# Recycling Performance of the Tire Remanufacturing with Production Capacity Constraints considering Carbon Tax and Technology Subsidy

Authors: Ruiqi Hu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

After considering the manufacturer’s production capacity constraints and market preference, this paper presents a closed-loop supply chain of automotive tires which consists of a remanufacturer, a retailer, and a recycler, where used tires are collected and reused. Based on the features of the closed-loop tire remanufacturing supply chain, four Stackelberg models are developed to investigate the influences of the carbon tax and the technology subsidy on recycling performance. The result shows that the carbon tax is conducive to improving the remanufacturing technology level and reducing emissions, but it reduces the profit of the manufacturer and the retailer. A subsidy can make up for their loss by the carbon tax. Moreover, an allied decision of the chain’s members can help them gain economic benefits, while an independent decision can improve environmental benefits.


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## Body

## 1. Introduction

Along with the development of the automobile industry, automotive tires are demanded and produced across the world. With around 11 million vehicles being produced and around 17 million vehicles being sold in the United States, the U.S. market calls for a large number of tire manufacturers. The market for replacement tires in the United States was almost 43 billion U.S. dollars in 2019 [1]. Black rubber is the main raw material used in the manufacturing of tires. To develop the proper characteristics of strength, resiliency, and wear resistance, the rubber must be treated with a variety of chemicals and then heated. A new tire is apt to deteriorate after five or six years and should be replaced, but the waste tires are called black pollution since the old tire can damage the environment [2]. After analyzing 1,249,108 residents, Badaloni, et al. [3] found strong associations between the long-term exposure to black tires and metals and mortality risk. One of the biggest problems with discarding old tires is that they contain chemicals and heavy metals that leach into the environment as the tires break down [4]. The leaching affects the soil and groundwater around the old tires. Used tires of course become a great fuel source if they are heated and burned [5]. But the burning process releases harmful chemicals into the air and poses a health and safety risk to the environment [6]. Truchot, et al. [7] designed a method to evaluate the toxic gas emissions in the combustion of tires.Some countries have tried to get rid of old tires by burning them up and suggested various approaches to manage waste tires [8]. Even if tires are not sent to a burning disposal site rather than recycled, they still pose a fire threat. They could combust, release their carcinogens into the air, and start a destructive fire. Most countries have banned the disposal of tires whole in landfills according to governmental regulations. Therefore, there are compelling environmental reasons to recycle old tires and the main recycling way is to reduce, reuse, recover, and recycle them. The remanufactured tires have the same performance and reliability as the new ones. In many countries, school buses, taxis, and even government vehicles use refurbished tires. However, remanufacturing old tires is a complicated process that involves many innovative techniques. To meet this challenge, many countries have launched initiatives such as the remanufacturing upgrade program in China to increase the recycling of used tires [9]. These programs try to save energy and reduce waste resources in a sustainable approach [10], that integrates manufacturers, retailers, customers, and the government into a reverse logistics system [11]. Remanufacturing initiatives not only help to improve the competitiveness of producers but also help them gain social and environmental benefits. Sometimes remanufacturing is unavoidable for a manufacturer when it has an imperfect production process for assembled products [12]. In a closed-loop remanufacturing supply chain, scholars have investigated the various pricing strategy between remanufactured and new products [13, 14].However, in response to the government’s call for remanufacturing programs, the manufacturer in the supply chain should adopt innovative high technology in remanufacturing tires so that they have the same performance as other new ones [15]. If customers are aware of the environmental problems, they would prefer to buy remanufactured tires. But a rational custom is more sensitive to the product’s price. However, the closed-loop tire remanufacturing supply chain is supported by the local government for its long-term environmental protection and potential economic development [16]. Government plays a critical role in boosting the development of the green and sustainable supply chain in various industries including the tire remanufacturing industry [17], e.g., they can optimize assorted measures such as a carbon tax or subsidy [18]. Therefore, this paper introduces both the carbon tax and subsidy policy in the closed-loop supply chain with the manufacturer’s production capacity constraints and market preference and investigates how it affects the remanufacturing tire technology and the performance of the chain. The main contributions are as follows: (1) introducing a carbon tax in the closed-loop tire remanufacturing supply chain with the manufacturer’s production capacity constraints and market preference, and revealing its impacts on remanufacturing technology, quantity of recycled product, and profits of members in the chain. (2) Introducing a subsidy to support the technology investment of remanufacturing tires and investigating the optimal decision results in the supply chain when the production capacity is limited and customers have a preference. (3) Comparing the carbon emissions and profits of the supply chain in various decisions and suggesting the optimal decision-making model after reviewing its economic and environmental benefits.The remainder of this paper is organized as follows: Section2 is a review of the literature on the closed-loop supply chain of remanufacturing products, including its pricing methods, innovative decisions, and members’ coordination. Section 3 presents the hypotheses and symbols of the supply chain system. Four models are formulated and compared in Section 4. Section 5 illustrates the results by a numerical example and reveals the tendencies of sensitive factors. Section 6 is the conclusion and further research.


## 2. Literature Review

As an effective means of energy conservation and emission reduction, the remanufacturing of old automotive tires has attracted the attention of states in terms of recycling resources [19], and it has also become the focus of scholars [20, 21]. The pricing mechanism of a supply chain is a hot topic for researchers [22], and the pricing research on the closed-loop remanufacturing supply chain is divided into two categories: homogeneous and heterogeneous pricing methods for remanufactured products and new products. In the homogeneous pricing model, new products and remanufactured ones have the same price [23]. Majumder and Groenevelt [24] resolved the Nash equilibrium of new products and remanufactured products in a closed-loop supply chain. In the heterogeneous pricing model, new products and remanufactured ones have different or dynamic prices [25]. When the quality of remanufactured products is inferior to new ones, their prices are usually lower than new ones [26] and most scholars have designed various supply chain systems to solve the heterogeneous pricing problems [27]. Vorasayan and Ryan [28] carried out discriminatory pricing for remanufactured products and new products and discussed the impact of government fund policies on the chain.He, et al. [29] presented a dual-channel closed-loop supply chain to explore differentiated prices of new and remanufactured products in the presence of possible government subsidies. Wang, et al. [30] designed three-channel strategies for marketing new and remanufactured products in their optimal channel structures where the manufacturer preferred to differentiate new and remanufactured products. Zhao, et al. [31] compared the prices, services, recycling decisions, and profits of supply chain members under different remanufacturing modes. Ferguson and Toktay [32] studied various pricing strategies of the manufacturer in remanufacturing and the recycler in remanufacturing intervention respectively after considering heterogeneous consumer groups. By considering the product life cycle in the two-stage, multi-stages, and infinite stages, Ferrer and Swaminathan [33] suggested the optimal pricing decision for new products and remanufactured products in a closed-loop supply chain.However, the differentiated pricing strategy somehow tells customers that the lower-priced products are remanufactured and their quality is inferior, then customers would select the new products and this pricing strategy may damage the development of remanufactured products [34]. When remanufactured products have the same price as new products, Savaskan, et al. [35] claimed that the homogeneous pricing strategy would be better for the supply chain. Supposing remanufactured products and new products are homogeneous, SeyedEsfahani, et al. [36] revealed the effect of advertising and the impact of product prices on consumer demand. Jena et al. [37] presented a decentralized decision-making model and a centralized decision-making model based on the same price of new products and remanufactured products and concluded that the centralized decision-making model was optimal after comparing economic and environmental benefits.However, consumers are aware of the quality between remanufactured products and new products if they have the same price, which can cause market disruption. Many scholars have studied technology innovation in a closed-loop supply chain [38]. Lin and Saggi [39] focused on the relationship between market competition and technological innovation. Liao, et al. [40] suggested that collaborative innovation had a significant impact on the supply chain to obtain competitive advantages. Gligor, et al. [41] revealed that an agile supply chain strategy could enhance its value level. Suetens [42] compared the features of technological spillovers in a cooperative and a non-cooperative supply chain. Banerjee and Lin [43] investigated motivations across a vertical cooperative supply chain based on a two-stage game. Ge, et al. [44] revealed the effect of investment spillover on the profits of manufacturers, retailers, and other members of a vertical supply chain. After reviewing barriers to innovation in a sustainable supply chain, Gupta, et al. [45] suggested strategies for innovation in supply chain sustainability innovation. These studies mainly aim to improve the quality of the product, reduce the cost in the production process, and improve the core competitiveness of the enterprises. However, few published papers focus on the combination of remanufacturing technology and sustainable development, intending to promote the recycling of used products.Government as a coordinating role is also a popular research topic in the supply chain; related papers focus on incentive and punishment policies, tax policies, subsidy policies, and other coordination strategies. Hammond and Beullens [46] developed an oligopolistic closed-loop supply chain model and investigated the influence of incentive and punishment parameters on the supply chain under the legislation. He and Chen [47] discussed the incentive effect of government subsidy policies on promoting the development of green buildings and found that the incentive effect of four subsidy policies was significantly enhanced along with the improvement of consumers’ green preferences and the potential benefits for developers. Li, et al. [48]studied the influence of the carbon subsidy on the decision-making model in a closed-loop supply chain for remanufacturing and revealed when and how the government implemented the carbon subsidy to encourage companies to reduce carbon emissions. Krass, et al. [49] utilized environmental tax to stimulate innovation, and Cohen, et al. [50] utilized consumer subsidies to stimulate manufacturers to adopt green technologies. Hong and Ke [51] constructed a closed-loop supply chain model with the government as the leader and studied how the supply chain members could make the optimal decision based on the government subsidy information. Heydari, et al. [52] compared the coordination effects of government tax policy and subsidy policy.Previous studies often assume that a closed-loop supply chain has an infinite production capacity, but actually, it has limited capacity. Compared with the supply chain without production capacity constraints, a supply chain with limited capacity may benefit from the improvement of dynamic performance. After reviewing capacity constraints, Zhang, et al. [53]found that consumers’ awareness of environmental protection has an impact on the output decisions of general products and green products. Hussain, et al. [54] investigated the nonlinear influence of production capacity constraints in a two-tier supply chain and suggested a trade-off between production capacity and safety stock in various tiers, which helped to make a better decision about its production capacity and stock. Cannella, et al. [55] studied the relationship between capacity restriction and supply chain performance and concluded that the degree of influence depends on the reaction ability of enterprises, market conditions, and inventory management policies. Wang, et al. [56] constructed a closed-loop supply chain consisting of competing raw material suppliers, recyclers, and manufacturers and identified the decision-making mechanism with the constraints of manufacturers’ capacity.The literature review shows that though the closed-loop supply chain of remanufacturing products has attracted many researchers who investigate the pricing strategies of remanufactured products and new products and agree with the government as a leading role in the chain, previous articles ignore the pricing changes in product life span, customer preference, and quality changes after remanufacturing. This paper aims to develop an innovative technology to ensure that remanufactured automotive tires have the same performance and quality as the original tires. Based on constraints on production capacity and market preference, this paper introduces both a carbon tax and a technology subsidy in the closed-loop tire remanufacturing supply chain and thoroughly investigates their impacts.


## 3. Model Assumptions and Symbolic Description

Consider a single-cycle closed-loop supply chain system consisting of an automotive tire manufacturerM, a retailer R, and a third-party recycler T, we present four models symbolized by DD,DA,SD, and SA (shown in Figure 1). All four models take a carbon tax into account. DD represents an independent decision-making model with a carbon tax, DA represents an allied decision-making model with a carbon tax, SD represents an independent decision-making model with a carbon tax and subsidy, and SA represents an allied decision-making model with a carbon tax and subsidy. To accelerate the recycling of used tires and encourage remanufacturing tires, this paper designs several mechanisms to investigate the impacts of government involvement and technology innovation on the market demand, recycling quantity, carbon emissions, and total profit in the supply chain.Figure 1
Closed-loop supply chain models with government involvement (a) DD model (b) DA model (c) SD model (d) SA model.
(a)(b)(c)(d)Assumptions and notations in the models are described below:


### 3.1. Model Assumptions

Hypothesis 1.
the tire manufacturer is the market leader, and the retailer and the recycler are the market followers. The decision of the retailer and the recycler is completely dependent on the decision of the manufacturer.Hypothesis 2.
the cost of manufacturing a new tire iscn, and the cost of remanufacturing a tire is cr. To ensure the profit of the remanufactured tires, cn>cr. The manufacturer sells all tires to the retailer at a wholesale price w, and then the retailer sells products to the consumer at a retail price p. Among which, p>w>cn>cr.Hypothesis 3.
all old tires have the same features which can be recycled for remanufacturing. The recycler pays a recycling pricef for buying used automotive tires from users, and the manufacturer pays a recycling cost b for buying used tires from the third-party recycler. According to the recycling function [57], the recycling quantity of used tires is G=β+δf, where β is fixed quantity of the recycled tires in the market; δ is the ratio of quantity of the recycled tire to its price.Hypothesis 4.
as mentioned by Ranjbar, et al. [58], a demand function of new tires is Qn=λd−θp, where d is the market maximum demand for all tires, θ is the sensitivity coefficient of consumers to tires price, and λ is the productivity coefficient of remanufactured products. The market demand for remanufactured tires is Qr, where Qr=1−λd+θpHypothesis 5.
all used tires are recycled and remanufactured into new ones. The manufacturer’s output of new products and remanufactured products just meets the market demand and is not more than the manufacturer’s maximum production capacityϕ: Qn+λQr=ϕ.Hypothesis 6.
carbon emissions come only from the production process while the carbon emission per new tire from its manufacturing process isen and the carbon emission per recycled tire from its remanufacturing process is er, and the carbon tax rate of a tire is r.Hypothesis 7.
to ensure that the remanufactured tires have the same performance as the new ones, the manufacturer must adopt innovative technologies in the remanufacturing process. The level of innovative remanufacturing technologies is represented byI. Referring to a cost function of technological innovation [38], it is assumed that the investment in the remanufacturing technology is 1/2kI2, where k is a coefficient of the investment in remanufacturing tires and k>0. When adopting a higher level of remanufacturing technology, the manufacturer can save a manufacturing cost (ϵI), where ϵ is a cost-saving coefficient.Hypothesis 8.
to promote the recycling of used tires and encourage the manufacturer to improve their remanufacturing technology, the government will pay the manufacturer a subsidy (the subsidy ratio isγ) according to the cost of remanufacturing.


### 3.2. Description of Parameters

Most parameters in this paper are defined in Table1.Table 1
Parameters and notations.
SymbolsNotationswWholesale price of a tirepRetail price of a tirecnCost of producing a new tirecrCost of producing a remanufactured tirebRecycling cost of a used tire paid by the manufacturerfRecycling price of a used tire paid by the recyclerILevel of remanufacturing technologyϵCost-saving coefficient of remanufacturing technologyγRatio of a technology subsidy to the remanufacturing costrCarbon tax rateerCarbon emission by a remanufactured tireenCarbon emission by a new tireβFixed quantity of recycled tires in the marketδRatio of quantity to the price of recycled tireskCoefficient of investment in remanufacturing technologydMarket maximum demand for all tiresϕMaximum production capacityθCoefficient of consumers to the tire priceλProduction capacity coefficient of remanufactured tires


## 3.1. Model Assumptions

Hypothesis 1.
the tire manufacturer is the market leader, and the retailer and the recycler are the market followers. The decision of the retailer and the recycler is completely dependent on the decision of the manufacturer.Hypothesis 2.
the cost of manufacturing a new tire iscn, and the cost of remanufacturing a tire is cr. To ensure the profit of the remanufactured tires, cn>cr. The manufacturer sells all tires to the retailer at a wholesale price w, and then the retailer sells products to the consumer at a retail price p. Among which, p>w>cn>cr.Hypothesis 3.
all old tires have the same features which can be recycled for remanufacturing. The recycler pays a recycling pricef for buying used automotive tires from users, and the manufacturer pays a recycling cost b for buying used tires from the third-party recycler. According to the recycling function [57], the recycling quantity of used tires is G=β+δf, where β is fixed quantity of the recycled tires in the market; δ is the ratio of quantity of the recycled tire to its price.Hypothesis 4.
as mentioned by Ranjbar, et al. [58], a demand function of new tires is Qn=λd−θp, where d is the market maximum demand for all tires, θ is the sensitivity coefficient of consumers to tires price, and λ is the productivity coefficient of remanufactured products. The market demand for remanufactured tires is Qr, where Qr=1−λd+θpHypothesis 5.
all used tires are recycled and remanufactured into new ones. The manufacturer’s output of new products and remanufactured products just meets the market demand and is not more than the manufacturer’s maximum production capacityϕ: Qn+λQr=ϕ.Hypothesis 6.
carbon emissions come only from the production process while the carbon emission per new tire from its manufacturing process isen and the carbon emission per recycled tire from its remanufacturing process is er, and the carbon tax rate of a tire is r.Hypothesis 7.
to ensure that the remanufactured tires have the same performance as the new ones, the manufacturer must adopt innovative technologies in the remanufacturing process. The level of innovative remanufacturing technologies is represented byI. Referring to a cost function of technological innovation [38], it is assumed that the investment in the remanufacturing technology is 1/2kI2, where k is a coefficient of the investment in remanufacturing tires and k>0. When adopting a higher level of remanufacturing technology, the manufacturer can save a manufacturing cost (ϵI), where ϵ is a cost-saving coefficient.Hypothesis 8.
to promote the recycling of used tires and encourage the manufacturer to improve their remanufacturing technology, the government will pay the manufacturer a subsidy (the subsidy ratio isγ) according to the cost of remanufacturing.


## 3.2. Description of Parameters

Most parameters in this paper are defined in Table1.Table 1
Parameters and notations.
SymbolsNotationswWholesale price of a tirepRetail price of a tirecnCost of producing a new tirecrCost of producing a remanufactured tirebRecycling cost of a used tire paid by the manufacturerfRecycling price of a used tire paid by the recyclerILevel of remanufacturing technologyϵCost-saving coefficient of remanufacturing technologyγRatio of a technology subsidy to the remanufacturing costrCarbon tax rateerCarbon emission by a remanufactured tireenCarbon emission by a new tireβFixed quantity of recycled tires in the marketδRatio of quantity to the price of recycled tireskCoefficient of investment in remanufacturing technologydMarket maximum demand for all tiresϕMaximum production capacityθCoefficient of consumers to the tire priceλProduction capacity coefficient of remanufactured tires


## 4. Model Formulations and Analyses

Four decision-making models of the supply chain are developed whereπi is the profit of a supply chain member i, where i=M,R,T, M is the manufacturer, R is the retailer, and T is the third-party recycler. Results including market demand, quantity of recycled products, carbon emission, profit, etc., are compared, and the influences of the carbon tax, government subsidies, and remanufacturing technology on the supply chain are discussed.


### 4.1. An Independent Decision-Making Model with a Carbon TaxDD

In this model, the government imposes a carbon tax on the manufacturer, and each member of the supply chain makes its decision by maximizing its profit. Their profit functions are defined by(1)πMDD=w−cr−b+ϵI−rerβ+δf−12kI2+w−cn−renλd−θp−β+δf,πRDD=p−wλd−θp,πTDD=b−fβ+δf.Proposition 1.
the optimal decisions for a manufacturer, retailer, and recycler in the DD model are as follows:(2)wDD∗=cnθ+enθr+λd2θ,pDD∗=cnθ+enθr+3ϕ4θ,bDD∗=2kβ+−cn+cr−enr+errδ−βδϵ2δ−4k+δϵ2,fDD∗=3kβ+−cn+cr+er−enrkδ−βδϵ2δ−4k+δϵ2,IDD∗=β+cnδ−crδ+enrδ−errδϵ4k−δϵ2.The optimal market demands and quantity of recycled products in the DD model are as follows:(3)QDD∗=14−cnθ−enrθ+λd,GDD∗=kβ+cn−cr+enr−errδ4k−δϵ2.The carbon emission in the DD model is:(4)CDD∗=enδϵ2cnθ+enrθ−λd−4kβ+cn−cr+enr−errδ+cn+enrθ−λd16k−4δϵ2+erkβ+cn−cr+enr−errδ4k−δϵ2.The optimal profits of the manufacturer, retailer, and recycler in the DD models are as follows:(5)πMDD∗=18δ−4k+δϵ2θδ2ε2cnθ+enrθ−λdcn+enrθ−λd−4kβ2θ+2cn−cr−er2+renβδθ+δθcn−cr+enr−errcn−cr−ren+er+2renδ+cn+enrcn−enr+2renθ−2enr+cnθλd+λd2,πRDD∗=cnθ+enrθ−λd216θ,πTDD∗=k2β+cn−cr+enr−errδ2δ−4k+δϵ22.The proof process is shown in Appendix: Proof of Proposition 1.


### 4.2. Allied Decision-Making Model with a Carbon TaxDA

In the DA model, the government imposes a carbon tax on the manufacturer. The manufacturer and the retailer make decisions by maximizing their allied profits while the recycler makes decisions by maximizing itself profit.MR represents the allied manufacturer and retailer, and their profit functions are represented by:(6)πMRDA=cn−cr−b+ϵI+ren−rerβ+δf−12kI2+p−cn−renλd−θp,πTDA=b−fβ+δf.Proposition 2.
the optimal decisions of the manufacturer, the retailer, and the recycler in the DA model are as follows:(7)pDA∗=cnθ+enθr+λd2θ,bDA∗=2kβ+−cn+cr−enr+errδ−βδϵ2δ−4k+δϵ2,fDA∗=3kβ+−cn+cr+er−enrkδ−βδϵ2δ−4k+δϵ2,IDA∗=β+cnδ−crδ+enrδ−errδϵ4k−δϵ2.The optimal market demands and quantity of recycled products are as follows:(8)QDA∗=12−cnθ−enrθ+λd,GDA∗=kβ+cn−cr+enr−errδ4k−δϵ2.The carbon emission in the DA model is(9)CDA∗=erβ+3kβ+k−cn+cr+−en+errδ−βδε2−4k+δε2+en−β−3kβ+k−cn+cr+−en+errδ−βδε2−4k+δε2+12−cnθ−enrθ−ϕ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(10)πMRDD∗=18δ−4k+δϵ2θδ2ε2cnθ+enrθ−λdcn+enrθ−λd−4kβ2θ+2cn−cr−er2+renβδθ+δθcn−cr+enr−errcn−cr−ren+er+2renδ+cn+enrcn−enr+2renθ−2enr+cnθλd+λd2,πTDA∗=k2β+cn−cr+enr−errδ2δ−4k+δϵ22.The proof process is shown in Appendix: Proof of Proposition 2.


### 4.3. Independent Decision-Making Model with a Carbon Tax and a Technology SubsidySD

In the SD model, the government imposes a carbon tax on the manufacturer and subsidizes remanufacturing costs in a ratio. The carbon tax rate isr and the subsidy ratio is γ. Each member of the supply chain makes decisions by maximizing its profit, and the profit functions are defined by:(11)πMSD=w−cr−b+ϵI−rerβ+δf−121−γkI2+w−cn−renλd−θp−β+δf,πRSD=p−wλd−θp,πTSD=b−fβ+δf.Proposition 3.
in the SD model, the optimal decisions for the manufacturer, the retailer, and the recycler are as follows:(12)wSD∗=cnθ+enθr+λd2θ,pSD∗=cnθ+enθr+3λd4θ,bSD∗=−fSD∗=−kγ−13β+−cn+cr+er−enrδ+βδϵ2δ4kγ−1+δϵ2,2kγ−1β+−cn+cr−enr+errδ+βδϵ2δ4kγ−1+δϵ2,ISD∗=−β+cnδ−crδ+enrδ−errδϵ4kγ−1+δϵ2.The optimal market demands and quantity of recycled products are as follows:(13)QSD∗=14−cnθ−enrθ+λd,GSD∗=kγ−1β+cn−cr+enr−errδ4kγ−1+δϵ2.The carbon emission in the SD model is(14)CSD∗=144kγ−1+δϵ24erkγ−1β+cn−cr−errδ−en2rδϵ2θ+4kγ−1δ+θ+en−4kγ−1β−crδ−2errδ+cnδ+θ−λd+δϵ2−cnθ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(15)πMSD∗=184kγ−1+δϵ224kγ−1β+cn−cr+enr−errδ2ϵ2+1θ4kγ−1+δε2δε2cnθ+enrθ−λd+4kγ−1β+cn−cr+enr−errδ+cn+enrθ−λdcn+enrθ−ϕ−1δθ4kγ−1β+cn−cr+enr−errδδ2ε2cn+enrθ−λd−4kγ−1βθ+δ−crθ−errθ+λd,πRSD∗=cnθ+enrθ−λd216θ,πTSD∗=k2γ−12β+cn−cr+enr−errδ2δ4kγ−1+δϵ22.The proof process is shown in Appendix: Proof of Proposition 3.


### 4.4. Allied Decision-Making Model with a Carbon Tax and a Technology subsidySA

In the SA model, the government imposes a carbon tax on the manufacturer and subsidizes the cost of remanufacturing in a ratio to the remanufacturing cost. The manufacturer and the retailer make decisions by maximizing their allied profits, while the recycler makes a decision by maximizing its profit. Their profit functions are defined as follows.(16)πMSA=cn−cr−b+ϵI+ren−rerβ+δf−121−γkI2+p−cn−renλd−θp,πTSA=b−fβ+δf.Proposition 4.
in the SA model, the optimal decisions for the manufacturer, the retailer, and the recycler are as follows:(17)pSA∗=cnθ+enθr+λd2θ,bSA∗=−2kγ−1β+−cn+cr−enr+errδ+βδϵ2δ4kγ−1+δϵ2,fSA∗=−kγ−13β+−cn+cr+er−enrδ+βδϵ2δ4kγ−1+δϵ2,ISA∗=−β+cnδ−crδ+enrδ−errδϵ4kγ−1+δϵ2.The optimal market demands and quantity of recycled products are as follows:(18)QSA∗=12−cnθ−enrθ+λd,GSA∗=kγ−1β+cn−cr+enr−errδ4kγ−1+δϵ2.The carbon emission in the SA model is(19)CSA∗=18kγ−1+2δϵ22erkγ−1β+cn−cr−errδ−en2rδϵ2θ+2kγ−1δ+2θ+en−2kγ−1β+cnδ−crδ−2errδ+2cnθ−2λd+δϵ2−cnθ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(20)πMSA∗=1δ4kγ−1+δϵ22kγ−1β+cn−cr+enr−errδ2kγ−1β+cn−cr+enr−rerδ+cnθ+enrθ−λdcnθ−enrθ+2renθ−λd4θ+12γ−1k−β+cn−cr+enr−errδϵ4kγ−1+δϵ22,πTSA∗=k2γ−12β+cn−cr+enr−errδ2δ4kγ−1+δϵ22.The proof process is shown in Appendix: Proof of Proposition 4.


## 4.1. An Independent Decision-Making Model with a Carbon TaxDD

In this model, the government imposes a carbon tax on the manufacturer, and each member of the supply chain makes its decision by maximizing its profit. Their profit functions are defined by(1)πMDD=w−cr−b+ϵI−rerβ+δf−12kI2+w−cn−renλd−θp−β+δf,πRDD=p−wλd−θp,πTDD=b−fβ+δf.Proposition 1.
the optimal decisions for a manufacturer, retailer, and recycler in the DD model are as follows:(2)wDD∗=cnθ+enθr+λd2θ,pDD∗=cnθ+enθr+3ϕ4θ,bDD∗=2kβ+−cn+cr−enr+errδ−βδϵ2δ−4k+δϵ2,fDD∗=3kβ+−cn+cr+er−enrkδ−βδϵ2δ−4k+δϵ2,IDD∗=β+cnδ−crδ+enrδ−errδϵ4k−δϵ2.The optimal market demands and quantity of recycled products in the DD model are as follows:(3)QDD∗=14−cnθ−enrθ+λd,GDD∗=kβ+cn−cr+enr−errδ4k−δϵ2.The carbon emission in the DD model is:(4)CDD∗=enδϵ2cnθ+enrθ−λd−4kβ+cn−cr+enr−errδ+cn+enrθ−λd16k−4δϵ2+erkβ+cn−cr+enr−errδ4k−δϵ2.The optimal profits of the manufacturer, retailer, and recycler in the DD models are as follows:(5)πMDD∗=18δ−4k+δϵ2θδ2ε2cnθ+enrθ−λdcn+enrθ−λd−4kβ2θ+2cn−cr−er2+renβδθ+δθcn−cr+enr−errcn−cr−ren+er+2renδ+cn+enrcn−enr+2renθ−2enr+cnθλd+λd2,πRDD∗=cnθ+enrθ−λd216θ,πTDD∗=k2β+cn−cr+enr−errδ2δ−4k+δϵ22.The proof process is shown in Appendix: Proof of Proposition 1.


## 4.2. Allied Decision-Making Model with a Carbon TaxDA

In the DA model, the government imposes a carbon tax on the manufacturer. The manufacturer and the retailer make decisions by maximizing their allied profits while the recycler makes decisions by maximizing itself profit.MR represents the allied manufacturer and retailer, and their profit functions are represented by:(6)πMRDA=cn−cr−b+ϵI+ren−rerβ+δf−12kI2+p−cn−renλd−θp,πTDA=b−fβ+δf.Proposition 2.
the optimal decisions of the manufacturer, the retailer, and the recycler in the DA model are as follows:(7)pDA∗=cnθ+enθr+λd2θ,bDA∗=2kβ+−cn+cr−enr+errδ−βδϵ2δ−4k+δϵ2,fDA∗=3kβ+−cn+cr+er−enrkδ−βδϵ2δ−4k+δϵ2,IDA∗=β+cnδ−crδ+enrδ−errδϵ4k−δϵ2.The optimal market demands and quantity of recycled products are as follows:(8)QDA∗=12−cnθ−enrθ+λd,GDA∗=kβ+cn−cr+enr−errδ4k−δϵ2.The carbon emission in the DA model is(9)CDA∗=erβ+3kβ+k−cn+cr+−en+errδ−βδε2−4k+δε2+en−β−3kβ+k−cn+cr+−en+errδ−βδε2−4k+δε2+12−cnθ−enrθ−ϕ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(10)πMRDD∗=18δ−4k+δϵ2θδ2ε2cnθ+enrθ−λdcn+enrθ−λd−4kβ2θ+2cn−cr−er2+renβδθ+δθcn−cr+enr−errcn−cr−ren+er+2renδ+cn+enrcn−enr+2renθ−2enr+cnθλd+λd2,πTDA∗=k2β+cn−cr+enr−errδ2δ−4k+δϵ22.The proof process is shown in Appendix: Proof of Proposition 2.


## 4.3. Independent Decision-Making Model with a Carbon Tax and a Technology SubsidySD

In the SD model, the government imposes a carbon tax on the manufacturer and subsidizes remanufacturing costs in a ratio. The carbon tax rate isr and the subsidy ratio is γ. Each member of the supply chain makes decisions by maximizing its profit, and the profit functions are defined by:(11)πMSD=w−cr−b+ϵI−rerβ+δf−121−γkI2+w−cn−renλd−θp−β+δf,πRSD=p−wλd−θp,πTSD=b−fβ+δf.Proposition 3.
in the SD model, the optimal decisions for the manufacturer, the retailer, and the recycler are as follows:(12)wSD∗=cnθ+enθr+λd2θ,pSD∗=cnθ+enθr+3λd4θ,bSD∗=−fSD∗=−kγ−13β+−cn+cr+er−enrδ+βδϵ2δ4kγ−1+δϵ2,2kγ−1β+−cn+cr−enr+errδ+βδϵ2δ4kγ−1+δϵ2,ISD∗=−β+cnδ−crδ+enrδ−errδϵ4kγ−1+δϵ2.The optimal market demands and quantity of recycled products are as follows:(13)QSD∗=14−cnθ−enrθ+λd,GSD∗=kγ−1β+cn−cr+enr−errδ4kγ−1+δϵ2.The carbon emission in the SD model is(14)CSD∗=144kγ−1+δϵ24erkγ−1β+cn−cr−errδ−en2rδϵ2θ+4kγ−1δ+θ+en−4kγ−1β−crδ−2errδ+cnδ+θ−λd+δϵ2−cnθ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(15)πMSD∗=184kγ−1+δϵ224kγ−1β+cn−cr+enr−errδ2ϵ2+1θ4kγ−1+δε2δε2cnθ+enrθ−λd+4kγ−1β+cn−cr+enr−errδ+cn+enrθ−λdcn+enrθ−ϕ−1δθ4kγ−1β+cn−cr+enr−errδδ2ε2cn+enrθ−λd−4kγ−1βθ+δ−crθ−errθ+λd,πRSD∗=cnθ+enrθ−λd216θ,πTSD∗=k2γ−12β+cn−cr+enr−errδ2δ4kγ−1+δϵ22.The proof process is shown in Appendix: Proof of Proposition 3.


## 4.4. Allied Decision-Making Model with a Carbon Tax and a Technology subsidySA

In the SA model, the government imposes a carbon tax on the manufacturer and subsidizes the cost of remanufacturing in a ratio to the remanufacturing cost. The manufacturer and the retailer make decisions by maximizing their allied profits, while the recycler makes a decision by maximizing its profit. Their profit functions are defined as follows.(16)πMSA=cn−cr−b+ϵI+ren−rerβ+δf−121−γkI2+p−cn−renλd−θp,πTSA=b−fβ+δf.Proposition 4.
in the SA model, the optimal decisions for the manufacturer, the retailer, and the recycler are as follows:(17)pSA∗=cnθ+enθr+λd2θ,bSA∗=−2kγ−1β+−cn+cr−enr+errδ+βδϵ2δ4kγ−1+δϵ2,fSA∗=−kγ−13β+−cn+cr+er−enrδ+βδϵ2δ4kγ−1+δϵ2,ISA∗=−β+cnδ−crδ+enrδ−errδϵ4kγ−1+δϵ2.The optimal market demands and quantity of recycled products are as follows:(18)QSA∗=12−cnθ−enrθ+λd,GSA∗=kγ−1β+cn−cr+enr−errδ4kγ−1+δϵ2.The carbon emission in the SA model is(19)CSA∗=18kγ−1+2δϵ22erkγ−1β+cn−cr−errδ−en2rδϵ2θ+2kγ−1δ+2θ+en−2kγ−1β+cnδ−crδ−2errδ+2cnθ−2λd+δϵ2−cnθ+λd.The optimal profits of the manufacturer, the retailer, and the recycler are as follows:(20)πMSA∗=1δ4kγ−1+δϵ22kγ−1β+cn−cr+enr−errδ2kγ−1β+cn−cr+enr−rerδ+cnθ+enrθ−λdcnθ−enrθ+2renθ−λd4θ+12γ−1k−β+cn−cr+enr−errδϵ4kγ−1+δϵ22,πTSA∗=k2γ−12β+cn−cr+enr−errδ2δ4kγ−1+δϵ22.The proof process is shown in Appendix: Proof of Proposition 4.


## 5. Numerical Analysis

To show more insights into the performance of the recycling supply chain in tire remanufacturing, this section examines the relationship between remanufacturing cost-saving, technology subsidy, remanufactured production capacity, product sales, quantity of recycled product, recycling price, carbon emission, supply chain members’ profits under four models. We make numerical analysis by investigating the impacts of three parameters including the remanufacturing technology level, technology subsidy, and remanufactured production capacity on the equilibrium solutions of the recycling supply chain. The numerical sensitivity analysis is based on the following parameter values:cr=140,cn=200,λ=0.6,d=1500,θ=1.2,β=10,δ=2,k=100,er=3,en=5. These values are obtained based on previous studies [37, 54]. The results are obtained by using the Wolfram Mathematica 12.3 as follows:


### 5.1. Effect of the Remanufacturing Technology Level

To investigate the effect of the remanufacturing technology level on the closed-loop supply chain, sensitive analysis of the reduced cost, which is a linear function of the remanufacturing technology (shown in Figure2), is thoroughly discussed. Figure 3 reveals the effect of the remanufacturing cost-saving coefficient ε on quantity of recycled tires. The effect of the remanufacturing cost-saving coefficient ε on carbon emissions and the third-party profit is shown in Figure 4. Its effect on the alliance profit and the total profit of the supply chain is shown in Figure 5.Figure 2
The linear relationship betweenε and the remanufacturing technology level.Figure 3
The effect ofϵ on quantity of recycled product (a) the effect on carbon emissions (b) the effect on profit of the recycler.Figure 4
The effect ofϵ on carbon emissions and the profit of the recycler.
(a)(b)Figure 5
The effect ofϵ on alliance profits and the total profit (a) the effect on alliance profit of the manufacturer and the retailer (b) the effect on the total profit of the supply chain.
(a)(b)The result shows that quantity of recycled tires, carbon emissions, and profits of all parties in the allied decision-making models are higher than those in the independent decision-making models. Supply chain members make decisions by maximizing their profits in the independent decision-making model, which will produce a double marginal effect and cause a loss of supply chain profit.The total profit and the carbon emission of the supply chain in the allied decision-making models are higher than in the independent decision-making models regardless of the technology subsidy. Therefore, the allied decision of the manufacturer and the retailer is superior to the independent decision because of the economic benefits, but the independent decision is superior to the allied decision because of the environmental benefits. The total profit in the allied decision is greater than in the independent decision, its reason is that all supply chain members make decisions by maximizing their profits in their independent decisions, which produces a double marginal effect and causes the loss of the supply chain profit.Improvement of remanufacturing technology, having a higher cost-saving coefficient, can reduce costs in the remanufacturing process and has a positive effect on quantity of recycled products, and profits of the supply chain, but a negative effect on carbon emissions. Therefore, the government should encourage manufacturers to improve remanufacturing technology.


### 5.2. Interactive Effect of the Remanufacturing Technology Level and Its Subsidy

To investigate the interactive effect of the remanufacturing technology level and its subsidy on the closed-loop supply chain, a two-dimensional analysis of the remanufacturing cost-saving coefficient and the technology subsidy on the recycling cost, recycling price, and recycled quantity of used tires is shown in Figure6. The sensitivity analysis on carbon emission (SD as an example) and recycler profit are shown in Figure 7. The sensitivity analysis of the profit of the alliance (SD as an example) and the total profit of the supply chain (SD as an example) is shown in Figure 8.Figure 6
The effect ofγ and ϵ on product prices and quantity of recycled tires (a) the effect of γ and ϵ on the recycling cost and the recycling price (b) the effect of γ and ϵ on quantity of recycled tires.
(a)(b)Figure 7
The effect ofγ and ϵ on carbon emissions and third-party profit (a) the effect on carbon emissions (SD as an example) (b) the effect on the third-party profit.
(a)(b)Figure 8
The effect ofγ and ϵ on alliance profits and total profit (a) the impact on alliance profits (b) the impact on the total profit of the supply chain (SD as an example).
(a)(b)The interactive effects of the remanufacturing technology level and its subsidy reveal that the technology subsidy which the government provides to the manufacturer can improve the recycling of old tires, which is conducive to improving the remanufacturing technology level. Along with the increase of the technology subsidy and the remanufacturing cost-saving coefficient, the remanufacturing cost and the carbon emission in the production process are reduced. The increase in recycling price stimulates more consumers to involve in the recycling of used tires, which ultimately promotes the overall profit of the supply chain. However, the wholesale price, retail price, and market demand for tires do not change along with changes in the technology subsidies.Therefore, government subsidy for remanufacturing technology has a greater effect on a closed-loop supply chain than a forward one, which can improve the recycling quantity, reduce carbon emissions, and improve the profits of all parties in the supply chain.When compared with previous models, a technology subsidy for remanufacturing tires can improve the remanufacturing technology level, quantity of recycled tires, and profits of all parties in the supply chain, and it can reduce carbon emissions. The recycling cost, recycling price, remanufacturing technology level, recycling quantity, and profits of all members in the supply chain with a technology subsidy are greater than without a technology subsidy.Another result is that the carbon tax can increase quantity of recycled tires and reduce carbon emissions, but it will reduce the market demand and the profits of the manufacturer and the retailer. A remanufacturing technology subsidy will compensate for the loss of profits of the manufacturer and retailer caused by the carbon tax. The carbon emission with a technology subsidy is lower than without a technology subsidy. This shows that the government’s technology subsidy can reduce the remanufacturing cost and carbon emissions, promote the recycling of used tires, and increase the profits of the supply chain members.This result suggests the government should balance the remanufacturing technology subsidy and the carbon tax to reach an overall optimization of the closed-loop supply chain.


### 5.3. Effect of the Remanufacturing Production Capacity

The product wholesale pricew and the product retail price p change along with the production capacity λ of remanufactured tires in various decision-making models, shown in Figure 9. The result reveals that the optimal wholesale price increases along with the production capacity, but it begins to decrease when the production capacity reaches a certain value (λ = 0.4), and the optimal retail price of tires increases slightly along with the production capacity in all four models. Retail prices are higher in both independent decision-making models than in both allied decision-making models, which indicates that an alliance of manufacturers and retailers can reduce the price of the product in any production capacity.Figure 9
The effect ofλ on w and p.The trend in profitπ of both manufacturers and retailers in the four models that changes along with the production capacity λ of remanufactured tires is shown in Figure 10.Figure 10
The effect ofλ on π.The results reveal that their profits increase slightly at the beginning and decrease after the production capacity is more than a certain value (λ = 0.4) in the SA and DA models. This result verifies that the carbon tax and the technology subsidy can benefit the manufacturer, but the disadvantage of the production capacity constraint has a lag effect. On the other hand, their profits take a downturn in the DD and SD models, which means that a higher production capacity of the remanufacturing tires is a disadvantage to the manufacturer, and then, the manufacturer should explore new remanufacturing technology to reduce its production of remanufactured tires.A trend of carbon emissions in four models changing along with the production capacityλ of remanufactured tires is shown in Figure 11. The carbon emissions in the SA and DA models are negatively correlated to the production capacity of remanufactured tires, but the carbon emissions in the DD and SD models are not correlated to the production capacity. This confirms that the manufacturer will improve its technology level in remanufacturing tires, reduce carbon emissions, and reduce the remanufacturing cost when the government imposes a higher carbon tax and the manufacturer’s production capacity is restrained. A decreased cost in remanufacturing tires will help the manufacturer raise the purchase price of old tires, and then it stimulates the third-party recycler to raise the recycling price of old tires and the recycling quantity, which will improve the profit of the third-party recycler.Figure 11
The impact ofλ on carbon emissions.There is a managerial insight for the government: when the government imposes a carbon tax on the manufacturer, it can effectively reduce carbon emissions. When the production capacity of remanufactured tires is restricted, the manufacturer will improve its level of remanufactured technology to reduce the cost of remanufacturing, and it will improve the recycling quantity and price of old tires, where the profit of the third-party recycler can be increased, but the retail price will increase, and the profits of both manufacturers and retailers will decrease since it reduces market demand.


## 5.1. Effect of the Remanufacturing Technology Level

To investigate the effect of the remanufacturing technology level on the closed-loop supply chain, sensitive analysis of the reduced cost, which is a linear function of the remanufacturing technology (shown in Figure2), is thoroughly discussed. Figure 3 reveals the effect of the remanufacturing cost-saving coefficient ε on quantity of recycled tires. The effect of the remanufacturing cost-saving coefficient ε on carbon emissions and the third-party profit is shown in Figure 4. Its effect on the alliance profit and the total profit of the supply chain is shown in Figure 5.Figure 2
The linear relationship betweenε and the remanufacturing technology level.Figure 3
The effect ofϵ on quantity of recycled product (a) the effect on carbon emissions (b) the effect on profit of the recycler.Figure 4
The effect ofϵ on carbon emissions and the profit of the recycler.
(a)(b)Figure 5
The effect ofϵ on alliance profits and the total profit (a) the effect on alliance profit of the manufacturer and the retailer (b) the effect on the total profit of the supply chain.
(a)(b)The result shows that quantity of recycled tires, carbon emissions, and profits of all parties in the allied decision-making models are higher than those in the independent decision-making models. Supply chain members make decisions by maximizing their profits in the independent decision-making model, which will produce a double marginal effect and cause a loss of supply chain profit.The total profit and the carbon emission of the supply chain in the allied decision-making models are higher than in the independent decision-making models regardless of the technology subsidy. Therefore, the allied decision of the manufacturer and the retailer is superior to the independent decision because of the economic benefits, but the independent decision is superior to the allied decision because of the environmental benefits. The total profit in the allied decision is greater than in the independent decision, its reason is that all supply chain members make decisions by maximizing their profits in their independent decisions, which produces a double marginal effect and causes the loss of the supply chain profit.Improvement of remanufacturing technology, having a higher cost-saving coefficient, can reduce costs in the remanufacturing process and has a positive effect on quantity of recycled products, and profits of the supply chain, but a negative effect on carbon emissions. Therefore, the government should encourage manufacturers to improve remanufacturing technology.


## 5.2. Interactive Effect of the Remanufacturing Technology Level and Its Subsidy

To investigate the interactive effect of the remanufacturing technology level and its subsidy on the closed-loop supply chain, a two-dimensional analysis of the remanufacturing cost-saving coefficient and the technology subsidy on the recycling cost, recycling price, and recycled quantity of used tires is shown in Figure6. The sensitivity analysis on carbon emission (SD as an example) and recycler profit are shown in Figure 7. The sensitivity analysis of the profit of the alliance (SD as an example) and the total profit of the supply chain (SD as an example) is shown in Figure 8.Figure 6
The effect ofγ and ϵ on product prices and quantity of recycled tires (a) the effect of γ and ϵ on the recycling cost and the recycling price (b) the effect of γ and ϵ on quantity of recycled tires.
(a)(b)Figure 7
The effect ofγ and ϵ on carbon emissions and third-party profit (a) the effect on carbon emissions (SD as an example) (b) the effect on the third-party profit.
(a)(b)Figure 8
The effect ofγ and ϵ on alliance profits and total profit (a) the impact on alliance profits (b) the impact on the total profit of the supply chain (SD as an example).
(a)(b)The interactive effects of the remanufacturing technology level and its subsidy reveal that the technology subsidy which the government provides to the manufacturer can improve the recycling of old tires, which is conducive to improving the remanufacturing technology level. Along with the increase of the technology subsidy and the remanufacturing cost-saving coefficient, the remanufacturing cost and the carbon emission in the production process are reduced. The increase in recycling price stimulates more consumers to involve in the recycling of used tires, which ultimately promotes the overall profit of the supply chain. However, the wholesale price, retail price, and market demand for tires do not change along with changes in the technology subsidies.Therefore, government subsidy for remanufacturing technology has a greater effect on a closed-loop supply chain than a forward one, which can improve the recycling quantity, reduce carbon emissions, and improve the profits of all parties in the supply chain.When compared with previous models, a technology subsidy for remanufacturing tires can improve the remanufacturing technology level, quantity of recycled tires, and profits of all parties in the supply chain, and it can reduce carbon emissions. The recycling cost, recycling price, remanufacturing technology level, recycling quantity, and profits of all members in the supply chain with a technology subsidy are greater than without a technology subsidy.Another result is that the carbon tax can increase quantity of recycled tires and reduce carbon emissions, but it will reduce the market demand and the profits of the manufacturer and the retailer. A remanufacturing technology subsidy will compensate for the loss of profits of the manufacturer and retailer caused by the carbon tax. The carbon emission with a technology subsidy is lower than without a technology subsidy. This shows that the government’s technology subsidy can reduce the remanufacturing cost and carbon emissions, promote the recycling of used tires, and increase the profits of the supply chain members.This result suggests the government should balance the remanufacturing technology subsidy and the carbon tax to reach an overall optimization of the closed-loop supply chain.


## 5.3. Effect of the Remanufacturing Production Capacity

The product wholesale pricew and the product retail price p change along with the production capacity λ of remanufactured tires in various decision-making models, shown in Figure 9. The result reveals that the optimal wholesale price increases along with the production capacity, but it begins to decrease when the production capacity reaches a certain value (λ = 0.4), and the optimal retail price of tires increases slightly along with the production capacity in all four models. Retail prices are higher in both independent decision-making models than in both allied decision-making models, which indicates that an alliance of manufacturers and retailers can reduce the price of the product in any production capacity.Figure 9
The effect ofλ on w and p.The trend in profitπ of both manufacturers and retailers in the four models that changes along with the production capacity λ of remanufactured tires is shown in Figure 10.Figure 10
The effect ofλ on π.The results reveal that their profits increase slightly at the beginning and decrease after the production capacity is more than a certain value (λ = 0.4) in the SA and DA models. This result verifies that the carbon tax and the technology subsidy can benefit the manufacturer, but the disadvantage of the production capacity constraint has a lag effect. On the other hand, their profits take a downturn in the DD and SD models, which means that a higher production capacity of the remanufacturing tires is a disadvantage to the manufacturer, and then, the manufacturer should explore new remanufacturing technology to reduce its production of remanufactured tires.A trend of carbon emissions in four models changing along with the production capacityλ of remanufactured tires is shown in Figure 11. The carbon emissions in the SA and DA models are negatively correlated to the production capacity of remanufactured tires, but the carbon emissions in the DD and SD models are not correlated to the production capacity. This confirms that the manufacturer will improve its technology level in remanufacturing tires, reduce carbon emissions, and reduce the remanufacturing cost when the government imposes a higher carbon tax and the manufacturer’s production capacity is restrained. A decreased cost in remanufacturing tires will help the manufacturer raise the purchase price of old tires, and then it stimulates the third-party recycler to raise the recycling price of old tires and the recycling quantity, which will improve the profit of the third-party recycler.Figure 11
The impact ofλ on carbon emissions.There is a managerial insight for the government: when the government imposes a carbon tax on the manufacturer, it can effectively reduce carbon emissions. When the production capacity of remanufactured tires is restricted, the manufacturer will improve its level of remanufactured technology to reduce the cost of remanufacturing, and it will improve the recycling quantity and price of old tires, where the profit of the third-party recycler can be increased, but the retail price will increase, and the profits of both manufacturers and retailers will decrease since it reduces market demand.


## 6. Conclusions

Considering the carbon tax imposed by the government, this paper studied the closed-loop supply chain decision problems with or without remanufacturing technology subsidies. Two independent decision-making models and two alliance decision-making models of the tire manufacturer and the retailer were developed while the manufacturer’s production capacity of remanufacturing tires was constrained and several market preference factors were also considered. Finally, the optimal equilibrium strategies of the supply chain members were investigated. Several results are recommended as follows.Firstly, the carbon tax imposed on the tire manufacturer can effectively reduce carbon emissions in the production process and promote the manufacturer to improve his technology. This policy can reduce the remanufacturing cost, increase the recycling quantity, and the profit of the third-party recycler, but reduce the profits of the manufacturer and the retailer.Secondly, the performance of the supply chain is better with a technology subsidy of remanufacturing than without it. Therefore, the government must increase technical incentives if we hope to reach the overall optimization of the supply chain.Thirdly, supply chain members make decisions by the maximization of their profits in the independent decision-making models, where they produce a double marginal effect and cause a loss of supply chain profit. After reviewing the economic benefits, the allied decision-making models in the supply chain are superior to the independent decision-making models. However, the independent decision-making models are superior to the allied ones in terms of environmental benefits.Fourthly, the production capacity coefficient of remanufactured tires has an impact on the optimal pricing and profits of manufacturers and retailers. In the case of limited production capacity, government subsidies have a great impact on the production and sales of products, and the profits of manufacturers and retailers will be reduced. To maintain a healthy market, the government’s subsidies should not be too high.The research work of this paper has certain limitations. Future studies can focus on multiple manufacturers, various pricing strategies, or third-party remanufacturing.



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*Source: 2484775-2022-08-28.xml*