A game-theoretic approach for decision analysis in end-of-life vehicle reverse supply chain regarding government subsidy
Introduction
Due to the recent proliferation of vehicles, the number of end-of-life vehicles (ELVs) has grown tremendously (Levizzari et al., 2002). For example, although prior research shows that in 2009 there were about 30 million ELVs worldwide (Ahmed et al., 2009), just in 2018, the production of vehicles in China was 27.81 million (Li et al., 2020). The number of ELVs is also expected to be 80 million units per year by 2020 (Selman et al., 2020).
Scraping ELVs can provide useful components for the secondary market. The recycling and reproduction of these vehicles help save raw materials, reduce energy usage, and alleviate greenhouse gas emissions (Jody et al., 2011). Mismanagement of ELVs can cause environmental degradation (Sakai et al., 2014, Wang et al., 2020). Vehicles become inefficient after a certain lifespan and consequently, they produce higher levels of greenhouse gas emissions. Additionally, continuing to use ELVs might lead to breakdown during usage. Street vehicle breakdowns have ramifications such as traffic congestion and disruption to transit. Furthermore, noise nuisance and undermining cities' aesthetics are of other problems caused by the presence of ELVs (Li et al., 2014, Ozer et al., 2009).
The collection of ELVs is one of the essential ways to address the problems pertinent to ELVs. For instance, scraping ELVs is a significant source of recycling in the United States in which advanced recycling techniques and a complete support system for recycling worn-out vehicles are utilized (Jawi et al., 2017). Due to limited resources and emphasis on sustainable development in Japan, the government obliged vehicle manufacturing plants to recycle their worn-out vehicles (Che et al., 2011). Similarly, the European Union has been working to standardize the recycling industry for aged vehicles by improving recovery efficiency (Simic, 2015).
Typically, ELVs’ technical examination determines how ELVs return to the market. If the vehicle is repairable, the vehicle will be re-introduced to the second-hand vehicle market by changing parts and adjusting it to the current standards. Otherwise, if the vehicle cannot be repaired, it is transferred to the vehicle scrapping center and its parts and materials are sold (Phuc et al., 2017).
This paper studies the reverse supply chain of ELVs. This chain comprises the government, the take-back center, the inspection center, and the repair center. The government aims to increase the ability of the take-back center to collect more vehicles. To this end, the government incentivizes people to hand over their ELVs by giving subsidies to the take-back center. The subsidy can promote the collection efforts of the take-back center to assemble more ELVs.
Fig. 1 shows the overall schema of the game structure. Since players' decisions interact with each other, the problem is formulated using the game theory approach.
Governments have been searching for ways to encourage users to deliver their ELVs as soon as possible to the take-back centers (Zhao and Chen, 2011). Hence, it is vital to examine the role of government support in the ELV collection process. In this regard, the following fundamental questions need to be answered. How to obtain the equilibrium values for supply chain players under the condition of a government grant to the take-back center, using the Stackelberg game model? How the government can incentivize people to sell the ELVs, and how government policies affect the decisions of the other players? What is the government trade-off between its economic and environmental costs and the profits of the other players? This study attempts to answer these questions.
This research utilizes a multi-level structure. Multi-level structures have been used in numerous researches (Du et al., 2019, Huo and Jiang, 2019, Kang et al., 2019) and appear to be useful for modeling. The objective of this study is to investigate the impact of government subsidy policy on the decisions of the take-back center for used vehicles as well as the decisions of the inspection and repair centers for recoverable vehicles using game theory approach. This research attempts to find the equilibrium price of a used vehicle purchase by the take-back center, the pricing of the repaired vehicle by the inspection center, as well as the level of repair of this type of vehicle for the repair center. The proposed approach examines the profit-sharing contract, the revenue-sharing contract, and a centralized game scenario between the inspection center and the repair center.
To the best of our knowledge, no research has examined government funding's effect through subsidies on ELV collection centers, inspection centers, and repair centers using a game-theoretic approach. Thus, the contributions of this study are twofold. First, the relation between the government subsidies and the ELV reverse supply chain containing the take-back center, inspection center, and the vehicle repair center are examined using the Stackelberg game models. The equilibrium decisions for each of these players are achieved. Second, the vehicle inspection center's pricing in various contracts between the vehicle repair center and the inspection center is examined.
The rest of this paper is organized as follows. In Section 2, the literature review is described. Section 3 lays out the problem. Section 4 formulates the models for centralized and decentralized scenarios where the decentralized scenarios are profit sharing and revenue sharing. Methodology is presented in Section 5. In Section 6 sensitivity analysis is presented. In Section 7, we discuss the findings of this study. Finally, the study concludes with findings and future research suggestions in Section 8.
Section snippets
Literature review
This section reviews prior studies related to the ELV collection, reverse supply chain, and game theory.
Problem description
As can be seen in Fig. 1, the problem structure consists of a three-level game. In this three-level game, the first level is the government as the leader. In this level, the amount of subsidy for ELVs is determined. The second level is the inspection center as the first follower. At this level, the inspection center decides on the price of the reparable vehicles. It is assumed that the sales price of irreparable vehicles is predetermined. The take-back center and the repair center are at the
Model formulation
According to the definition of the problem and the presented assumptions, the demand functions for the repaired vehicles and the scrapped ELVs, the supply function of the ELVs, and the consumer surplus are formulated by Eqs. (1), (2), (3), (4), respectively.
The consumer surplus is considered as an indicator of social welfare and displays the difference between the prices that the customers are willing to pay and the actual
Problem solving
In this section, the equilibrium decisions of the players in the profit sharing and the revenue sharing contracts as well as the centralized scenario are obtained.
Sensitivity analysis
This section presents parametric and numerical results to illustrate the relations and the equilibrium values obtained in the preceding sections.
Discussion
In this section, we discuss the findings of this study based on previous analysis. Based on the Corollary 1, Corollary 2, Corollary 3, Corollary 4, Corollary 5, Corollary 6, the centralized scenario (a cooperation between the inspection center and the repair center) has the most significant advantage compared to the two contracts of profit sharing and cost sharing. For example, with the cooperation of the inspection center and the repair center, the repair level of the ELVs, the amount of
Conclusions and future suggestions
In this study, a reverse supply chain of ELVs is studied which includes the following players: the government, the inspection center, the take-back center, and the repair center. The government's strategy to collect ELVs has a wide range of benefits, such as reduction in greenhouse gas emissions, less energy consumption, and monetary savings. The government can play a significant role in collecting more ELVs through subsidy. Therefore, the government pays a subsidy to the take-back center to
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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