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Resources, Conservation & Recycling

journal homepage: www.elsevier.com/locate/resconrec

Full length article

Tire forward and reverse supply chain design considering customer relationship management

Maedeh Yadollahiniaa, Ebrahim Teimourya, Mohammad Mahdi Paydarb,⁎

a School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran b Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, Iran

A R T I C L E I N F O

Keywords: Supply chain network design Customer relationship management Uncertainty Tire Robust optimization Multi-choice goal programming

A B S T R A C T

During the last decade, reverse logistics networks have grown dramatically within many supply chains in dif- ferent industries. Several evolving factors including economic climate, green image, environment protection laws and social respolities force companies to revise their strategies. In this paper, a tire forward and reverse supply chain is designed, and a multi-objective, multi-period, multi-product mixed integer linear programming model considering uncertainty is developed. Moreover, a novel idea of integrating customer relationship man- agement concept and supply chain management is proposed and incorporated into the mathematical modeling framework. The proposed scenario-based multi-objective model is then solved following robust optimization and revised multi-choice goal programming approaches. In order to discuss the managerial implications of the model and its results, the realization rates of the objectives, considering their importance to the supply chain, are illustrated. The model is implemented in LINGO 9 software package and solved utilizing the branch-and-bound method. The results demonstrate the applicability of the model in real world situations.

1. Introduction

Statistics show that over 17 million tons of scrap tires are generated annually all over the world (Simic and Dabic-Ostojic, 2016). Used tires contain hazardous materials that can threaten human health, pollute air and water resources and endanger life on Earth; therefore, end-of-life tires can cause serious problems if not considered properly (Subulan et al., 2015). In addition, some critical factors such as government regulations, economic issues, increscent customer awareness and social responsibilities have made both academia and industrial practitioners pay a special attention to finding out best ways to deal with the problem of used tires in recent years.

Proper supply chain management (SCM) can be a solution to the problem of planning scrap tires. Due to the fact that there are numerous forward supply chains (SCs) currently working worldwide, it will be much more valuable and practical if the planning considers the fact that some elements of SCs are now working and need to be optimized while other elements need to be designed and integrated with the existing ones. Reverse logistics, as opposed to the traditional forward logistics, is the collection of all activities that deliver wastes or end-of-use/life products that are no longer needed by users to special facilities for further recovery or environmentally conscious disposal (Fleischmann et al., 1997).

One of the main challenges in reverse logistics, especially in the case of used tires, is the absence of a systematic procedure to collect end-of- life products for the aim of recycling (de Souza and D’Agosto, 2013). Legislating much more rigid regulations might be the first and easiest answer to this problem. However, even with enforcing regulations, an efficient strategy for the supply chain to collect used tires must be de- vised in order to help businesses survive the competitive market. A well-known tool that has brought competitive advantages to many companies is customer relationship management (CRM), which is shown to be effective if incorporated into the SCM planning and deci- sion-making process.

Integrating the SCM and CRM enables companies to achieve a number of improvements in their financial and performance metrics. However, most companies rarely consider these two concepts simulta- neously (Kracklauer et al., 2004). Liu and You (2011) stated that the CRM is approached from a classical point of view and needs to be considered through SCs.

Several definitions are proposed for the CRM in the literature and the best clarified ones are as follows. The CRM is a concept that tries to develop a relationship by considering two important factors of mar- keting and customers (Kotler and Keller, 2012). It is a communicating procedure between an organization’s service and its customers in order to attract and also keep the organization’s truthful customers

https://doi.org/10.1016/j.resconrec.2018.07.018 Received 23 July 2017; Received in revised form 8 July 2018; Accepted 15 July 2018

⁎ Corresponding author. E-mail addresses: [email protected] (M. Yadollahinia), [email protected] (E. Teimoury), [email protected] (M.M. Paydar).

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0921-3449/ © 2018 Elsevier B.V. All rights reserved.

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(Grönroos, 2000). It could be said that the CRM is to introduce the right product to the right customer at the right time through the right channel for the aim of fulfilling the customer’s extending demand.

The CRM needs a customer-centered business philosophy and a culture that supports impressive service processes, marketing and sales. The point in the CRM is to establish enduring and mutually useful re- lationships, in which the seller and buyer aim to develop satisfying interchanges. Discovering new customers and keeping existing ones informed, engaged and loyal play an important role in the CRM.

One of the main challenges in this article is to incorporate the concept of the CRM into strategic and tactical SCM decisions; specifi- cally, network design as a strategic decision is of interest due to the following reasons. First, a good network design enables a company to have effective and efficient relationships with its customers. This, in turn, facilitates activities of the company to recognize and fulfill real needs of customers, which results in an atmosphere in which customers are eager to buy the company’s products in the forward flow for the first time. These customers are initially considered as temporary buyers. By concentrating on CRM strategies, these temporary customers can be- come the company’s loyal/key customers through time. Second, with the CRM in mind, new action plans can be defined for the aim of maximizing customer satisfaction, which can help to motivate custo- mers to cooperate with the SC in collecting end-of-use products in the reverse flow. Third, considering customer requirement, which means enhancing customer value, can differentiate the SC in the global com- petitive marketplace, resulting in revenue growth.

Another challenge in reverse logistics of used tires is to find best ways to process end-of-life products. The first and easiest way might be disposing used tires in landfills. However, this traditional method of waste treatment is subject to several known drawbacks and risks. Used tires are almost non-degradable and occupy considerable landfill spaces. Increasing global environmental awareness and limited disposal space have led researchers to seek alternative ways to deal with used tires, some of which are as follows:

1 Retread: Retreading involves removing the outside or tread of the tire and adding a new tread.

2 Tire-derived fuel: One of the special features of materials used in tires is their high heating value. Therefore, it is beneficial to use scrap tires as fuel. Although it is not recycling indeed, it is preferred to landfilling. Since scrap tires could be utilized in much more useful ways, this approach is not very common.

3 Pyrolysis: Chemical decomposition of the tire by high heat under the restrained condition is called pyrolysis, which can result in carbon black, oil and steel. Although the mentioned process is totally sci- entifically achievable, it is not economically affordable. Therefore, it is not a common treatment of waste tires.

4 Reclaim: Reclaiming is a procedure, in which scrap tire rubber is converted into a state using mechanical and thermal energy and chemicals, where it can be mixed, processed, and vulcanized again.

5 Ground rubber applications: 6 Asphalt rubber is the largest single market for ground rubber. Blending ground tire rubber with asphalt can improve some features of highway asphalt such as longer lasting road surfaces, reduced road maintenance, lower road noise, shorter breaking distances, etc.

7 Athletic and recreational applications including ground cover under playground equipment and running track material

8 Agricultural and horticultural applications as well as soil betterment 9 Molded rubber products, e.g., carpet underlay, dock bumpers, roof walkway pads, rubber tiles and bricks, etc.

Regarding the above explanations, the old negative attitude towards used tires as an environmental hazard costing problem can be changed into a positive perspective with an economic chance and a great op- portunity. In other words, by holistic and accurate planning in this field, not only the environmental issues of used tires can be resolved,

but also great financial gains could be achieved. Today, millions of tires are used each year and with the growing

concern about environmental issues in recent years, the problem of used tires disposal has attracted many practitioners and researchers. Wide-ranging research efforts are made to reduce the impact of used tires on the environment; however, applicable operational research articles on management systems of used tires are still scarce and the literature provides only a few mathematical models as explained in Section 2. Moreover, to the best of the authors’ knowledge, no pub- lished article has addressed the integration of the SCM and CRM in the operational research models of the problem.

The remainder of this paper is organized as follows. In Section 3, the problem is defined in detail and a novel scenario-based tri-objective mathematical model is presented for the proposed problem and its as- sumptions. For the solution procedure, a two-stage solution approach including robust optimization and revised multi-choice goal program- ming is explained in Section 4. The proposed model is validated by an industrial case study, which is represented in Section 5. Finally, in Section 6, conclusions and further research guidelines are given.

2. Literature review

2.1. Previous researches in product recovery considering uncertainty

Product recovery is the use of end-of-life products with the aim of reducing waste and thereby increasing profit. In supply chain network design, product recovery can be applied to reverse logistics, a closed- loop supply chain (CLSC) and also forward/reverse SC, depending on the nature of the product.

For example, in reverse logistics, Realf et al. (2004) discussed the strategic design of a reverse production system for carpet recycling industry in the United States. They presented a mixed integer linear programming (MILP) model to maximize the net profit. They used ro- bust optimization to consider the uncertainty in their model. Kara and Onut (2010) addressed the paper recycling reverse supply chain net- work design and proposed a mixed integer revenue-maximization model following a two-stage stochastic and robust optimization ap- proach. Ayvaz et al. (2015) presented a two-stage stochastic program- ming model to maximize the profit from electrical and electronic equipment waste recycling companies. Yu and Solvang (2017) proposed a single-objective stochastic programming model with carbon emission constraint for sustainable reverse logistics design. Rahimi and Ghezavati (2018) developed multi-objective MILP for recycling con- struction and demolition waste reverse logistics network design using two-stage stochastic programming. In their model, the objectives were to maximize profit and social impact and minimize environmental ef- fects.

In the CLSC, Mohamadpour Tosarkani and Hassanzadeh Amin (2018) introduced a multi-objective model considering green factors for battery CLSC using fully fuzzy programming. Paydar et al. (2017) de- signed a CLSC network for used engine oil and considered two objective functions of maximizing profit and minimizing risk. In order to deal with uncertainty, they used robust optimization techniques.

As mentioned before, depending on the nature of products, their recovery can be done in forward and reverse directions in a supply chain. In this area, El-Sayed et al. (2010) developed a stochastic MILP model for forward-reverse logistics network design under risk with the objective of maximizing expected profit. Hatefi and Jolai (2014) con- sidered both uncertain parameters and facility disruptions in their forward-reverse logistics network design. The objective function of the model was to minimize the nominal cost, and robust optimization was utilized to consider the uncertainty in the network. Mirmajlesi and Shafaei (2016) investigated short-lifetime products and presented ro- bust MILP for the forward-reverse supply chain.

This brief review of the researches on product recovery systems was to clarify the fact that depending on the product and/or industry being

M. Yadollahinia et al. Resources, Conservation & Recycling 138 (2018) 215–228

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considered in the study, the structure of the SC can be different. In this paper, a tire forward and reverse supply chain design is investigated, as explained in detail in Section 3.

2.2. Previous researches in used tires

In the used tire industry, there are few articles following the mathematical modeling approach in designing SCs. To the best of the authors’ knowledge, the newest and most famous researches in this field are as follows:

Dehghanian and Mansour (2009) designed a sustainable recovery network for the waste tire industry using life cycle analysis to assess the environmental impacts of various end-of-life alternatives. They be- lieved that retreading plants work below their capacities because cus- tomers find retreaded tires uneconomical. They selected grinding rubber and incineration in cement kiln as more appropriate approaches to deal with used tires. In the mentioned paper, a deterministic model was presented considering only the reverse direction of the supply chain. Subulan et al. (2015) proposed a deterministic MILP model for the tire closed-loop supply chain. They considered environmental issues by means of a life cycle assessment and Eco-indicator 99. To deal with scrap tires, they suggested retreading, recycling, landfilling and using as fuel. Finally, it was highly recommended to consider uncertainties of various parameters in tire supply chain modeling in future researches.

Pedram et al. (2017) proposed a single objective, single period MILP model considering the uncertainty of some parameters by the scenario analysis for the tire CLSC. In their model, it was assumed that used tires with minimum quality level for remanufacturing are sent for retreading and the rest are shipped to recycling centers. Their suggestion for fur- ther research was to work on multi-objective models of the problem. Amin et al. (2017) developed a single objective MILP model for the tire CLSC considering uncertainty for a case in Toronto, Canada, with the aim of maximizing the total profit of the network. In their simple supply chain network, only a general option of recycling used tires was con- sidered and various options for scrap tires were not studied.

A critical analysis of the literature calls for scrutinizing the various used tires handling methods mentioned in the previous section. The most controversial method on which the most number of articles are published is retreading. For many years, retreading has been considered as an efficient way to solve the problem of used tires regarding its en- vironmental impact and economical aspect. Since users mostly have doubt about safety of retreaded tires and the expectation of consumers preferring brand new tires rather than second-hand ones has increased, retreading slowly fell out of favor giving space for introduction of a more appealing solution.

Studies show that grinded rubber can be used as an efficient raw material in many industries as clarified in Section 1. Adding ground rubber to the ingredients of some special products, e.g. asphalt, im- proves many of their features. Farina et al. (2017) showed that asphalt pavements containing crumb rubber are better than their more common counterparts in terms of life cycle. Furthermore, this approach is very cost-effective and great profit could be made using appropriate and comprehensive planning. The main purpose of this study is to provide such extensive planning for real world problems of this kind.

Obviously, if the grinding of used tires and their application as ad- ditives is to be considered, the structure of the supply chain could not be the CLSC anymore. This is one of the main differentiating features of this study from those previously published considering retreading. More spe- cifically, the CLSC structure is replaced by forward and reverse SC con- figuration. In addition, the uncertainty of parameters, which is their in- herent feature in the real world, should be considered in applied studies. In this study, a multi-objective, multi-period, multi-product MILP model under uncertain demands and capacities is proposed, and the CRM concept is innovatively incorporated into the SCM structure. This is one of novel- ties and advantages of this study over the previous studies. In addition, no previous research is reported on integrating the CRM and SCM.

3. Problem explanation

3.1. Problem definition

The structure of the investigated forward SC, showing the manu- facturing plant, distribution centers and customers, is illustrated in Fig. 1. The manufacturing plant produces new products, which are delivered to customers via distribution centers. This is a schematic re- presentation of a supply chain in the tire industry operating in Iran. Obviously, the treatment of used tires is totally neglected in this SC.

In order to improve the existing forward SC in terms of used tire waste management, a design for the reverse network for used products with a focus on collecting and recycling considering the coordination in the whole SC is developed as shown in Fig. 2. The proposed open-loop (forward/reverse) SC network in this study is a multi-echelon network including a manufacturing plant, recycling plants, distribution, collec- tion and hybrid centers and three types of customers.

In the proposed network configuration, in the forward path, new products are conveyed from the existing manufacturing plant to type 1

Fig. 1. Structure of the existing forward SC.

Fig. 2. Structure of the proposed SC network.

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customers via the existing distribution centers. In the backward path, the returned (used) products from Types 1 and 2 customers are trans- ported to collection centers and hybrid centers. Finally, the used pro- ducts are shipped to recycling plants, from which the recycled products are delivered to Type 3 customers.

The key assumptions of this research are as follows:

• Since one of the main strategies of the CRM is to value key custo- mers, customer segmentation, as of the fundamental essences of the CRM, is utilized in this study to categorize customers into three types of customers. Specifically, Type 1 customers are the ones who buy our new products in the forward flow and return their used products to the SC in the reverse flow. It is worth mentioning that customers of this type are the most valuable SC customers and are considered as key customers. Type 2 customers are those in the reverse flow of the SC buying the used products. Finally, Type 3 customers purchase the recycled products.

• In order to incorporate the reverse flow into the existing forward SC, collection centers should be decided on carefully. In this paper, three options are considered. Option 1 is to enable the existing distribution centers to also work as collection centers. In other words, distribution centers can be changed into hybrid (collection/ distribution) ones. Option 2 is to open some new collection centers and Option 3 is to establish hybrid centers capable of acting as collection and distribution centers simultaneously.

• The model is a case-based logistics network. It is basically designed for the new and emerging industry of recycling used tires in Iran. However, without loss of generality, through minor modifications, the proposed model can be applied to many other industries, such as digital and electronic equipment industries.

• Demand in both forward and reverse directions, i.e. demand for new and recycled products, is assumed to be subject to uncertainty. Moreover, it is assumed that the capacity of manufacturing and recycling plants can be expanded to some extent through optimi- zation and soft improvement attempts such as working time effi- ciency enhancement. Uncertain parameters in this paper are ex- plained in terms of scenarios.

• Because of the nature of the product, i.e. tires, the structure of the proposed SC network is open loop. In other words, forward and reverse flows are considered without being connected and/or closed. The recycled tire is not necessarily used in the tire industry. Specifically, the recycled tire rubber can be used in tire derived fuel, construction industry, molded rubber products, agriculture industry, and recreational and sports applications as well as in rubber mod- ified asphalt applications (Presti, 2013).

• There are multiple products and multiple periods. • The location of customers, the manufacturing plant and distribution centers is fixed and predefined.

• The potential location of recycling plants, collection centers and hybrid centers is known.

• For distribution, collection and hybrid centers, a minimum accep- table utilized capacity and a maximum capacity in both forward and reverse directions are considered due to the type of facilities, as described in detail in Section 3.2.3.

• As mentioned above, in this paper, the CRM concept is incorporated into the SCM decision-making process. Therefore, some CRM op- tions and also electronic CRM (ECRM) options are defined and considered as binary variables in model formulation. The details of the CRM options are as follows:

• This is an option, in which the SC would give a new product for free to customers in exchange of β units of the used product being brought to SC collection centers by customers.

• It is an option that focuses on key customers (Type 1 customers) exclusively. Here, guarantee is considered only for key customers in order to differentiate between customers with the aim of enhancing the value of key customers as well as motivating customers of other

categories to be much more loyal to the SC.

• In this option, vehicles are sent to customers who return more than 10 units of the used product to the SC.

• This is an option to propagate the culture of returning and conse- quently recycling used products by means of advertising.

The ECRM options are:

A It is an option to enhance customers’ willingness to be in contact with the SC by facilitating the means of telecommunication, i.e. establishing channels such as SMS, internet and interactive voice response (IVR) systems with the following goals: 1) explaining the significance of recycling for this specific kind of used product as well as its reasons and necessity in order to increase customer awareness level, which, in turn, results in an increase in customer cooperation and involvement; 2) Answering customers’ possible questions and clarifying their doubts and ambiguities, e.g. about the location of the nearest collection or hybrid center to a customer’s place to re- turn used products.

B This is an option, in which the SC would inform the customers in the forward direction about the useful lifecycle of their products and reminds them when products reach their end-of-life period and should be returned to the SC for recycling.

With the above assumptions in mind, the main issues to be ad- dressed by this study are to choose the location and determine the number of collection, hybrid centers and recycling plants as well as to determine the existing distribution centers that need to be changed into hybrid ones as well as the quantity of products transported between each pair of network facilities along each capacity-constrained stage under uncertainty of parameters. Moreover, production and recycling quantity, inventory and backorder levels at each period and CRM de- cision variables are determined to optimize the objectives described in what follows.

The proposed model is to optimize three objective functions. The first objective is to maximize the total profit of the chain, the second one seeks to maximize the total collected used products from customers by means of increasing customer satisfaction and CRM strategies, and the third objective is to minimize the total distance travelled between the collecting facilities that are meant to be opened and the location of customers who return their used products the most. In other words, this objective is to locate and open the collecting facilities that are closer to customers with the highest cooperation with the reverse chain. It is worth mentioning that the second and third objectives, which in- corporate the CRM concept in this study, search in line with each other and the reason for their separate formulation is that they are inherently different.

3.2. Problem formulation

To describe the aforementioned SC network, the following notations are used in the model formulation:

3.2.1. Notations Indices:

l Index for fixed locations of manufacturing plants, (l = 1,2,…,L) i Index for fixed locations of distribution centers, (i = 1,2,…,I) j Index for potential locations for collection centers, (j = 1,2,…,J) k Index for potential locations for hybrid centers, (k = 1,2,…,K) m Index for fixed locations of Types1 and 2 customers,

(m = 1,2,…,M) n Index for potential locations available for recycling plants,

(n = 1,2,…,N) o Index for fixed locations of Type 3 customers, (i = 1,2,…,O)

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p Index for products in the forward direction, (i = 1,2,…,P) p′ Index for recycled products in the reverse direction,

(p′ = 1,2,…,P′) t Index for periods, (t = 1,2,…,T) a Index for CRM options s Index for scenarios, (s = 1,2,…,S)

Parameters:

PPpt Unit price of product p in period t PAp′t Unit price of recycled product p′ in ton in

period t PCpt Unit supply and production cost of product

p in period t RCp′t Unit supply and production cost of

recycled product p′ in ton in period t Dmpts Demand of customer m for product p in

period t under scenario s D′op′ts Demand of customer o for recycled

product p′ in ton in period t under scenario s

TDpt Unit transportation cost for product p shipped from manufacturing plant to distribution/ hybrid centers in period t

TRpt Unit transportation cost for product p shipped from collection/hybrid centers to recycling plants in period t

TO p′t Unit transportation cost for recycled product p ́ shipped from recycling plants to Type 3 customers in period t

ICi Fixed cost for changing distribution center i into a hybrid one

FCCj Fixed cost for opening collection center j FCHk Fixed cost for opening hybrid center k FCn Fixed cost for opening recycling plant n αt Quantity of used products that can be dealt

with without customer engagement, e.g. finding and using a landfill in time period t

γ Average quantity of products being used in the country in each period

β Number of used products that customers should return in order to have a free new product

DAli The distance between manufacturing plant l and distribution center i

DBlk The distance between manufacturing plant l and hybrid center k

DCkn The distance between hybrid center k and recycling plant n

DDjn The distance between collection center j and recycling plant n

DEin The distance between distribution center i and recycling plant n

DFno The distance between recycling plant n and customer o

MXCj Maximum capacity of collection center j MNCj Minimum acceptable capacity utilization

of collection center j XCFk Maximum capacity of hybrid center k in

receiving products in the forward direction NCFk Minimum acceptable capacity of hybrid

center k in receiving products in the forward direction

XCRk Maximum capacity of hybrid center k in receiving used products in the backward direction

NCRk Minimum acceptable capacity of hybrid center k in receiving used products in the backward direction

UFi Maximum capacity of distribution center i in the forward direction

URi Maximum capacity of distribution center i that changed into hybrid in the backward direction

CAPpls Capacity of manufacturing product p in manufacturing plant l under scenario s

CNns Capacity of recycling plant n under scenario s

MMp′ The matrix to change the number of unit of products into the equivalent weight of products’ components in ton

HHplt Unit inventory holding cost of product p in manufacturing plant l in period t

CBOpt Unit backorder cost of product p in period t M A sufficiently large positive number COB Cost of option B COC Cost of option C COD Cost of option D COE Cost of option E COF Cost of option F a=[aA,aB,aC,aD,aE,aF] The influence vector representing the

impact level of the defined CRM options on customer satisfaction

Decision variables:

Qplt Quantity of product p produced by manufacturing plant l in period t

Q′p′nt Quantity of recycled product p′ produced by recycling plant n in period t

ABplit Quantity of product p shipped from manufacturing plant l to distribution center i in period t

ACplkt Quantity of product p shipped from manufacturing plant l to hybrid center k in period t

ADpimt Quantity of product p shipped from distribution center i to customer m in period t

AEpkmt Quantity of product p shipped from hybrid center k to customer m in period t

AFpmkt Quantity of product p shipped from customer m to hybrid center k in period t

AGpmjt Quantity of product p shipped from customer m to collection center j in period t

AHpmit Quantity of product p shipped from customer m to distribution center i in period t

AIpjnt Quantity of product p shipped from collection center j to recycling plant n in period t

AJpint Quantity of product p shipped from distribution center i to recycling plant n in period t

AKpknt Quantity of product p shipped from hybrid center k to recycling plant n in period t

AL p′n-

ot

Quantity of recycled product p′ shipped from recycling plant n to customer o in period t

ANplts Inventory level of product p at plant l in period t under scenario s

BOmpts Backorder level of customer m for product p in period t under scenario s

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Xi 1 If distribution center i is opened, 0 otherwise Yj 1 If collection center j is opened, 0 otherwise Zk 1 If hybrid center k is opened, 0 otherwise Wn 1 If recycling plant n is opened, 0 otherwise OA 1 If option A is activated, 0 otherwise OB 1 If option B is activated, 0 otherwise OC 1 If option C is activated, 0 otherwise OD 1 If option D is activated, 0 otherwise OE 1 If option E is activated, 0 otherwise OF 1 If option F is activated, 0 otherwise FFpmt Total number of free product p given to customer m as

defined in CRM options in period t

3.2.2. Objective functions The three objectives of the presented model are maximizing the

total profit, maximizing total customer satisfaction and minimizing total distance between collecting facilities that are meant to be opened and customers who return their used products the most.

∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

= +

+ ′

′ ′

f AD AE PP

AL PA

Max ( )s t p i m

pimt k m

pkmt pt

t p n o p not p t

1

(1)

∑ ∑ ∑ ∑ ∑ ∑− − ′ ′

′ ′PC Q RC Q t p l

pt plt t n p

p t p nt (2)

∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑

− +

+ −

− +

′ ′ ′

TR AK DC AI DD

AJ DE TO AL DF

TD AB DA AC DB

(

)

( )

t p pt

k n pknt kn

j n pjnt jn

i n p in

t p n o p t p not no

t p pt

l i plit li

l k plkt lk

int

(3)

∑ ∑ ∑ ∑− − − −FCC Y FCH Z FC W IC X j

j j k

k k n

n n i

i i (4)

∑ ∑ ∑ ∑ ∑ ∑− × − ×HH IN CBO BO t l p

plt plts m p t

pt mpts (5)

∑ ∑ ∑− × × − × − ×

− × − × − ×

FF PP OA COB OB COC OC

COD OD COE OE COF OF

( ) ( ) ( )

( ) ( ) ( )

t p m pmt pt

(6)

=f γ

V U aMax 1

( ( ) )2 (10)

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

= +

+

f AF DG AG DH

AH DI

Min t p m k

pmkt mk t p m j

pmjt mj

t p m i pmit mi

3

(11)

The first objective is to maximize the total profit by subtracting the total cost from the total revenue. The terms of this objective are as follows: (1) Total revenue of selling new products in the forward di- rection and the recycled products in the reverse direction; (2) the total supply and production cost in manufacturing plants and recycling cost in recycling plants; (3) the total transportation cost; (4) the fixed cost for establishing new facilities such as collection centers, hybrid centers, recycling plants and the fixed cost of converting the existing distribu- tion centers into hybrid ones; (5) the total inventory carrying cost and backorder cost; (6) the total CRM cost. It is notable that the term

×FF PPpmt pt in (6) calculates the cost of option A. The second objective is to maximize the number of used products

being collected from customers. In order to do that, the compound function V(U(a)) is defined. U(a) is considered as a function for cal- culating customer satisfaction level, and generally can be defined in different forms. In this study, the mentioned function U(a) is introduced

as follows:

=

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

U a a a a a a a

OA OB OC OD OE OF

( ) [ , , , , , ]A B C D E F

(12)

In order to increase customer satisfaction, some CRM options OA- OF, which are predefined and described in Section 3.2.1, are fed into the model as binary variables. These options are established on the basis of CRM strategies based on the three reasons mentioned in Section 3.1 and with the aim of increasing customer engagement. The influence coefficient vector, a=[aA,aB,aC,aD,aE,aF], represents the impact level of CRM options on customer satisfaction.

The range of the function U, described above, is the domain of the function V that calculates the quantity of the total received used pro- ducts from customers considering customer satisfaction. Here, the function is assumed to be linear; however, in case of non-linearity, it can be approximated satisfyingly using linear formulation and fine tuning through interviews, questionnaires and other data collection tools. Finally, the compound function is divided by the average quantity of products being used in the country in every period shown by γ. This makes the value of the objective function normalized and fall between 0 and 1. The third objective, which can also be considered as a CRM objective, is to minimize the distance between collecting facilities (collection, hybrid and distribution centers that are converted into hybrid ones) that are meant to be opened and customers who return their used products the most.

3.2.3. Constraints This subsection is devoted to present the constraints of the proposed

model. The constraints are categorized into different categories ex- plained in what follows.

3.2.3.1. Balance constraints. These constraints, presented in following equalities and inequalities, are used to ensure the balance in flow and inventory of products throughout the entire SC.

− + = ∑ + ∑ ∀−Q IN IN AB AC p l t, ,plt plts plt s i plit k plkt1 (13)

∑ = ∑ − ∑ ∑ + ∑ ∑

+ ∑

∀

−

BO D AD AE

BO

p t s( ) , ,m mpts m mpts i m pimt k m pkmt

m mpt s1

(14)

′ = × ∑ ∑ + ∑ + ∑ + ∀ ′′ ′Q MM AK AI AJ α p t n( ) , ,p nt p p k pknt j pjnt i pint t

(15)

∑ ≤ ′ ∀ ′′ ′AL D p o n s, , ,n p not op ts (16)

′ = ∑ ∑ ∀ ′′ ′Q AL p t n, ,p nt n o p not (17)

∑ = ∑ ∀AD AB p i t, ,m pimt l plit (18)

∑ = ∑ ∀AH AJ p i t, ,m pmit n pint (19)

∑ = ∑ ∀AC AE p k t, ,l plkt m pkmt (20)

∑ = ∑ ∀AF AK p k t, ,m pmkt n pknt (21)

∑ = ∑ ∀AG AI p j t, ,m pmjt n pjnt (22)

∑ ∑ + ∑ + ∑ ≤ ∀AF AG AH γ p t( ) ,m k pmkt j pmjt i pmit (23)

Constraint (13) ensures that at each period and for each product, the flow entering each manufacturing plant and its residual inventory from the previous period is equal to the summation of the amount

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transported to distribution centers and the residual inventory. Constraint (14) ensures that in each time period and for each product and under each scenario, the sum of the total flow to customers and total amount of backorders is equal to the sum of the total demand and accumulated backorders. Constraint (15) ensures that the total amount of recycled products produced by each recycling plant is equal to the sum of the collected used product flow entering the plant. Constraint (16) ensures that in each period and under each scenario, the total amount of each product transported to each customer does not exceed the total demand of the customer for that product. Constraint (17) ensures that the total amount of recycled products produced by each recycling plant is equal to the total amount transported to each Type 3 customer. Constraints (18)–(21) are the balance constraints in the forward and reverse direction of the distribution and hybrid centers, respectively. Constraint (22) is the balance constraint of collection centers. Constraint (23) is to restrict the sum of the collected used products.

3.2.3.2. Capacity constraints. The following constraints are to define and apply capacities of facilities.

≤ ∀Q CAP p t l s, , ,plt pls (24)

∑ ′ ≤ × ∀′ ′Q CN W t n s, ,p p nt ns n (25)

∑ ∑ ≤ × ∀AG MXC Y j t,p m pmjt j j (26)

∑ ∑ ≥ × ∀AG MNC Y j t,p m pmjt j j (27)

∑ ∑ ≤ × ∀AC XCF Z k t,p l plkt k k (28)

∑ ∑ ≥ × ∀AC NCF Z k t,p l plkt k k (29)

∑ ∑ ≤ × ∀AF XCR Z k t,p m pmkt k k (30)

∑ ∑ ≥ × ∀AF NCR Z k t,p m pmkt k k (31)

∑ ∑ ≤ ∀AB UF i t,p l plit i (32)

∑ ∑ ≤ ∀AH UR i t,p m pmit i (33)

Constraints (24) and (25) ensure that the total amount of products processed in each manufacturing and recycling plant does not exceed the corresponding capacity limit of each facility under each scenario, respectively. Eqs. (26) and (27) are the maximum and minimum ca- pacity constraints for opening collection centers. For opening hybrid centers, maximum and minimum capacity constraints are considered for both the forward and reverse directions through Constraints (28)–(31). Since it is assumed that the existing distribution centers can be changed into hybrid ones, only maximum capacity constraints in the forward and reverse flows, as presented in Constraints (32) and (33), are applicable.

3.2.3.3. Shipping-linking constraints. In order to preserve the consistency and integrity of the model regarding the network links and shipping, the following constraints are considered. Therefore, Constraints (34)–(45) ensure that there is no shipping between any non-linked locations.

≤ × ∀AC M Z p t l k, , ,plkt k (34)

≤ × ∀AE M Z p t m k, , ,pkmt k (35)

≤ × ∀AF M Z p t m k, , ,pmkt k (36)

≤ × ∀AG M Y p t m j, , ,pmjt j (37)

≤ × ∀AH M X p t m i, , ,pmit i (38)

≤ × ∀AK M W p t k n, , ,pknt n (39)

≤ × ∀AK M Z p t k n, , ,pknt k (40)

≤ × ∀AI M W p t j n, , ,pjnt n (41)

≤ × ∀AI M Y p t j n, , ,pjnt j (42)

≤ × ∀AJ M W p t i n, , ,p nint (43)

≤ × ∀AJ M X p t i n, , ,p iint (44)

≤ × ∀ ′′AL M W p t n o, , ,p not n (45)

3.2.3.4. CRM constraint. Constraint (46) calculates the number of new products that the SC must yield for free to customers who return their used products to the chain if option A is activated.

= ⎢ ⎣⎢

⎥ ⎦⎥

∀ ∑ + ∑ + ∑

FF p m t, ,pmt AF AG AH

β k pmkt j pmjt i pmit

(46)

3.2.3.5. Logical constraints. Constraints (47) and (48) impose the binary and non-negativity restriction on the corresponding decision variables.

∈ ∀X Y Z W OA OB OC OD OE OF o i j k n, , , , , , , , , { , 1} , , ,i j k n (47)

′ ≥

∀ ′ ′

′

Q Q AB AC AD AE AF AG AH AI AJ AK AL IN BO FF

p p t i j k l m n o s , , , , , , , ,

, , , , , , , 0 , , , , , , , , , ,

plt p nt plit plkt pimt pkmt pmkt pmjt

pmit pjnt p pknt p not pts mpts pmtint

(48)

3.2.4. Linearization Clearly, the first objective function is non-linear in term (6). To

linearize this term, a non-negative auxiliary variable is introduced as = ×FOA FF OApmt pmt and the following constraints are added to the

original model.

≥ − − ∀FOA FF M OA p m t(1 ) , ,pmt pmt (49)

≤ + − ∀FOA FF M OA p m t(1 ) , ,pmt pmt (50)

≤ × ∀FOA M OA p m t, ,pmt (51)

≥ ∀FOA p m t0,integer , ,pmt (52)

Proof: Two states are imaginable for FOApmt: (i) If OA = 0, then FOApmt = 0. In this case, we have

≥ −FOA FF Mpmt pmt

≤ +FOA FF Mpmt pmt

≤ ×FOA M 0.pmt

Since FFpmt is a positive integer variable, it clearly takes zero. (ii) If OA = 1, then FOApmt=FFpmt. In this case, we have

≥FOA FFpmt pmt

≤FOA FFpmt pmt

≤ ×FOA M 1.pmt

In this situation, it is clear that FOApmt=FFpmt. Obviously with the definition of the auxiliary variable, the non-

linear part of the first objective function is changed to:

∑ ∑ ∑− × − × − ×

− × − × − ×

FOA PP COB OB COC OC

COD OD COE OE COF OF

( ) ( ) ( )

( ) ( ) ( )

t p m pmt pt

(53)

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4. Solution procedure

To solve the proposed scenario-based model presented in Section 3.2, a two-phase procedure is utilized. The model is adapted to an equivalent robust counterpart in the first phase. A revised multi-choice goal programming method (RMCGP) is used for obtaining an efficient solution in the second phase.

4.1. Step1: robust optimization

In this paper, the robust optimization is applied to deal with un- certainty because of the advantages of the robust approach. More spe- cifically, the SC design not only has to be aligned with the expected conditions, but also has to be robust and flexible enough to adjust to the inherent changes emerging in uncertain future realizations. Robust solutions allow for flexibility to enable stable performance of the SC under uncertain conditions. The robust optimization is an operation research framework that deals with uncertainties in generic optimiza- tion problems and finds robust solutions to these problems (Paixao and Souza, 2015). More specifically, it is possible to encompass service-level or decision-makers’ (DMs’) risk aversion function by means of the ro- bust optimization approach, which was first introduced by Mulvey et al. (1995) and also to attain a series of solutions that are progressively less sensitive to the realizations of the data in a scenario set. For the men- tioned reasons, robust optimization is used in this study rather than a more used approach called stochastic approach. In stochastic linear programming, there is no use of penalty terms and stabilizing the so- lution over a period of time is not possible; it just simply minimizes the expected cost or maximizes the expected profit.

The optimal solution acquired by a robust optimization model is called robust if the solution remains ‘close’ to optimal after changing the input data. This is known as solution robustness. Furthermore, the model robustness becomes important when a solution is ‘almost’ fea- sible for small changes in the input data. The robust optimization model structure is as follows:

Min cTx + dTx

s.t. Ax = b

i + Cy = i

x,y ≥ 0

where the coefficient A is the matrix of certain parameters and x is a vector of design variables. Moreover, coefficients B and C are the ma- trices of noisy parameters and y is the vector of control variables.

In a scenario-based approach, we have a set of scenarios Ω=[1,2, …,S], in which each scenario is associated with a set of control con- straints [ds, Bs, Cs, es] and a probability of occurrence ps where ob- viously Σ Ps = 1. Based on the above standard problem, the robust optimization problem can be formulated as below:

Min σ(x,y1,y2,y1,…,ys) + ωp(δ1,δ2,…,δs)

s.t.

Ax = b

+ + = ∀B x C v δ e ss s s s

≥ ∀x y s, 0

The second term of the above objective function preserves the model robustness and considers the fact that with a set of input para- meters under some scenarios, infeasible results may be obtained. In the above problem, ω is the infeasibility weight of a scenario. For the first term of the objective function mentioned above, Leung et al. (2002) presented a much more applicable formulation as follows:

∑ × + × ∑ × − ∑ ′ +

− ∑ × + ≥ ≥

= = ′= ′

′= ′ ′

p ξ λ p ξ p ξ θ s t ξ p ξ θ θ

Min [( ) 2 ] . .

0 0

s S

s s s S

s s s S

s s s

s s S

s s s

s

1 1 1

1

where ξs is the minimization objective function in the original optimi- zation problem. For more detailed information, the works of Mulvey and Ruszczyński (1995); Mulvey et al. (1995) and Leung et al. (2002) are recommended.

By focusing on robust optimization, the robust counterpart of the proposed scenario-based model presented in Section 3.2 can be for- mulated. In this model, the parameters Dmpts, Dʹoptʹs, CAPpls, and CNns vary in a given uncertainty set S. The following parameters should also be added to the presented model.

ps Probability of occurrence scenario s W1 Penalty of one unit under-fulfillment of demand of product p in

the forward direction W2 Penalty of one unit under-fulfillment of demand of recycled

product p′ in the backward direction W3 Penalty of leakage capacity for producing of product p W4 Penalty of leakage capacity for producing of recycled product p′

The control variables of the model are as follows:

δ1mpts The under-fulfillment of demand of product p for customer m in period t under scenario s

δ2op′ts The under-fulfillment of demand of product p for customer o in period t under scenario s

δ3pls The under-fulfillment of capacity for producing product p at plant l under scenario s

δ4ns The under-fulfillment of capacity for producing at recycling plant n under scenario s

Due to the uncertain parameters explained above, only the first objective function, which is maximizing the total profit, is subject to uncertainty. Therefore, in the robust counterpart of the model, the second and third objective functions (10) and (11) are considered with no changes. However, the first objective is as follows:

∑ ∑ ∑

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑ ∑

∑ ∑

′ = − × + ⎡

⎣ ⎢ − × +

⎤

⎦ ⎥

+ × ×

+ × × + × ×

+ × ×

′ ′

f P f λ P f P f θ

W P δ

W P δ W P δ

W P δ

Min ( ) 2

1

2 3

4

s s s

s s s

s s s s

m p t s s mpts

o p t s s op ts

p l s s pls

n s s ns

1 1 1 1

1

2 3

4 (54)

Since our first original objective function f1s is to be maximized, in order to replace that as ξs, which is to be minimized as mentioned above, the term ∑ ×p fs s s1 is written with a negative sign in (54).

∑ = ∑ − ∑ ∑ + ∑ ∑

+ ∑ +

∀

−

BO D AD AE

BO δ

p t s( )

1

, ,m mpts m mpts i m pimt k m pkmt

m mpt s mpts1

(55)

∑ ≤ ′ + ∀ ′′ ′ ′AL D δ p o n s2 , , ,n p not op ts op ts (56)

≤ + ∀Q CAP δ p t l s3 , , ,plt pls pls (57)

∑ ′ ≤ + × ∀′ ′Q CN δ W t n s( 4 ) , ,p p nt ns ns n (58)

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− ∑ × + ≥ ∀f P f θ s0s s s s s1 1 (59)

≥ ∀′θ δ δ δ δ p p t l m n s, 1 , 2 , 3 , 4 0 , , , , , ,s mpts op ts pls ns (60)

All the constraints (13)–(52) described for the presented scenario- based model in Section 3.2 are considered in the robust counterpart in the same form, except for (14), (16), (24), and (25) that are changed into (55)–(58), respectively. Constraint (59) is for the linearization of the objective function, which is defined in the work of Leung et al. (2002). Finally, Equation (60) imposes the variables as positive real numbers.

4.2. Step2: multi-objective methodology: RMCGP

The goal programming (GP) is a vital technique for decision-makers to solve multi-objective decision-making (MODM) problems in achieving a set of satisfying solutions. Charnes and Cooper (1957) first introduced the GP; a standard model of GP can be shown as follows:

∑ +

− + = =

= ≤ ≥ = ≥ =

= + −

+ −

+ −

ω d d s t f X d d b i n

h X k q d d i n

Min ( ) . . ( ) 1, 2, ...,

( ) ( or ) 0 1, 2, ..., , 0 1, 2, ...,

i n

i i i

i i i i

k

i i

1

where fi(X): goal constraint i hk(X): system constraint k ωi: the weight of the ith goal bi: the aspiration level of goal i d+i and d

− i : positive and negative deviations from the target value of

goal i, respectively, which

= ⎧ ⎨⎩

− <

= ⎧ ⎨⎩

− >

−

+

d b f X f X b

d f X b f X b

( ) if ( ) 0 otherwise

( ) if ( ) 0 otherwise

i i i i i

i i i i i

The standard GP technique emphasizes obtaining a solution next to the aspiration level for every single objective function and imposes a penalty on the deviation away from the aspiration level. However, in practice, the DM usually selects a conservative initial aspiration level based on the limited resource and available information. Hence, Chang (2007) proposed a new method of the MCGP for the MODM with multiple aspiration levels, which allows the DM to set multi-choice aspiration levels for objective functions. Afterwards, Chang (2008) ex- tended the MCGP to the RMCGP as the following two cases.

The first case: ‘The less the better’ is expressed as:

∑ + + +

= ≤ ≥ = − + = =

− + = = ≤ ≤ =

≥ =

= + − + −

+ −

+ −

+ − + −

ω d d ρ e e s t h X k q f X d d R i n

R e e g i n g R g i n

d d e e i n

Min [ ( ) ( ) ] . .

( ) ( or ) 0 1, 2, ..., ( ) 1, 2, ...,

1, 2, ..., 1, 2, ...,

, , , 0 1, 2, ...,

i n

i i i i i i

k

i i i i

i i i i

i i i

i i i i

1

.min

.min .max

The second case: ‘The more the better’ is expressed as:

∑ + + +

= ≤ ≥ = − + = =

− + = = ≤ ≤ =

≥ =

= + − + −

+ −

+ −

+ − + −

ω d d ρ e e s t h X k q f X d d R i n

R e e g i n g R g i n

d d e e i n

Min [ ( ) ( ) ] . .

( ) ( or ) 1, 2, ..., ( ) 1, 2, ...,

1, 2, ..., 1, 2, ...,

, , , 0 1, 2, ...,

i n

i i i i i i

k

i i i i

i i i i

i i i

i i i i

1

.max

.min .max

where gi.max: the upper bound of the ith aspiration level gi.min: the lower bound of the ith aspiration level Ri: the continuous variable with a range of gi.min≤ Ri≤ gi.max, d+i and d

− i are positive and negative deviations from −f X R| ( ) |i i

ωi: the weight of the ith goal For the first case: e+i and e

− i : positive and negative deviations from −R g| |i i.max

ρi: the weight of the sum of deviations of −R g| |i i.min For the second case: e+i and e

− i : positive and negative deviations from −R g| |i i i.

ρi : the weight of the sum of deviations of −R g| |i i.max According to the multi-objective methodology mentioned above, the

objective function of the RMCGP form of the proposed model is as follows:

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

= ⎛ ⎝ −

⎞ ⎠

+ + ⎛ ⎝ −

⎞ ⎠

+

+ ⎛ ⎝ −

⎞ ⎠

+ + ⎛ ⎝ −

⎞ ⎠

+

+ ⎛ ⎝ −

⎞ ⎠

+ + ⎛ ⎝ −

⎞ ⎠

+

+ − + −

+ − + −

+ − + −

f ω

g g d d

ρ g g

e e

ω g g

d d ρ

g g e e

ω g g

d d ρ

g g e e

Min ( ) ( )

( ) ( )

( ) ( )

4 1

1. max 1. min 1 1

1

1. max 1. min 1 1

2

2. max 2. min 2 2

2

2. max 2. min 2 2

3

3. max 3. min 3 3

3

3. max 3. min 3 3

(61)

Including the constraints of the robust counterpart, the following new constraints emerge in the RMCGP form as explained earlier in this section:

′ − + =+ −f d d R1 1 1 1 (62)

− + =+ −R e e g1 1 1 1. min (63)

≤ ≤g R g1. min 1 1. max (64)

− + =+ −f d d R2 2 2 2 (65)

− + =+ −R e e g2 2 2 2. max (66)

≤ ≤g R g2. min 2 2. max (67)

− + =+ −f d d R3 3 3 3 (68)

− + =+ −R e e g3 3 3 3. min (69)

≤ ≤g R g3. min 3 3. max (70)

≥+ − + − + − + − + − + −d d e e d d e e d d e e, , , , , , , , , , , 01 1 1 1 2 2 2 2 3 3 3 3 (71)

Six sub-problems with individual objective function can be solved to find gi.max and gi.min, in which:

g1.min can be found by Min f′1 g1.max can be found by Max f′1 g2.min can be found by Min f2 g2.max can be found by Max f2 g3.min can be found by Min f3 g3.i can be found by Max f3 The DM is provided by the solutions to these sub-problems.

Consulting with experts, she/he makes decisions about the parameters.

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5. Case study

As mentioned in the previous sections, the proposed model is based on a real-world problem and attempts to improve an existing forward SC in the tire industry, design the reverse structure of the SC with the aim of collecting and recycling waste tires, and coordinate the whole SC under uncertainty while considering the CRM concept.

5.1. Description and input data

The existing forward tire SC network considered in the case study is illustrated in Fig. 3. A manufacturing plant in Tehran and two dis- tribution centers, one in Tehran and one in Isfahan, are operating. Eight cities across the country are considered as main customer-located areas.

According to a report by the Iran Ministry of Mining and Industry, the number of people per car is about 9 while the number of people per scrap is about 6 in Iran (Dehghanian and Mansour, 2009). In other words, 3.6 kg of scrap tire is produced per capita per year. This amount is equivalent to 15 million tires, which translates to 60 thousands tons of scrap based on the current population of the country. This amount is expected to grow 0.02% annually. Currently, less than one third of the produced waste tires in Iran are being recycled. This shows that tire recycling industry is a new and emerging industry in this country.

In the described supply chain network, potential candidates for fa- cility locations are chosen from populated cities because they are the main points of scrap tire production. For collection centers, Tehran and Isfahan, for hybrid centers, Isfahan and Mashhad, and for recycling plans, Tehran and Isfahan are selected. Eight main nodes for forward direction customers and three main nodes for backward direction cus- tomers are considered. Two kinds of products, in each forward/back- ward flow, are considered; in the forward direction, car and truck tires and in the backward direction, crumb rubber and steel flow. Processing

1 ton of scrap tires gives 0.6 tons of crumb rubber (Dehghanian and Mansour, 2009). Considering the approximate weight of a tire equal to 4 kg and using the aforementioned matrix MMp′, it is possible to convert the forward flow, which is expressed in numbers, to the backward flow, which is expressed in tons.

́ = =MM 0.004 [0.6 0.4] [0.0024 0.0016]p

In our case, a planning horizon of two time periods, each re- presenting one year, is considered. Fixed opening costs for the facilities are depicted in Table 1. The dynamic prices and costs of the chain are illustrated in Table 2. The weight of the goals and costs of the CRM options are displayed in Table 3. As mentioned before, the cost of op- tion A is not predefined and is calculated in the model by COA = FFpmt× PPpt.

Three scenarios are defined and indexed as 1, 2 and 3, which re- present pessimistic, moderate, and optimistic situations, respectively. Each of the scenarios represents a different situation reflecting varia- tions in demand and capacities of the plants. It is assumed that by some low cost efforts such as eliminating idle times of facilities, the capacity of the manufacturing and recycling plants can be expanded to some extent. Scenario number 3 represents the optimistic scenario because under this scenario, capacities of the demand and plants are at max- imum, which translate to higher earnings for the chain. The demand in

Fig. 3. The existing SC network.

Table 1 Fixed Opening Costs for the Facilities (in 10,000 Rials).

Facility type Place 1 Place 2

Distribution centers 50,000 30,000 Collection centers 7000 6000 Hybrid centers 80000 85000 Recycling plants 350000 320000

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the forward and backward directions and uncertainty in the capacity of the manufacturing and recycling plants are shown in Tables 4–6, re- spectively. Table 7 shows the maximum and minimum capacity of the distribution, collection and hybrid centers.

5.2. Computational results

The proposed model is implemented by Lingo 9 software package and solved by the branch-and-bound method. The main results are presented below. The optimal SC network obtained by the model is il- lustrated in Fig. 4, showing that in the optimal solution, a collection center in Tehran, a hybrid center in Mashhad and two recycling plants in the two candidate locations, i.e. Tehran and Isfahan, are opened. Furthermore, the optimal solution indicates that it is profitable to alter the existing distribution centers into hybrid ones rather than opening new collection or hybrid centers because in the optimal solution, both the distribution centers are transformed into hybrid ones.

The DM is provided by the solutions of the sub-problems gi.min and gi.max, as explained in Section 4.2. These results are shown in Table 8 and the deviations are listed in Table 9. The quantity of the profit ob- jective function over each scenario (f1s), expected profit, quantity of the objective functions in the robust counterpart model, i.e. f 1׳ ,f2,f3, and optimal minimization objective function in the goal programming model (f4) are reported in Table 10.

From the results, it can be implied that the first objective is fully

satisfied since the deviations from the first goal (d+1 , d − 1 ) are zero. Due

to the tradeoff between profit and customer satisfaction, the model decided to activate all the CRM options defined in Section 3, except for option A as shown in Table 11. Moreover, the optimal quantity of products manufactured in the manufacturing plant and the recycled products produced in recycling plants in each time period are presented in Table 12.

5.3. Sensitivity analysis

In this section, sensitivity analyses on important parameters of the proposed model are conducted in order to provide managerial insights. First, β, the number of used products that should be provided by cus- tomers so that they can receive a free new product in one of the CRM options (A). In the computational results in Section 5.2, with β = 16, the model decided not to activate Option A. In order to find the value of β for which the model decided to activate Option A and the

Table 2 The Prices and Costs of the Chain (in 10,000 Rials).

t1 t2

Parameter p1 P2 P1 P2

PCpt 90 200 100 250 RCp′t 400 400 500 500 HHplt 10 11 12 13 CBOpt 50 70 60 80 TDpt 0.010 0.015 0.015 0.020 TRpt 0.005 0.010 0.010 0.015 TOp′t 1 1.5 1.5 2 PPpt 90 200 100 250 PAp′t 400 400 500 500

Table 3 Parameter Data Setting (in 10,000 Rials).

Parameter Value parameter value

COB 1000 ω1 50 COC 300 ω2 400 COD 150 ω3 50 COE 170 ω4 500 COF 1200

Table 4 Demand in the Forward Direction (in thousands).

t1 t2

s1 s2 s3 s1 s2 s3

Customer p1 p2 p1 p2 p1 p2 p1 p2 p1 p2 p1 p2

m1 1000 200 1100 250 1200 300 1020 204 1122 255 1224 306 m2 300 100 350 150 400 200 306 102 357 153 408 204 m3 300 100 350 150 400 200 306 102 357 153 408 204 m4 200 80 250 90 300 100 204 95 255 91.8 306 102 m5 300 100 350 150 400 200 306 102 357 153 408 204 m6 200 100 250 150 300 200 204 102 255 153 306 204 m7 200 150 250 200 300 250 204 155 255 204 306 255 m8 200 80 250 90 300 100 204 95 255 91.8 306 102

Table 5 Demand in the Backward Direction (in thousands).

t1 t2

s1 s2 s3 s1 s2 s3

Customer type3 p′1 p′2 p′1 p′2 p′1 p′2 p′1 p′2 p′1 p′2 p′1 p′2

o1 9 5 10 6 11 7 9.1 5.1 10.1 6.1 11.1 7.1 o2 5 3 6 4 7 5 5.1 3.1 6.1 4.1 7.1 5.1 o3 3 2 4 3 5 4 3.1 2.1 4.1 3.1 5.1 4.1

Table 6 Uncertainty in Capacity (in thousands).

s1 s2 s3

Parameter p1 p2 p1 p2 p1 p2

CAPpls 3500 1000 3600 1100 3700 1200 CNns 19 15 20 16 21 17

Table 7 Capacity of Distribution, Collection and Hybrid Centers (in thousands).

Parameter Place 1 Place 2

MXCj 5000 4000 MNCj 3000 2000 XCFk 1000 900 NCFk 800 700 XCRk 6000 4000 NCRk 4000 3000 UFi 3000 3000 URi 3000 3000

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consequences of activating this option, the model was run with various values of β. Finally, it was observed that the smallest value for this parameter for which the model decided to activate Option A was 20. At β = 20, the amount of total profit increased significantly to 275945200, showing an approximate 12.5% growth. Besides that, there was a great change in the customer satisfaction objective function raising from 0.05333 to 0.06667, which showed an approximate 25% growth. It is obvious that based on this analysis, DMs or senior managers of the SC are able to assign a more appropriate value for the mentioned para- meter.

As described in Section 4.2, in the MCGP model, ωi is a parameter that shows the weight of positive and negative deviations from the goal value of objective function i. These parameters are designated by DMs and directly affect the optimal solution. Therefore, DMs or senior managers of the SC should assign appropriate parameters as coefficients for every single objective function cautiously. That is why in this paper, the effect of different weights of each objective function on the mini- mization objective function in the goal programming model (f4) is in- spected in order to help DMs in assigning these weights in a way to

Fig. 4. The optimal SC network.

Table 8 The Upper/Lower Bound of the Aspiration Levels.

=g1. min 0.2452637E+10 = +g1. max 0.3188428E 10 =g2. min 0.03 =g2. max 0.07 =g3. min 8500 = +g3. max 0.2E 9

Table 9 Deviations.

=+d 01 = −d 01 =+e 100961 =

−e 01 =+d 02 =

−d 0.01662 =+e 02 = −e 02

=+d 14003 = −d 03 =+e 03 =

−e 03

Table 10 Optimal Solutions of Objective Functions and Expected Profit (in 10,000 Rials).

f1s if s = 1 203570,000 ′f 1 245263,700 f1s if s=2 202683,200 f2 0.05333 f1s if s=3 195272,000 f3 9900 expected profit 201052,100 f4 0.1666

Table 11 Activated and Non-Activated CRM Options.

Option A 0 Option D 1 Option B 1 Option E 1 Option C 1 Option F 1

Table 12 Optimal Quantity of Production in Manufacturing and Recycling Plants.

t1 t2

Qplt Tehran p1 3700,000 3700,000 p2 1200,000 1200,000

Q′ p′nt Tehran p′1 19,212 19,209 p′2 12,808 12,806

Isfahan p′1 21,612 21,609 p′2 14,406 14,408

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reach the minimum deviations from the target value. To do so, by changing the values of the deviation weight for the first objective, i.e. ω1, in the interval (0,1), the deviations from the goals (f4) are calculated and depicted in Fig. 5. Similarly, the effect of changing ω2 and ω3 on f4 is displayed in Figs. 6 and 7, respectively.

As shown in Figs. 5–7, the magnitude of deviations from the goals reaches its corresponding maximum values when the value of ω1 is less than 0.25, value of ω2 is more than 0.9, and value of ω3 is either less than 0.25 or more than 0.75. This can help DMs and senior managers of the SC to assign much more appropriate weights to each objective in order to minimize the deviations from the goals. The amount of the expected profit in the scenario-based model depends on the scenario that takes place. This is illustrated in Fig. 8 where each of the three scenarios is considered to occur with the probability of 0.25, 0.5, and 0.25, respectively. However, the robust counterpart assures that re- gardless of the scenarios, the expected profit is optimized.

6. Conclusions and further research directions

In recent years, the field of reverse logistics has received more at- tention from manufacturers from different economic, environmental and political points of view. Accordingly, considering reverse supply chains along with forward supply chains has become essential more than ever. On the other hand, the ever-increasing amount of used tires brings on serious environmental problems. In addition, the approach followed to deal with used tires plays an important role in terms of economic benefits, market demand, etc. In this regard, a comprehensive and effective planning is needed to collect and recycle end-of-life tires in an appropriate way.

These were the primary sources of motivation in this paper to pre- sent a multi-objective, multi-period, multi-product MILP model under uncertain demands and capacities for the tire industry. In the proposed model, three objective functions of maximizing total profit, maximizing customer satisfaction and minimizing distance between collecting fa- cilities and customers were considered. In this study, the CRM concept was innovatively incorporated into the SCM concept in order to have a more customer-centric SC and thus enable the SC to survive and thrive in the global competitive business environment. To achieve this, dif- ferent CRM options were defined and the corresponding decisions were modeled as binary variables considering their estimated costs. To solve the proposed scenario-based model, it was converted to an equivalent robust counterpart and a revised multi-choice goal programming method was applied for obtaining an efficient solution with the three objective functions of the model.

A case study of the tire industry was conducted including a manu- facturing plant, two distribution centers and eight main customers in the existing forward tire SC network. In this case, car and truck tires in the forward flow and crumb rubber and steel in the backward flow were considered. In the optimal SC network, obtained by the proposed model, a collection center, a hybrid center and two recycling plants were opened. From the obtained results, the first objective function was fully satisfied. Moreover, sensitivity analysis showed that activating Option A as a CRM action resulted in a 12.5 percent increase in the total profit of the chain.

There are some potential future research directions, such as:

• The function that calculated the quantity of the total received used products from the customers by means of considering customer sa- tisfaction in the second objective function was assumed to be linear; however, it can be approximated more accurately using interviews, questionnaires and other data collection tools.

• In Option A of the CRM options, β could be considered as a decision variable rather than a parameter.

• Uncertainty in other important parameters of the model can be formulated.

• Attention must be given to other new and emerging recycling in- dustries.

References

Amin, S.H., Zhang, G., Akhtar, P., 2017. Effects of uncertainty on a tire closed-loop supply chain network. Expert Syst. Appl. 73, 82–91.

Ayvaz, B., Bolat, B., Aydın, N., 2015. Stochastic reverse logistics network design for waste of electrical and electronic equipment. Resour. Conserv. Recycl. 104, 391–404.

Chang, C.-T., 2007. Multi-choice goal programming. Omega 35, 389–396. Chang, C.-T., 2008. Revised multi-choice goal programming. Appl. Math. Model. 32,

2587–2595. Charnes, A., Cooper, W.W., 1957. Management models and industrial applications of

linear programming. Manage. Sci. 4, 38–91. De Souza, C.D.R., D’Agosto, M.D.A., 2013. Value chain analysis applied to the scrap tire

reverse logistics chain: an applied study of co-processing in the cement industry. Resour. Conserv. Recycl. 78, 15–25.

Dehghanian, F., Mansour, S., 2009. Designing sustainable recovery network of end-of-life products using genetic algorithm. Resour. Conserv. Recycl. 53, 559–570.

Farina, A., Zanetti, M.C., Santagata, E., Blengini, G.A., 2017. Life cycle assessment applied to bituminous mixtures containing recycled materials: crumb rubber and reclaimed

Fig. 5. The effect of changing ω1 on f4.

Fig. 6. The effect of changing ω2 on f4.

Fig. 7. The effect of changing ω3 on f4.

Fig. 8. Expected profit in the scenario-based model vs. the robust counterpart.

M. Yadollahinia et al. Resources, Conservation & Recycling 138 (2018) 215–228

227

asphalt pavement. Resour. Conserv. Recycl. 117 (Part B), 204–212. Fleischmann, M., Bloemhof-Ruwaard, J.M., Dekker, R., Van Der Laan, E., Van Nunen,

J.A.E.E., Van Wassenhove, L.N., 1997. Quantitative models for reverse logistics: a review. Eur. J. Oper. Res. 103, 1–17.

Grönroos, c., 2000. service management and marketing: a customer relationship man- agement approach. Wiley.

Hatefi, S.M., Jolai, F., 2014. Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions. Appl. Math. Model. 38, 2630–2647.

Hao Yu, H., Solvang, W.D., 2017. A new two-stage stochastic model for reverse logistics network design under government subsidy and low-carbon emission requirement, Industrial Engineering and Engineering Management (IEEM). IEEE International Conference on 90–94.

Kara, S.S., Onut, S., 2010. A stochastic optimization approach for paper recycling reverse logistics network design under uncertainty. Int. J. Environ. Sci. Technol. 7 (4), 717–730.

Kotler, P., Keller, K.L., 2012. Marketing Management. Prentice Hall, Upper Saddle River, N.J.

Kracklauer, A.H., Mills, D.Q., Seifert, D., Barz, M., 2004. The integration of supply chain management and customer relationship management. In: Kracklauer, A.H., Mills, D.Q., Seifert, D. (Eds.), Collaborative Customer Relationship Management: Taking CRM to the Next Level. Berlin, Heidelberg, Springer Berlin Heidelberg.

Leung, S.C.H., Wu, Y., Lai, K.K., 2002. A robust optimization model for a cross-border logistics problem with fleet composition in an uncertain environment. Math. Comput. Model. 36, 1221–1234.

Liu, F., You, Y., 2011. Study and explores on CRM based on the supply chain integration. Manag. Sci. Eng. 5, 1.

Mohamadpour Tosarkani, B., Hassanzadeh Amin, S., 2018. A possibilistic solution to configure a battery closed-loop supply chain: Multi-objective approach. Expert Syst. Appl. 92, 12–26.

Mulvey, J.M., Ruszczyński, A., 1995. A new scenario decomposition method for large- scale stochastic optimization. Oper. Res. 43, 477–490.

Mulvey, J.M., Vanderbei, R.J., Zenios, S.A., 1995. Robust optimization of large-scale systems. Oper. Res. 43, 264–281.

Paixao, M., Souza, J., 2015. A robust optimization approach to the next release problem in the presence of uncertainties. J. Syst. Softw. 103, 281–295.

Paydar, M.M., Babaveisi, V., Safaei, A.S., 2017. Engine oil closed- loop supply chain considering collection risk. Comput. Chem. Eng. 104, 38–55.

Pedram, A., Yusoff, N.B., Udoncy, O.E., Mahat, A.B., Pedram, P., Babalola, A., 2017. Integrated forward and reverse supply chain: a tire case study. Waste Manag. 60, 460–470.

Presti, D.L., 2013. Recycled tyre rubber modified bitumens for road asphalt mixtures: a literature review. Constr. Build. Mater. 49, 863–881.

Rahimi, M., Ghezavati, V., 2018. Sustainable multi-period reverse logistics network de- sign and planning under uncertainty utilizing conditional value at risk (CVaR) for recycling construction and demolition waste. J. Cleaner Prod. 172, 1567–1581.

Realff, M., Ammons, J.C., Newton, D.J., 2004. Robust reverse production system design for carpet recycling. IIE Trans. 36 (8), 767–776.

Simic, V., Dabic-Ostojic, S., 2016. Interval-parameter chance-constrained programming model for uncertainty-based decision making in tire retreading industry. J. Clean. Prod.

Subulan, K., Taşan, A.S., Baykasoğlu, A., 2015. Designing an environmentally conscious tire closed-loop supply chain network with multiple recovery options using inter- active fuzzy goal programming. Appl. Math. Model. 39, 2661–2702.

M. Yadollahinia et al. Resources, Conservation & Recycling 138 (2018) 215–228

228