘∈𝐾

= 𝑊 ∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾𝑐∈𝐶

∀𝑖 ∈ 𝐼 (7)

∑ ∑ 𝑐𝑙𝑖𝑝𝑘 = (1 − 𝑊)

𝑝∈𝑃𝑘∈𝐾

∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾

𝑐∈𝐶

∀𝑖 ∈ 𝐼 (8)

∑ ∑ 𝑥𝑝𝑏𝑘 𝑏∈𝐵𝑘∈𝐾

≤ ∑ 𝑍𝑓𝑝 𝑓∈𝐹

𝜕𝑓𝑝 ∀𝑝 ∈ 𝑃 (9)

∑ ∑ 𝑥𝑝𝑏𝑘 𝑘∈𝐾𝑝∈𝑃

≤ ∑ 𝑂𝑓𝑏 𝑓∈𝐹

𝜑𝑓𝑏 ∀𝑏 ∈ 𝐵 (10)

∑ ∑ 𝑢𝑏𝑐𝑘 𝑐∈𝐶

≤

𝑘∈𝐾

∑ 𝑂𝑓𝑏 𝑓∈𝐹

𝜑𝑓𝑏 ∀𝑏 ∈ 𝐵 (11)

∑ ∑ 𝑞𝑐𝑖𝑘 𝑘∈𝐾𝑐∈𝐶

≤ ∑ 𝑀𝑓𝑖 𝑓∈𝐹

𝜔𝑓𝑖 ∀𝑖 ∈ 𝐼 (12)

∑ ∑ 𝑦𝑖𝑔𝑘 𝑘∈𝐾𝑖∈𝐼

≤ ∑ 𝑁𝑓𝑔 𝑓∈𝐹

𝛾𝑓𝑔 ∀𝑔 ∈ 𝐺 (13)

∑ ∑ 𝑐𝑙𝑖𝑝𝑘 𝑘∈𝐾𝑖∈𝐼

≤ ∑ 𝑍𝑓𝑝 𝑓∈𝐹

𝜕𝑓𝑝 ∀𝑝 ∈ 𝑃 (14)

∑ ∑ 𝑦𝑖𝑔𝑘 𝑘∈𝐾𝑔∈𝐺

+ ∑ ∑ 𝑐𝑙𝑖𝑝𝑘 𝑘∈𝐾𝑝∈𝑃

≤ ∑ 𝑀𝑓𝑖 𝑓∈𝐹

𝜔𝑓𝑖 ∀𝑖 ∈ 𝐼 (15)

∑ ∑ 𝑐𝑙𝑖𝑝𝑘 ≤ α ∑ ∑ 𝑥𝑝𝑏𝑘 𝑏∈𝐵𝑝∈𝑃𝑝∈𝑃𝑖∈𝐼

∀𝑖 ∈ 𝐼 (16)

∑ ∑ 𝑥𝑝𝑏𝑘 𝑏∈𝐵𝑝∈𝑃

≤ 𝑐𝑎𝑦𝑘 ∀𝑘 ∈ 𝐾 (17)

∑ ∑ 𝑢𝑏𝑐𝑘 𝑐∈𝐶𝑏∈𝐵

≤ 𝑐𝑎𝑦𝑘 ∀𝑘 ∈ 𝐾 (18)

∑ ∑ 𝑐𝑙𝑖𝑝𝑘 𝑝∈𝑃𝑖∈𝐼

≤ 𝑐𝑎𝑦𝑘 ∀𝑘 ∈ 𝐾 (19)

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∑ ∑ 𝑞𝑐𝑖𝑘 𝑖∈𝐼𝑐∈𝐶

≤ 𝑐𝑎𝑦𝑘 ∀𝑘 ∈ 𝐾 (20)

∑ ∑ 𝑦𝑖𝑔𝑘 𝑔∈𝐺𝑖∈𝐼

≤ 𝑐𝑎𝑦𝑘 ∀𝑘 ∈ 𝐾 (21)

∑ 𝑍𝑓𝑝 𝑓∈𝐹

≤ 1 ∀𝑝 ∈ 𝑃 (22)

∑ 𝑂𝑓𝑏 𝑓∈𝐹

≤ 1 ∀𝑏 ∈ 𝐵 (23)

∑ 𝑀𝑓𝑖 𝑓∈𝐹

≤ 1 ∀𝑖 ∈ 𝐼 (24)

∑ 𝑁𝑓𝑔 𝑓∈𝐹

≤ 1 ∀𝑔 ∈ 𝐺 (25)

2𝑡𝑓𝑓′𝑗 ≤ 𝑚𝑓′𝑗 + 𝑜𝑓𝑗 ∀𝑗 ∈ 𝐽 , ∀𝑓 ∈ 𝐹, ∀𝑓′ ∈ 𝐹 , (26)

𝑍𝑓𝑝 , 𝑂𝑓𝑏 , 𝑀𝑓𝑖 , 𝑁𝑓𝑔 ∈ {0,1} ∀𝑔 ∈ 𝐺, ∀𝑖 ∈ 𝐼, ∀𝑏 ∈ 𝐵, ∀𝑝 ∈ 𝑃 (27)

𝑥𝑝𝑏𝑘 , 𝑢𝑏𝑐𝑘 , 𝑞𝑐𝑖𝑘 , 𝑐𝑙𝑖𝑝𝑘 , 𝑦𝑖𝑔𝑘 b∈ 𝐵 p∈ 𝑃 c∈ 𝐶 𝑖 ∈ 𝐼 𝑔 ∈ 𝐺 (28)

Objective function (1) minimizes the total cost including fixed opening cost, transportation costs and the cost saving

because of the collection and distribution centers allocated in the same location. Objective function (2) maximizes the

forward and reverse responsiveness of the integrated network. Objective function (3) minimizes the dangerous CO 2

emission released from vehicles. Constraints (4) and (5) demonstrate that the demands of all customers are satisfied and

the returned products from all customer zones are collected. Constraints (6)-(8) assure the flow balance at

production/recovery, distribution, collection/inspection, disposal and customer centers. Constraints (9)-(16) are capacity

constraints on facilities, which also prevent the units of products, returned products, recoverable and scrapped products

from being transferred to facilities which are not open. Constraints (17)-(21) are capacity constraints on vehicles in terms

of the quantity of products shipped from different centers by transportation vehicles. Finally, Constraints (22)-(25) ensure

that a facility can be assigned at most one capacity level. The constraint (26) shows that the value of 𝑡𝑓𝑓′𝑗 could not be 1

in three conditions. Finally, Constraint (27) and (28) place the binary and non-negative restrictions on the corresponding

decision variables.

4. Methodology

The proposed model in this research aims to not only minimize the total cost and CO2 emission but also maximize the

responsiveness of logistics network for the first, second, and third objective functions. Using multi-objective

evolutionary algorithms is supported in this study because of the existence of contradiction between multiple objectives

functions and the NP-hard nature of the problem (Davis and Ray, 1969).

Therefore, two well-known multi-objective evolutionary algorithms which have been investigated widely by researches

are utilized in this study. In other words, the non-dominated sorting genetic algorithm (NSGA-ӀӀ) and Multi-objective

particle swarm optimization (MOPSO) algorithm are used in order to tackle the proposed problem. The next section

explains these algorithms and the process of individual solution decoding.

4.1. solution representation Complexity and calculating time considerably rely on a scheme of solution representation. The structure of the problem

is based on the order recognized as the most efficient method to encode the solutions of problem.

To decode the problem, the chromosome is divided into several sections devoted to the number of node and related to

each echelon of forward/reverse logistics network. Each section also determines components of systems. Each

chromosome is described based on the order of the problems nodes and components. In this paper, the coding of this

approach solution is considered as 3 (B + P + C + I + G) matrix in which B, P, C, I and G denote the number of production center, number of distribution center, number of customer, number of inspection center, and number of

disposal center, respectively (See Figure 2). In this structure, the characterization of the first, second and third rows of

chromosome is determined respectively as follows:

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 Generation of random numbers by uniform distribution is utilized in order to characterize the first row of the chromosome which shows the allocation of centers in terms of ranking the number of cells. In other words, each

row is characterized by generating numbers in the range of 0 to 1. These numbers show the priority of nodes in

descending order.

 The second row of the chromosome is devoted to the capacity level of facilities. Three levels have been considered for each facility. This level is generated randomly.

 Type of vehicles used for transporting goods is shown in the third row. Because of considering three types of vehicles, the number of this row is generated by integer numbers in the range of 1 to 3.

Figure 2. Solution representation

The decoding procedure is then introduced in order to convert this structure into meaningful solutions and to extract the

decision variables related to each solution representation. First, in the forward logistics the production and distribution

center is devoted to customers. The ranking of customers obtained through sorting the number of first row is considered

for selection. Then, by considering the demand of customers and assigning the appropriate customer, capacity of the

distribution center is determined. After responding to all demands of customers and determining the distribution nodes,

the production center is devoted and assigned through ranking the numbers. Similarly, in the reverse logistics, the first

devotion is related to customers. Returned products are shipped to inspection by considering the rank and capacity of the

node. The transportation systems are then assigned to all facilities by randomly-generated numbers and the capacity level

considered for each center is assigned in terms of the generated number in each cell. Figure 2 illustrates this procedure.

In the production center the customer with the higher rank order, that is equal to 0.46, is selected. Then, its capacity level

and vehicle mode can be determined, and the remaining nodes of the concerned supply chain are specified.

Because of the straightforward implementation of this description scheme for two algorithms, namely NSGA-II and

MOPSO, it seems that the same procedure should be used in presenting a chromosome.

4.2. proposed NSGA-ӀӀ The Non-dominated Sorting Genetic Algorithm (NSGA-II) is proposed which has been widely applied to multi-objective

optimization problems with two or more conflicting objective functions (Farrokhi-asl et el. 2016). It is a genetic algorithm

with the selection of characteristics in the phase of selection. Consequently, in such problems just one global optimum

solution does not exist for optimizing objective functions simultaneously. The Pareto-optimal solution which is not

dominated by any other solution has been utilized in this algorithm and improved by deteriorating at least one objective

function.

A basic representation of NSGA-II algorithm is demonstrated in Figure 3. In NSGA-II algorithm, every solution is ranked

by a fast sorting procedure. As is shown in the flowchart, the population P0 with population size Np is initialized in

NSGA-II randomly and the population P0 is sorted in order to obtain the best population P0. Selection is applied utilizing

the value of the ranked Pareto and crowded distance to discriminate within the rank. Offspring population O0 is generated

according to the rate of crossover Pc and mutation Pm. Firstly, tournament selection operators are used to select the

individuals as parents. Through this selection method, the individuals which have a better rank and less distance of

crowding have a high probability of being selected. In accordance with sorting the non-dominated and crowded distance,

union population Rt =Pt∪Qt is formed. Then, using the best individuals of union population the next population Pt+1 is constructed. This algorithm will be iterated until satisfying the criterion. Pareto optimal solutions are obtained through

ranking the individuals of the last population. The first rank of the individuals is the Pareto solution.

4.3. NSGA- ӀӀ operators Two operators are employed in order to justify a much better spread of solutions. In other words, this makes us certain

that total space of the solution has been fully explored. More specifically, mutation and crossover operators have been

utilized to generate new individuals from their old chromosome. Then the pair of chromosomes recombine and influence

continuity of the process of evolutionary algorithm. After the recombination, new chromosomes are bored which may

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Generate the initial solutions

population P 0 of size N

Assess the value of fitness objective

function population

Use selection, crossover and mutation

to creat offspring Qt

Sort Non-dominated based on ranking

and crowding distance

Criteria is satisfied

Obtain the best solutions

Combine parent and offspring

population to create the union

poulation

Yes

No

Select population with size N based on

ranking

Figure 3. flowchart of NSGA-ӀӀ

have better features compared with their parents. Local optimum has been obtained through diversity of solutions and

prohibiting the process of search which have been guaranteed by the mutation operator. These operators are of many

types. Details of the selected operators and how to implement them are explained below.

4.3.1. Crossover The steps of crossover two parents and generating two new children are shown in Figure 4. Single point crossover

technique is used by regarding the structure of the chromosomes. To put it another way, each row of the chromosome

used single point crossover separately. First, one point of the chromosome is selected randomly. Then, the right

information of the first parents is scanned from the beginning to the crossover point in the first child and the left

information is copied in the second child. The right information of the second parents is copied in the second child and

the left information is scanned in the first child. The crossover approach guarantees the feasibility of the new populations.

4.3.2. Mutation Figure 5 shows the implementation of the mutation operator. In inversion mutation, we select a subset of genes like in

scramble mutation, but instead of shuffling the subset, we merely invert the entire string in the subset.

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Figure 4. Single point crossover operator

Figure 5 .Inversion mutation operator

4.4. MOPSO algorithm An extension of Particle Swarm Optimization algorithm for solving multi-objective problems such as simplicity of

implementation and coverage of search process to an acceptable solution is proposed by Coello et al. (2004) and is called

Multi Objective Particle Swarm Optimization algorithm (MOPSO). The intelligence group is the main idea of this

algorithm that includes knowledge of previous best position (𝑥𝑝𝑏𝑒𝑠𝑡 )and the global best position of all swarm (𝑥𝑔𝑏𝑒𝑠𝑡 ).

Updating the velocity and the position of particle 𝑎 for 𝑗h dimension at iteration 𝑡 + 1 explained by 𝑣𝑎𝑗 (𝑡 + 1) and

𝑥𝑎𝑗 (𝑡 + 1)is done based on Equations (29) and (30).

𝑣𝑎𝑗 (𝑡 + 1) = 𝑤 × 𝑣𝑎𝑗 (𝑡) + 𝑐1 × 𝑟1 × (𝑥𝑝𝑏𝑒𝑠𝑡 (𝑡) − 𝑥𝑎𝑗 (𝑡) + 𝑐2 × 𝑟2 × (𝑥𝑔𝑏𝑒𝑠𝑡 (t)- 𝑣𝑎𝑗 (𝑡)) (29)

𝑥𝑎𝑗 (𝑡 + 1) = 𝑥𝑎𝑗 (𝑡) + 𝑣𝑎𝑗 (𝑡 + 1) (30)

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where 𝑟1 and 𝑟2 are random values, 𝑥𝑎𝑗 (𝑡 + 1) is the updated position, 𝑣𝑎𝑗 (𝑡 + 1) is the updated velocity, and w is the

weight that is applied to adjust exploration and exploitation. 𝑐1 and 𝑐2 denote particles move closer to the (𝑥𝑝𝑏𝑒𝑠𝑡 )or

(𝑥𝑔𝑏𝑒𝑠𝑡 ) positions. The flowchart of this algorithm is shown in Figure 6.

Figure 6. flowchart of MOPSO

5. Parametric tuning

Estimating tuning parameters has assumed importance because of the influence of these parameters on the efficiency and

reliability of the evolutionary algorithms. The Taguchi method is adopted as an appropriate tool for parameter tuning in

order to improve the experimental results of this study for both algorithms of NSGA-II and MOPSO. The Taguchi method

enjoys the advantage of obtaining the largest amount of information with the least number of experiments. It is used to

analyze the penetration of NSGA-II parameters such as population size and maximum iterations rate of crossover and

mutation (Pc and Pm). Four levels of parameters are used in the Taguchi method which makes decision based on the

best value of each objective function. The Taguchi design is used for medium-scale problems in Minitab software that

is shown in Figure 7. Additionally, it is used to tune the optimal levels of swarm size (Np), the total number of iterations

(Max Iteration), and repository size (Nr) for MOPSO algorithm shown in Figure 8. Results of the Taguchi design for

both algorithm parameters are presented in Table 3.

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Figure 7. Analyses of NSGA- II based on the Taguchi Method

Figure 8. Analyses of MOPSO based on the Taguchi Method

Table 2. Parameter tuning for NSGA-ӀӀ and MOPSO algorithm

6. Computational results

6.1. Model validation Several computational results are obtained in order to prove the validity of the proposed model. These solution results

are presented in this section. The solution results are acquired through GAMS software and are indicated in Table 3.

Due to the existence of multiple objective functions in the proposed formulation, the problem is solved through

minimizing both the total cost and CO2 emission as well as maximizing the responsiveness individually. For example,

after minimizing the total cost, the objective functions related to CO2 emission and responsiveness are obtained from the

optimal solution of cost objective function and so on. As shown in Figure 9, the Pareto of three objective functions are

designed. Also, the results of GAMS in Table 3 show the optimum state of the objective function, and that the quantities

of objective functions such as CO2 emission, responsiveness, and total cost are considered.

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After validating and verifying the proposed model by GAMS software to find the best and most appropriate solution

approach, some computational results are presented in this section. Both NSGA-II and MOPSO algorithms are coded in

MATLAB R2014a software and execute an intel Corei7 with 8 GB.

Figure 9. Pareto surface of solutions obtained from GAMS for three-objective functions problem

Table 3. Experimental results obtained from GAMS software

Desirable direction Z1 Z2 Z3

Min Z1(total cost) 240 506 238

Max Z2(responsiveness) 0.8 1 0.8

Min Z3(CO2 emission) 322 320 453

𝐳𝐢 𝐍𝐈𝐒 506 0.8 453

zi NIS: Negative ideal value of the ith objective function

6.2. Comparison metrics

To specify strengths and weaknesses of multi-objective evolutionary algorithms, numerous criteria have been

presented by researchers. This study employs four of the comparison metrics to assess the performance of the NSGA-II

and MOPSO algorithms in order to obtain better solution sets. These metrics are as follows:

 Spacing metric

This metric determines the spread of solutions in the objective space, and is calculated by Equation 31 (Rabbani et al.,

2010; Rabbani et al., 2016):

𝑆𝑝𝑎𝑐𝑖𝑛𝑔 𝑚𝑒𝑡𝑟𝑖𝑐 = ∑ |𝑑𝑖𝑠𝑗 − 𝑑𝑖𝑠̅̅ ̅̅ |

𝑁−1 𝑗=1

(𝑁 − 1)�̅�𝑖𝑠

(31)

where 𝑑𝑖 is the Euclidean distance between obtained solutions, �̅� is the mean of Euclidean distance, and N is the number of non-dominated solutions.

 Quantity of metric

The number of Pareto optimal solutions at the concurrent run for all solution approaches is evaluated by this

metric. The high value of this metric reveals that the algorithm can converge to the real Pareto front.

 Diversity metric

This metric calculated the maximum Euclidean distance of Pareto optimal solutions. The algorithm with a high value

of this metric could coverage a great space of solutions.

The computational results of solving various test problems are presented in Table 5. Also, Figures 10-13 compare

both metaheuristic algorithms based on three comparison metrics. Based on them, NSGA-II algorithm has a better

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performance than MOPSO according to the computational time, diversity, spacing, and quantity. Two test problems

of non-dominated solutions are shown in Figure 14.

Table 4. Comparison of problem instances in terms of different metrics

P ro

b le

m n

u m

b e r

P ro

b le

m d

im e n

si o n

NSGA-ӀӀ MOPSO

C P

U t

im e

Q u

a n

ti ty

o f

P a re

to

S p

a c in

g (×

1 0

4 )

D iv

e rs

it y

(× 1

0 5

C P

U t

im e

Q u

a n

ti ty

S p

a c in

g (×

1 0

4 )

D iv

e rs

it y

(× 1

0 5

1 (2,3,5,2,2) 53.68 36 0.4516 2.68192 29.39 11 3.3038 3.70261

2 (8,12,20,8,8) 55.55 82 7.7091 27.21098 33.68 14 7.4439 16.41678

3 (10,15,25,10,10) 4.82 30 17.5918 27.73432 32.15 10 45.8112 32.39852

4 (14,21,35,14,14) 10.36 28 13.4710 30.81531 35.46 13 13.4462 23.38441

5 (18,27,45,18,18) 2.54 30 12.4679 31.82044 38.31 14 12.0613 29.73697

6 (20,30,50,20,20) 57.69 87 9.1225 25.10688 37.51 11 20.3498 26.90615

7 (24,36,60,24,24) 4.59 29 10.8580 25.07438 42.72 17 32.1251 48.40148

8 (30,45,75,30,30) 60.2 70 9.9258 46.85153 44.36 13 44.9496 49.51978

9 (40,60,100,40,40) 61.54 97 7.6405 52.64127 46.71 11 30.1601 41.76726

10 (50,75,125,50,50) 66.05 86 7.4789 78.5262 56.27 6 16.4585 30.33947

11 (60,90,150,60,60) 67.92 84 7.6199 35.27615 60.70 11 89.5426 54.27544

12 (70,105,175,70,70) 70.68 97 12.3475 80.79395 83.59 11 60.0069 72.46748

13 (80,120,200,80,80) 77.02 94 15.4812 66.81290 68.78 13 42.5058 73.76128

14 (90,135,225,90,90) 77.79 81 14.3615 103.42936 78.36 8 185.7784 61.97190

15 (100,150,250,100,100) 82.47 99 13.2908 128.84865 83.67 12 56.2866 99.84797

Average 50.19 69 10.65 50.90 51.44 12 44.01 44.32

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Figure 10. Comparison of NSGA- ӀӀ and MOPSO in terms of the CPU metric

Figure 11. Comparison of NSGA- ӀӀ and MOPSO in terms of the diversity metric

Figure 12. Comparison of NSGA- ӀӀ and MOPSO in terms of the quantity metric

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Figure 13. Comparison of NSGA- ӀӀ and MOPSO in terms of the spacing metric

(b) MOPSO (a) NSGA- ӀӀ

Figure 14. Approximation of Pareto from instance 8

7. Conclusion

In the current study, the forward/logistics supply chain is presented with regarding environmental considerations. CO2

emission is the most important issue which affects the environment. When the activities of human beings proliferate, the

CO2 emission increases too. Thus, finding solutions for decreasing costs and greenhouse gases has been deemed

necessary. In this regard, in this research, a new mathematical model is developed to control the risks and dangers of

environmental issues. Three objective functions are considered in the model to keep a balance and tradeoff between

environmental, economic, and social considerations. The model is validated and supported through a small scale problem

instance by using GAMS software. Another contribution of this paper is the applicability of two algorithms, namely

NSGA-ӀӀ and MOPSO. They were chosen to solve the various sets of the NP-hard problem efficiently. Finally, the

comparison between these algorithms was made based on different metrics in order to evaluate the accuracy and

performance of the solutions. The results demonstrated that with respect to four performance metrics including quantity,

spacing, diversity, and computational time, NSGA-ӀӀ had a better performance than the other approach.

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