Journal of Advanced Transportation

Volume 2019, Article ID 3894064, 24 pages

https://doi.org/10.1155/2019/3894064

## Optimizing Transportation Network of Recovering End-of-Life Vehicles by Compromising Program in Polymorphic Uncertain Environment

^{1}Experimental Teaching Center, Guangdong University of Foreign Studies, Guangdong, Guangzhou, China^{2}School of Mathematics and Statistics, Central South University, Changsha, China

Correspondence should be addressed to Zhong Wan; moc.361@htamnaw

Received 13 November 2018; Revised 10 February 2019; Accepted 14 March 2019; Published 12 May 2019

Guest Editor: Helena Ramalhinho

Copyright © 2019 Jing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With rapid development of technology and improvement of living standards, the per capita holding of automobiles greatly increases, and the amount of end-of-life vehicles (ELVs) becomes larger and larger such that it is valuable to investigate an effective strategy for recycling ELVs from the viewpoints of environmental protection and resource utilization. In this paper, an optimization model with fuzzy and stochastic parameters is built to formulate the transportation planning problems of recycling ELVs in polymorphic uncertain environment, where the unit processing and transportation costs, the selling price of reused items, and the fixed cost are all fuzzy, while the demand in secondary market and the production capacity are random owing to features underlying the practical data. For this complicated polymorphic uncertain optimization model, a unified compromising approach is proposed to hedge the uncertainty of this model such that some powerful optimization algorithms can be applied to make an optimal recycling plan. Then, an interactive algorithm is developed to find a compromising solution of the uncertain model. Numerical results show efficiency of the algorithm and a number of important managerial insights are revealed from the proposed model by scenario analysis and sensitivity analysis.

#### 1. Introduction

##### 1.1. Background

With rapid development of technology and improvement of living standards, the per capita holding of automobiles greatly increases. In China, as the largest developing country with a population of around 1.3 billion, huge amount of end-of-life vehicles (ELVs) is bringing enormous pressure on its environment and human life. Actually, the civilian car ownership in China has reached 137 million in 2013, and has been almost doubling every four years. If the average lifespan of a car is 8-9 years, then the number of ELVs will exceed 14 million in 2020 [1]. In the world, it is estimated that the number of vehicles will rise to 1.85 billion by 2030, and the scrap generated from the ELVs will be 3.71 billion tonnes [2]. In an era of resources shortage and environmental deterioration, recycling the ELVs can give birth to new-style industry as a typical low-carbon and sustainable production approach [3, 4].

It is well known that the ELVs contain a great amount of reusable components and materials such as steel, copper, rubber, etc. Therefore, recycling the ELVs offer considerable economic and environmental benefits [5]. This fact has been paid great attention either by governments, by industry or by academia. Actually, the European Union (EU) has established legal regulation that manufacturers are responsible for take-back of ELVs from end-users, dismantling, shredding, and recycling of ELVs [6]. Directive 2000/53/EC required that, no later than 1 January 2015, for all the ELVs, the reuse and recovery rate shall be increased to a minimum of 95% by an average weight per vehicle and year. Within the same time limit, the reuse and recycling rate shall be increased to a minimum of 85% by an average weight per vehicle and year. Japan had an ELV recovery rate of 85% in 2002, its attained target reached 95% by 2015 [7].

In China, a series of relevant policies and regulations have been issued to improve the management mechanism for the ELV recycling industry since 2001. The “automotive products recycling technology policy” was implemented in 2006, which specifies utilization rate targets of the recyclable products in China [8]. The established China automotive material data system (CAMDS) in 2009 has played an important role in implementing the automotive products recyclable rate and the managing the ELVs. Chinese government has legislated that “yellow label cars” (heavily polluting vehicles) must be eliminated by 2017 [3]. Automotive components remanufacturing, as an essential part in automotive life-cycle development, has become a prominent direction to promote sustainable planning of automobile industry in China [9]. Actually, these policies are bringing a great of economic and environmental benefits to China.

##### 1.2. Literature Review

In recent years, recovery of used products has become increasingly important owing to economic reasons and growing environmental or legislative concern [10]. Particularly, the ELV recycling plays an important role for sustainable development. For example, each remanufactured engine could save 68-83% of the energy required to manufacture a new engine, and decrease carbon dioxide emissions by 73-87%. The coolants and batteries in ELVs can also be recycled, and it reduces emissions of greenhouse gases and gases that lead to acidification. The main ingredient of coolant is Solid CO_{2}, and the electrolyte of lead accumulator is lead accumulator [1]. Recycling metals from the ELVs could decrease the amounts of resources consumed building new cars. If all the vehicle materials can be recycled to produce new vehicles, about 30% of the energy consumption can be saved [11].

Summarily, the ELVs contain a great quantity of reusable components and materials such as steel, copper, rubber, plastics, etc. which can be reused or remanufactured. Thus, the remanufacturing industry of ELVs necessarily has strategic significance as it better utilizes resources and creates higher values. Especially, recycling ELVs can play an important role in realizing the country’s sustainable development goals. In 2003, China has introduced extended producer responsibility (EPR), which requires that any manufacturer should participate in ELV take-back, dismantling, remanufacturing, and so on [12]. The “automotive product recycling technology policy” in China requires carmakers to improve the design of vehicles, spare parts, and raw materials, as well as reduce the use of lead and other environmentally hazardous substances. Actually, this policy is an encouragement to the carmakers such that more recycled materials from the ELVs are used [13].

It is easy to see that recycling the ELVs depends on establishment of an efficient ELV recycling network, which not only can reduce the impact on the environment during the recycling process, but also can facilitate the effective reuse of recycled resources [14]. Furthermore, construction of optimization models for production planning problems of recycling the ELVs is helpful to provide the decision-makers an optimal plan for the practical operation of the recycling system [15].

In this connection, Cruz-Rivera et al. developed a reverse logistics network design for collection of the ELVs in Mexico [16]. Demirel et al. proposed a deterministic mixed integer linear programming (MILP) model for the ELV recycling network design, where all of the end-users, collection centers, dismantlers, shredders, landfills, recycling facilities, and secondary markets are included [6]. On the basis of [6], Demirel et al. in 2017 developed a closed-loop supply chain for the ELVs recycling, where some reusable components after processing are sold to suppliers for remanufacturing [17]. Finally, new vehicles with the remanufactured components will flow to consumers. Ene et al. considered refurbishment in ELVs recycling network; the reusable parts must be refurbished before they could be sold to secondary markets [18]. Phuc et al. designed inspection centers in the ELVs recycling system; those ELVs passing inspection is repaired in the repair centers and then is sold to the used vehicle markets [19]. Additionally, in [2], municipal solid waste incinerator and advanced thermal treatment measures are applied to dispose autoshredder residue (ASR) besides land-filling.

In some of the existing models for recycling the ELVs, various kinds of uncertainties have also been considered. It suggests in [20] that uncertainty seems to be the key factor influencing the management of ELVs. Özkır et al. stated that the selling price of products can be described by trapezoidal fuzzy sets such that both seller’s and buyer’s satisfaction levels are reflected [21]. In [19], the fixed cost, the transportation cost and the processing cost were also regarded as trapezoidal fuzzy sets in a reverse ELV recovery network. In [22], the capacities of sorting entities for recycling the ELVs were observed as random parameters, while the procurement cost, the transportation cost, the processing cost, and the storage cost were assumed to be interval parameters. In a global supply chain management model proposed by Wan et al., the demand of products for retailers is assumed to be stochastic and depends on the price of products [23].

Very recently, a polymorphic uncertain equilibrium model (PUEM) was developed by Wan et al. for the problem of decentralized supply chain management, where the demand of consumers was regarded as a continuous random variable, and the holding cost of the retailer and the transaction cost between the manufacturer and retailer were described by fuzzy sets [24]. Then, for the PUEM, a deterministic equivalent formulation (DEF) was first derived by compromise programming approach such that the existing powerful algorithms in the standard smooth optimization were employed to find an approximate equilibrium point for the uncertain problem. It is also noted that there are many different approaches to removing uncertainty in the uncertain model. For example, expectation method was applied in [19] to deal with the fuzzy objective such that the fuzzy objective can be converted into a deterministic one. Chance-constrained programming method was adopted in [22] to deal with the random constraints.

However, in the existing results for optimizing the system of recycling the ELVs, there are still some deficiencies, which can be briefly summarized as follows.

Polymorphic uncertainty is rarely considered in this special reverse logistics network. Especially, randomness of the demand in the secondary markets of reusable components has not been taken account into design of an optimal ELV recovery network.

To hedge fuzziness of the objective function, the expectation method is often applied to transform the fuzzy objective into a deterministic one. Clearly, this method can not address the feature of variance in a fuzzy set. A more reasonable method should capture all information in a fuzzy objective function, which includes the lower and upper variances of a fuzzy set, as well as its center value.

##### 1.3. Motivation of This Research

From the above literature review, it is necessary to build a new polymorphic uncertain optimization model for a more efficient system of the ELV recovery management. In particular, this model should simultaneously capture fuzziness and randomness of model parameters in a ELV recovery network design. Then, as done in [24], a unified compromising programming approach should be presented to convert the PUOM into a deterministic one such that the existing powerful optimization algorithms can be applied to find an approximately optimal strategy for recycling the ELVs.

In this paper, just like the mentioned reasons in [19, 21, 23, 24], we suppose that all of the fixed cost, the unit transportation cost, the unit processing cost, and the unit selling price of reused parts are fuzzy model parameters, and both of the capacity and the demand are regarded to be random variables. Then, our investigation proceeds along the following three subsequent steps.

*Step 1. *In a polymorphic uncertain environment, we construct a new optimization model to formulate the production planning problems of ELV recovery system.

*Step 2. *To hedge uncertainty of the model, a unified compromising programming approach will be proposed, which is associated with the following two phases: in the first phase, the original problem is converted into an auxiliary crisp multiple-objective mixed integer linear programming problem; in the second phase, a novel interactive fuzzy programming approach is proposed to find a preferred compromising solution through an interaction between the decision-maker with preference and the rational model [25].

*Step 3. *To answer what is the practical significance of the new model and the developed algorithm in this paper, we will reveal some important managerial insights from the proposed model by scenario analysis and sensitivity analysis.

The rest of the paper is organized as follows. Next section is devoted to the description of problem and construction of model. In Section 3, an interactive algorithm is developed. In Section 4, numerical results of case study are reported. In Section 5, sensitivity analysis is conducted, and some practical managerial implications are revealed from the constructed model. Some conclusions and suggestions on future research are presented in the last section.

#### 2. Problem Description and Formulation

##### 2.1. Problem Description

Similar to the setting in [6], the network structure of ELV recovery system to be addressed in this paper is shown in Figure 1.