Blockchain-Enabled Closed-Loop Supply Chain Optimization for Power Battery Recycling and Cascading Utilization

Abstract

This article investigates decision-making strategies for power battery recycling and cascading utilization within the context of rapidly advancing blockchain technology, aiming to enhance the sustainability and efficiency of energy storage systems. A closed-loop recycling supply chain model is proposed, integrating key stakeholders such as power battery manufacturers, OEM (original equipment manufacturer) vehicle manufacturers, third-party recyclers, tiered users, and consumers. The study focuses on critical factors including competition among recycling channels, the level of blockchain-enabled traceability, and the cascading utilization rate of retired batteries. By analyzing four hybrid recycling modes, the research identifies optimal recycling strategies and evaluates their economic and environmental impacts. The findings provide a theoretical foundation and practical insights for improving the sustainability of power battery recycling, contributing to the development of cleaner and more efficient energy systems.

1. Introduction

In recent years, global climate conditions have continued to deteriorate, with changes caused by the greenhouse effect impacting human survival and development. To address this urgent issue, countries around the world have actively responded and worked together to achieve their goals of reaching “carbon peak” and “carbon neutrality”. Nations have developed multiple strategies to support these objectives, including resource recycling strategies and energy security strategies. Additionally, the international resource supply chain is influenced by various factors, leading to significant uncertainty. Many countries, particularly those with high levels of industrialization, have a substantial dependence on external resources. For instance, oil, a critical energy resource, is heavily reliant on imports for numerous nations. Therefore, implementing resource recycling strategies and energy substitution strategies is especially crucial on a global scale at this time. These measures not only help mitigate the impacts of climate change but also enhance energy security and reduce vulnerability to international supply chain disruptions.

As an important component of new energy vehicles, power batteries have strict regulations on their management and use. When the power battery level decays to 70–80%, it cannot continue to be used in new energy vehicles. With the widespread adoption of new energy vehicles globally, most countries in the world entered a large-scale retirement period for power batteries. Effectively tracking and recycling power batteries has become an urgent problem to be solved.

When dealing with these challenges, cooperative recycling based on alliances has emerged as a strategic method. It engages multiple stakeholders, including power battery manufacturers, OEM vehicle manufacturers, third-party recyclers, consumers, and secondary users. These stakeholders collaborate to enhance recycling efficiency and optimize resource allocation.

Table 1. Four typical cooperative recycling models.

Type	Case	Battery Recyclers
MOR	CATL collaborate with Xiaomi and BAIC to complete the recycling project	Power Battery Manufacturers OEM Vehicle Manufacturers
MTR	GEM cooperate with LGC/CATL/Samsung to promote battery recycling [1]	Power Battery Manufacturers Third-party recyclers
OTR	BYD partnered with Shenzhen Pandpower Co., Ltd., to develop battery recycling	OEM Vehicle Manufacturers Third-party recyclers
MOTR	Mercedes-Benz signed a contract with CATL and GEM to start a recycling project [2]	Power Battery Manufacturers OEM Vehicle Manufacturers Third-party recyclers

presents four typical cooperative recycling models, along with relevant examples. This article presents four recycling models, all of which involve multi-party joint recycling.

(1)

MOR Model: This model represents a hybrid recycling collaboration between power battery manufacturers and original equipment manufacturer (OEM) vehicle manufacturers.

(2)

MTR Model: This model involves a hybrid recycling approach between power battery manufacturers and third-party recyclers.

(3)

OTR Model: In this model, the collaboration is between OEM vehicle manufacturers and third-party recyclers.

(4)

MOTR Model: This model encompasses a hybrid recycling approach among power battery manufacturers, OEM vehicle manufacturers, and third-party recyclers.

According to the literature of Majumder and Groenevelt [3], each participant has a competitive relationship. In this context, the competition coefficient is introduced to analyze the relationships between the variables.

Currently, the recycling of power batteries utilizes tools and big data, with blockchain gradually gaining public attention. Blockchain has the advantages of decentralization, immutability, and security and is widely used in the finance, fresh food, and pharmaceutical industries. It can effectively track and record products and then achieve product traceability. When applied to the field of power battery recycling, it can achieve convenient tracking, effectively record the usage of power batteries, and save costs for subsequent cascading utilization stages. The government has issued relevant document, which clearly states that in the field of key components, blockchain should be used to establish a product traceability system covering multiple parties and achieve full lifecycle tracking. BMW, a German company, improves the visibility of raw materials and components through blockchain technology; a Sweden company, Volvo, uses blockchain technology to track cobalt materials for power batteries. Meanwhile, blockchain technology also faces numerous challenges in the field of battery recycling. On the one hand, integrating blockchain with existing supply chain management systems and IoT devices can be technically challenging. On the other hand, ensuring the privacy and security of sensitive data (e.g., battery performance and manufacturer details) while maintaining transparency is a complex task. At the same time, many companies are adopting a wait-and-see attitude toward blockchain technology, and the application of blockchain in the field of power battery recycling is worth exploring.

The structure of the article is organized as follows: Section 2 presents a literature review that identifies the innovative aspects of this article. Section 3 focuses on model construction and the assumptions underlying the models. Section 4 addresses four recycling models. Section 5 conducts a simulation analysis to determine the optimal recycling selection across different recycling modes. This analysis examines the relationship between the hierarchical recycling utilization rate and various variables, as well as the relationship between the competition coefficient and other factors. Section 6 summarizes the main conclusions of the article and offers relevant management insights.

2. Literature Review

This study pertains to four areas of literature: (1) battery recycling; (2) blockchain application in the supply chain; (3) recycling channels; (4) supply chain member relationships.

2.1. Battery Recycling

The recycling of power batteries mainly includes two aspects of research content. On the one hand, it is the exploration of recycling methods and material aspects. Currently, the methods of battery recycling mainly contain hydrometallurgy, pyrometallurgy, and direct recycling; Dobó et al. [4] analyze the development in recycling methods. In the process of recycling, there are many procedures that could be optimized. Wang et al. [5] comprehensively review the current situation and technical challenges of recycling lithium iron phosphate (LFP) batteries. Then, Rettenmeier et al. [6] pick a stage of disassembly and complete research for the benefits and development. Because batteries are used in different scenarios, it means that there are a wide variety of types. Sathya et al. [7] study polymeric binders (PAA, CMC, and their blends) for SiOx-Si-C electrodes. The electrode with 100% PAA binder shows the best performance in terms of discharge capacity, which is ascribed to strong hydrogen-bonding. Versaci et al. [8] detail the development of a lithium nickel manganese oxide (LNMO)/lithium iron phosphate (LFP) blended cathode for high-performance LIBs and investigate the impact of blending on morphological and electrochemical aspects. Fagiolari et al. [9] focus on potassium-based batteries and emphasize the importance of defining electrodes and electrolytes with reproducible performance.

On the other hand, in order to protect the environment, many scholars have conducted research on environment sustainability. Yi et al. [10] propose the topic of hydrogen to solve the energy shortage, that is, the idea of alternative development. Additionally, in order to ensure the maximization use of power battery, utilization is a hot topic in this area. As there is growing attention into power batteries and environment protection, the government has adopted a series of measures to ensure the smooth progress of the power battery echelon utilization process: for example, government funding and deposits [11], government subsidies [12], carbon cap-trade and reward-penalty policies [13]. In addition to the efforts made by the government, researchers are also conducting studies on other aspects related to this topic. Xiao et al. [14] discuss various possible application methods of echelon utilization, including hierarchical analysis methods based on various battery evaluation indexes. Wang et al. [15] examine the current challenges of the cascade utilization of retired power LIBs and prospectively point out their broad prospects. Casals et al. [16] economically and in terms of aging performance analyze the possibility of giving a second life to these batteries in buildings. The existing European markets allowing aggregated demand—response services are also analyzed. At the same time, Catton et al. [17] discuss the situation in Canada. Chen et al. [18] emphasize the need for the proper handling of end-of-life (EOL) vehicle LIBs, considering factors like fluctuating material costs. Harper et al. [19] summarize and assess the current approaches to the recycling and reuse of electric-vehicle lithium-ion batteries and identify areas for future development. Yu et al. [20] present a specific analysis process to discuss how to select appropriate battery types and capacity margins.

The studies discussed above emphasize enhancing the efficiency of power battery recycling through two main approaches: First, they explore new recycling methods, materials, and technological innovations to improve recycling processes. Second, they focus on recycling and reuse, introducing the concept of hierarchical utilization to maximize the efficiency of power battery usage. These insights offer valuable theoretical support for a comprehensive understanding of the processes and model development related to power battery recycling. Additionally, this article incorporates a hierarchical user into the model, making it more reflective of real-world recycling scenarios.

2.2. Blockchain Application in Supply Chain

Blockchain offers significant advantages in data processing and has been widely applied across various fields. Morkunas et al. [21] and Mulligan et al. [22] explain relevant terms and outline different types of blockchain technologies, providing illustrations for blockchain development. The former focuses on concepts, while the latter emphasizes policy interpretation. Belchior et al. [23] explore “interoperability”, one of the important features of blockchain, and then clarify the future direction. By integrating blockchain with supply chains, a wider array of application scenarios can be explored. Park and Li [24] center on supply chain management and its sustainability performances based on blockchain in environmental protection, social equity, and governance efficiency. Then, they assess whether the three sustainability indicators can be indirectly improved in blockchain—based supply chains. Luo et al. [25] provide an item of blockchain consensus mechanisms that is important to all parties of supply chain. In the field of battery recycling, Xiao et al. [26] construct a CLSC composed of a power-battery supplier, a new-energy vehicle manufacturer, and a third-party recycler to study the optimal collaborative recycling mode considering blockchain and recycling competition. Zhang et al. [27] propose a blockchain-based power batteries reverse supply chain management integration framework, whereby the double-chain structure and its storage mechanism, the information tracing module, and the smart-contract-enabled battery trading management are studied. Florea and Taralunga [28] present two blockchain implementations for an EV BMS, using blockchain as the network and data layer of the application. Gao et al. [29] revolves around how lithium-ion battery (LIB)-related companies can utilize blockchain technology to record battery health status data, thereby achieving environmentally friendly and economically viable recycling of decommissioned batteries. Shen et al. [30] explore how blockchain-based battery tracking technology can address issues such as information asymmetry, counterfeit battery risks, and technical barriers in battery condition assessments. Li et al. [31] analyze the willingness to take blockchain under three scenarios.

In the field of agriculture, Wassenaer et al. [32] aim to solve this problem by providing an overview of the choices at three layers of a blockchain application: the ledger, the governance structure, and the ecosystem. This can serve as a reference framework for understanding different blockchain applications and choosing key parameters for new use cases in the agrifood sector. Rogerson and Parry [33] explore “blockchain can improve supply chain visibility”, while Pun et al. [34] show how to defeat counterfeit goods.

In the field of healthcare, Agbo et al. [35] and Ghosh et al. [36] present systematic reviews of the ongoing research on the application of blockchain technology in healthcare. Tanwar et al. [37] explore several solutions to improve the current limitations of healthcare systems using blockchain technology, including frameworks and tools for measuring the performance of such systems, and then propose an Access Control Policy Algorithm to improve data accessibility among healthcare providers. Yaqoob et al. [38] explore how applying blockchain to healthcare data management systems can stimulate innovation and bring significant improvements and then expound on the key features of blockchain and discuss its main advantages and the opportunities it offers to the healthcare industry.

In addition to the application areas mentioned above, other fields are also actively exploring the use cases of blockchain in the context of digitalization.

2.3. Recycling Supply Chain

The recycling supply chain refers to the network structure formed around a series of processes, including raw material procurement, manufacturing, sales and distribution, and final recycling. It involves numerous interrelated enterprises and organizations.

Tan et al. [39] aim to maximize customer satisfaction and minimize the total cost of logistics and distribution, exploring how the resources and operational status of established urban recycling and dismantling centers affect the power-battery reverse supply chain. Li et al. [40] develop a three-party evolutionary game model involving “new energy vehicle manufacturers, power battery manufacturers, and power battery recyclers”. It simulates the dynamic evolution process of each player’s strategy and analyzes the impacts of the digital transformation factor and other factors on the evolutionary trend. Gong et al. [41] examine a dual-channel reverse supply chain composed of formal and informal electric vehicle battery recyclers under government intervention with subsidy and penalty policies. Wu et al. [42] establish two recycling modes to analyze the impaction of environment performance and overall profits. Tang et al. [43] consider entrusted recycling and direct recycling and then compare the results. Wu et al. [44] construct three recycling modes: single, mixed, and alliance modes. Wang et al. analyze the difficulty of the current recycling modes and then propose direct recycling method to promote the efficiency.

2.4. The Interrelationships Among Members in Supply Chain

In the supply chain, members have different relationships, such as cooperation: they make an alliance mode through member combinations. In order to ensure the smooth flow of power batteries at all stages, members play a crucial supporting role in the development. On the other hand, moderate competition frequently emerges within supply chains to maintain their vitality and continuously drive industry advancement. Zhao and Ma [45] construct a three-party game supply chain model involving one battery manufacturer, one car manufacturer, and one third-party recycler. Feng et al. [46] delve into the interaction between supplier development and supplier integration within competing electric vehicle (EV) supply chains that involve power battery recycling. Shao et al. [47] explore different cooperation modes under carbon cap and trade policy. Huang and Ni [48] explore four cooperation recycling modes between online platform and retailer. Yu et al. [49] construct non-cooperation and incomplete and complete cooperation by applying Stackelberg theories. Liu et al. [50] research recycling investment competition between OEMs and retailers.

2.5. Related Work Review and Analysis

Summarize the literature and obtain the distinctions between existing studies and our research, see

Table 2. Distinctions between existing studies and our research.

References	Power Battery Recycle	Utilization	Blockchain Applications	Recycling Channel Analysis	Member Relationships
[4,5,6,7,8,9]	√	×	×	×	×
[10,11,12,13,14,15,16,17,18,19,20]	√	√	×	×	×
[21,22,23,24,25] [32,33,34,35,36,37,38]	×	×	√	×	×
[26,27,28,29,30,31]	√	×	√	×	×
[39,40,41,42,43,44]	√	×	×	√	×
[45,46,47,48,49,50]	√	×	×	√	√
Our research	√	√	√	√	√

for detail.

3. Methods

3.1. Model Descriptions

The core participants in the closed-loop supply chain of power batteries include power battery manufacturers, OEM vehicle manufacturers, third-party recyclers, consumers, and secondary users. In the forward supply chain, power battery manufacturers are responsible for purchasing raw materials for the production of various models of power batteries, with a production cost of C₀. After the production process is completed, they are sold to OEM vehicle manufacturers at wholesale prices and then sold to consumers at retail prices after completing the assembly process of power batteries. In the reverse supply chain, consider recycling waste power batteries through cascading and regenerative methods, as shown in Figure 1.

In the context of blockchain technology, the closed-loop supply chain hybrid recycling model for power batteries is divided into four categories, shown as Figure 2: (1) MOR Model; (2) MTR Model; (3) OTR Model; (4) MOTR Model.

This study considers various factors, such as consumer sensitivity to retail prices of power batteries, recycling prices, levels of blockchain traceability, and the competition coefficients among the participants. It explores the different recycling models involving core participants in the supply chain, makes recycling decisions, and provides the necessary theoretical support.

3.2. Model Assumptions

The relevant symbols and constants involved in the model are shown in

Table 3. Definition of parameters of the game.

Parameter	Description
C0	The cost of producing power batteries for power battery manufacturers
w	Wholesale price of power batteries
D	Demand for power batteries in the market
a	Potential demand for power batteries in the market
α	Consumer sensitivity to retail prices of power batteries
β	Consumer sensitivity to the price of retired battery recycling
δ	Cost coefficient of blockchain investment
φ	Cost coefficient of battery recycling
ε	Consumer sensitivity to the traceability level of power batteries
p	Retail price of power battery
pm	Retired power battery recycling price (power battery manufacturer → consumer)
pv	Retired power battery recycling price (OEM vehicle manufacturer → consumer)
pt	Retired power battery recycling price (third-party recyclers → consumers)
pn	Retired power battery recycling price (power battery manufacturer → OEM vehicle manufacturer/third-party recycler)
Ca	Retired power battery costs (including but not limited to dismantling, evaluation, and transportation expenses)
Cb	Cost of blockchain investment
e θ R	Level of investment in blockchain The proportion of retired batteries that can be recycled and reused (the hierarchical utilization ratio) Profit per unit of power battery cascading utilization
M	Consumers voluntarily return the quantity of power batteries
F	Total revenue from dismantling and recycling power batteries
${\pi }_{\mathrm{j}}^{\mathrm{i}}$	Profit function of i under mode j
h	Competition coefficient among members in the process of recycling waste batteries

.

3.3. Basic Assumption

The decision-making of all participants in the closed-loop supply chain of power batteries is influenced by multiple factors. To fully explore the research problem, combining relevant theories and existing research to make the following assumptions, we propose the following:

(1)

The members of the closed-loop supply chain for power batteries are all completely rational, and, in the decision-making process, there is a sequence of actions between power battery manufacturers and OEM vehicle manufacturers. In the case of incomplete information symmetry, the power battery manufacturer is the leader, and the OEM vehicle manufacturer is the follower, determining their own behavior based on the leader’s behavior.

(2)

Referring to relevant research, the demand function for power batteries is set to $D=\mathrm{a}-\alpha \mathrm{p}+\epsilon \mathrm{e}$, and the amount of retired batteries recovered is $Q_{\mathrm{j}}=\beta p_d-h{p}_d$ (d, optional m, v, t, and n). When using blockchain, it indicates that consumers are sensitive to traceability levels; when blockchain is not used, it indicates that consumers have zero sensitivity to traceability levels.

(3)

To optimize the recycling process of the power battery supply chain, power battery manufacturers adopt blockchain technology for management, with an investment cost of $C_{\mathrm{b}}={\displaystyle \frac{1}{2}}\delta {\mathrm{e}}^2$.

(4)

OEM vehicle manufacturers sell power batteries at retail price p, which only considers the retail price of the power battery and does not include other additional products, related spare parts costs, and labor costs.

(5)

For the hierarchical utilization process, this article adheres to the principle that if the battery capacity is below 80% and cannot be used for new energy vehicles, it will be recycled and used for other scenarios, with a single profit of R; for power batteries that cannot be reused, the batteries are tested and reassembled, and usable raw materials are extracted for regeneration and recycling. As the amount of regeneration and recycling cannot be determined, the total profit is set as F. Since the recycling of batteries is relatively small for OEM vehicle manufacturers and third-party recyclers, and the selling price is low, assuming it is ignored, transportation costs and other expenses are borne by the power battery manufacturer.

(6)

With the development of new energy vehicles, the types of batteries are becoming more diverse. To ensure research rigor, it is set that all power batteries are of the same model and capacity.

(7)

Using blockchain technology, the proportion of retired batteries that can be used for cascading utilization will be quickly identified through information technology.

(8)

In reality, it is rare to purchase power batteries separately. To ensure the reliability of the research, it is set that power batteries have independent wholesale prices, retail prices, and recycling prices, which can be independently accounted for.

3.4. Methodology

The application of blockchain technology to the power battery recycling supply chain primarily involves installing components such as sensors in power batteries to measure battery performance and capacity in real time, and uploading these data to the blockchain. Due to the immutable nature of blockchain, it enables the transmission and prediction of information. When a power battery is nearing its recycling threshold, consumers can receive notifications; when members of the supply chain engage in the recycling of power batteries, they can access real-time information about the battery by scanning a QR code or logging into a shared platform, thereby achieving the goals of reducing disassembly costs and enhancing recycling efficiency.

During the model computation, each participant in the supply chain seeks to maximize their own profits, and the solution is derived according to the sequence of the game. Firstly, it employs the Hessian matrix to ascertain the existence of an optimal solution for the function. Subsequently, partial derivatives of the variables are solved, and by setting them equal to zero, the optimal solution for the variables can be obtained.

4. Results

This chapter will explore the scenarios under four different recycling models, respectively, providing a foundation for the subsequent discussion.

4.1. Hybrid Recycling Mode (MOR Mode) Between Power Battery Manufacturers and OEM Vehicle Manufacturers

When the capacity of the power battery decays to a certain extent, it needs to be recycled. In this recycling mode, power battery manufacturers and OEM vehicle manufacturers provide different recycling prices for power battery recycling. Finally, the OEM hands over the recycled battery to the power battery manufacturer for hierarchical utilization and regeneration, resulting in the following:

The profit function of power battery manufacturers is

$$\begin{array}{l}{\pi }_{\mathrm{M}}^{\mathrm{MOR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{MOR}}+\epsilon {\mathrm{e}}_{\mathrm{MOR}})(w_{\mathrm{MOR}}-C_0)-p_{\mathrm{m}}^{\mathrm{MOR}}(\beta p_{\mathrm{m}}^{\mathrm{MOR}}-h{p}_{\mathrm{v}}^{\mathrm{MOR}})-p_{\mathrm{n}}^{\mathrm{MOR}}(\beta p_{\mathrm{v}}^{\mathrm{MOR}}-h{p}_{\mathrm{m}}^{\mathrm{MOR}})\\ +\theta R(\beta p_{\mathrm{m}}^{\mathrm{MOR}}-h{p}_{\mathrm{v}}^{\mathrm{MOR}}+\beta p_{\mathrm{v}}^{\mathrm{MOR}}-h{p}_{\mathrm{m}}^{\mathrm{MOR}})++F-{\displaystyle \frac{1}{2}}\delta {e_{\mathrm{MOR}}}^2\end{array}$$

(1)

The profit function of OEM vehicle manufacturers is

$${\pi }_{\mathrm{O}}^{MOR}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{MOR}}+\epsilon {\mathrm{e}}_{\mathrm{MOR}})(p_{\mathrm{MOR}}-w_{\mathrm{MOR}})-p_{\mathrm{v}}^{\mathrm{MOR}}(\beta p_{\mathrm{v}}^{\mathrm{MOR}}-h{p}_{\mathrm{m}}^{\mathrm{MOR}})+p_{\mathrm{n}}^{\mathrm{MOR}}(\beta p_{\mathrm{v}}^{\mathrm{MOR}}-h{p}_{\mathrm{m}}^{\mathrm{MOR}})$$

(2)

Theorem 1.

In the mixed-recycling mode between power battery manufacturers and OEM vehicle manufacturers, the optimal pricing strategy for power battery manufacturers and OEM vehicle manufacturers is

$$w_{\mathrm{MOR}}={\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$$

(3)

$$p_{\mathrm{MOR}}={\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$$

(4)

$$e_{\mathrm{MOR}}={\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$$

(5)

$$p_{\mathrm{m}}^{\mathrm{MOR}}={\displaystyle \frac{\beta \theta R}{2(h+\beta )}}$$

(6)

$$p_{\mathrm{n}}^{\mathrm{MOR}}={\displaystyle \frac{\theta Rh}{2(h+\beta )}}$$

(7)

$$p_{\mathrm{v}}^{\mathrm{MOR}}={\displaystyle \frac{\beta \theta h}{2(h+\beta )}}$$

(8)

Substitute $w_{MOR}$, $p_{MOR}$, $p_{\mathrm{m}}^{MOR}$, $e_{MOR}$, $p_{\mathrm{n}}^{MOR}$, and $p_{\mathrm{v}}^{MOR}$ into Formulas (1) and (2).

That is to say,

$${\pi }_M^{MOR}=F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}-{\displaystyle \frac{{\beta }^{2}R{\theta }^2(-h+\beta R+\beta -R)}{4{(h+\beta )}^2}}+{\displaystyle \frac{\beta {\theta }^2(h+R)(\beta -\mathrm{h})}{2(h+\beta )}}$$

(9)

$${\pi }_O^{MOR}={\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}+{\displaystyle \frac{\beta {\theta }^2{h}^2(2\beta R-R^2-{\beta }^2)}{4{(\beta +h)}^2}}$$

(10)

Theorem 1 can be proven.

4.2. Hybrid Recycling Mode Between Power Battery Manufacturers and Third-Party Recyclers (MTR Mode)

When the capacity of the power battery decays to a certain extent, it needs to be recycled. In this recycling mode, power battery manufacturers and third-party recyclers provide different recycling prices for power battery recycling. All recycled power batteries are handed over to the secondary utilization provider, and the rest are handed over to the power battery manufacturer for secondary utilization and regeneration. From this, the following is proposed:

The profit function of power battery manufacturers is

$$\begin{array}{l}{\pi }_{\mathrm{M}}^{\mathrm{MTR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{MTR}}+\epsilon {\mathrm{e}}_{\mathrm{MTR}})(w_{\mathrm{MTR}}-C_0)-p_{\mathrm{m}}^{\mathrm{MTR}}(\beta p_{\mathrm{m}}^{\mathrm{MTR}}-h{p}_{\mathrm{t}}^{\mathrm{MTR}})-p_{\mathrm{n}}^{\mathrm{MTR}}(\beta p_{\mathrm{t}}^{\mathrm{MTR}}-h{p}_{\mathrm{m}}^{\mathrm{MTR}})\\ +{\theta }_{\mathrm{b}}R(\beta p_{\mathrm{m}}^{\mathrm{MTR}}-h{p}_{\mathrm{t}}^{\mathrm{MTR}}+\beta p_{\mathrm{t}}^{\mathrm{MTR}}-h{p}_{\mathrm{m}}^{\mathrm{MTR}})+F-{\displaystyle \frac{1}{2}}\delta {e_{\mathrm{MTR}}}^2\end{array}$$

(11)

The profit function of OEM vehicle manufacturers is

$${\pi }_{\mathrm{O}}^{MTR}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{MTR}+\epsilon {\mathrm{e}}_{MTR})(p_{MTR}-w_{MTR})$$

(12)

The profit function of third-party recyclers is

$${\pi }_{\mathrm{T}}^{MTR}=-p_t^{MTR}(\beta p_{\mathrm{t}}^{MTR}-h{p}_{\mathrm{m}}^{MTR})+p_n^{MTR}(\beta p_{\mathrm{t}}^{MTR}-h{p}_{\mathrm{m}}^{MTR})$$

(13)

Theorem 2.

In the mixed-recycling mode between power battery manufacturers and third-party recyclers, the optimal pricing strategy for power battery manufacturers and third-party recyclers is

$$w_{MTR}={\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$$

(14)

$$p_{MTR}={\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$$

(15)

$$e_{MTR}={\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$$

(16)

$$p_{\mathrm{m}}^{MTR}={\displaystyle \frac{\beta \theta R}{2(h+\beta )}}$$

(17)

$$p_{\mathrm{n}}^{MTR}={\displaystyle \frac{\theta Rh}{2(h+\beta )}}$$

(18)

$$p_{\mathrm{t}}^{MTR}={\displaystyle \frac{\beta \theta h}{2(h+\beta )}}$$

(19)

Substitute $w_{MTR}$, $p_{MTR}$, $p_{\mathrm{m}}^{MTR}$, $e_{MTR}$, $p_{\mathrm{n}}^{MTR}$, and $p_{\mathrm{t}}^{MTR}$ into Formulas (11)–(13).

That is to say,

$${\pi }_M^{MTR}=F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}+{\displaystyle \frac{\beta {\theta }^{2}R(h+R)(\beta -h)}{2(\beta +h)}}-{\displaystyle \frac{\beta {\theta }^2{R}^2({\beta }^2-h^2)}{4{(\beta +h)}^2}}$$

(20)

$${\pi }_O^{MTR}={\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}$$

(21)

$${\pi }_T^{MTR}={\displaystyle \frac{\beta h^2{\theta }^2{(R-\beta )}^2}{4{(\beta +h)}^2}}$$

(22)

Theorem 2 can be proven.

4.3. Hybrid Recycling Mode (OTR Mode) Between OEM Vehicle Manufacturers and Third-Party Recyclers

In this recycling mode, OEM vehicle manufacturers and third-party recyclers provide different recycling prices for power battery recycling. All recycled power batteries are handed over to the power battery manufacturer for testing, and those that meet the requirements can be applied to other scenarios by the cascade user. Those that cannot be used for cascade utilization can be used for regeneration. Therefore, the following is proposed:

The profit function of power battery manufacturers is

$$\begin{array}{l}{\pi }_{\mathrm{M}}^{\mathrm{OTR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{OTR}}+\epsilon {\mathrm{e}}_{\mathrm{OTR}})(w_{\mathrm{OTR}}-C_0)+{\theta }_{b}R(\beta p_{\mathrm{t}}^{\mathrm{OTR}}-h{p}_{\mathrm{v}}^{\mathrm{OTR}}+\beta p_{\mathrm{v}}^{\mathrm{OTR}}-h{p}_{\mathrm{t}}^{\mathrm{OTR}})\\ -{p_n}^{\mathrm{OTR}}(\beta {p_v}^{\mathrm{OTR}}-h{p_t}^{\mathrm{OTR}})-p_n^{\mathrm{OTR}}(\beta p_{\mathrm{t}}^{\mathrm{OTR}}-h{p}_{\mathrm{v}}^{\mathrm{OTR}})-{\displaystyle \frac{1}{2}}\delta {e_{\mathrm{OTR}}}^2+F\end{array}$$

(23)

The profit function of OEM vehicle manufacturers is

$${\pi }_{\mathrm{O}}^{\mathrm{OTR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{OTR}}+\epsilon {\mathrm{e}}_{\mathrm{OTR}})(p_{\mathrm{OTR}}-w_{\mathrm{OTR}})-p_v^{OTR}(\beta p_v^{OTR}-h{p}_t^{OTR})+p_n^{OTR}(\beta p_v^{OTR}-h{p}_t^{OTR})$$

(24)

The profit function of third-party recyclers is

$${\pi }_{\mathrm{T}}^{\mathrm{OTR}}=-p_t^{\mathrm{OTR}}(\beta p_{\mathrm{t}}^{\mathrm{OTR}}-h{p}_{\mathrm{v}}^{\mathrm{OTR}})+p_n^{\mathrm{OTR}}(\beta p_{\mathrm{t}}^{\mathrm{OTR}}-h{p}_{\mathrm{v}}^{\mathrm{OTR}})$$

(25)

Theorem 3.

In the mixed-recycling mode between OEM vehicle manufacturers and third-party recyclers, the optimal pricing strategy for OEM vehicle manufacturers and third-party recyclers is

$$w_{OTR}={\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$$

(26)

$$p_{OTR}={\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$$

(27)

$$e_{OTR}={\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$$

(28)

$$p_{\mathrm{v}}^{OTR}={\displaystyle \frac{\beta \theta R}{6\beta -h}}$$

(29)

$$p_{\mathrm{n}}^{OTR}={\displaystyle \frac{(2\beta -h)\theta R}{6\beta -h}}$$

(30)

$$p_{\mathrm{t}}^{OTR}={\displaystyle \frac{\beta \theta R}{6\beta -h}}$$

(31)

Substitute $w_{OTR}$, $p_{\mathrm{OTR}}$, $e_{\mathrm{OTR}}$, $p_v^{OTR}$, $p_{\mathrm{n}}^{OTR}$, and $p_{\mathrm{t}}^{OTR}$ into Formulas (23)–(25).

That is to say,

$${\pi }_M^{OTR}=F-{\displaystyle \frac{{\delta }^2}{2}}+{\displaystyle \frac{{(a-\alpha C_0)}^2\alpha {\delta }^2}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}+{\displaystyle \frac{8{\beta }^2{\theta }^2{R}^2(\beta -h)}{{(6\beta -h)}^2}}$$

(32)

$${\pi }_O^{OTR}={\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}+{\displaystyle \frac{\beta {\theta }^2{R}^2{(\beta -h)}^2}{{(6\beta -h)}^2}}$$

(33)

$${\pi }_T^{OTR}={\displaystyle \frac{\beta {\theta }^2{R}^2{(\beta -h)}^2}{{(6\beta -h)}^2}}$$

(34)

Theorem 3 can be proven.

4.4. Hybrid Recycling Mode (MOTR Mode) for Power Battery Manufacturers, OEM Vehicle Manufacturers, and Third-Party Recyclers

In this recycling mode, power battery manufacturers, OEM vehicle manufacturers, and third-party recyclers provide different recycling prices for power battery recycling. All recycled power batteries are handed over to the power battery manufacturer for testing, and those that meet the requirements can be applied to other scenarios by the cascade user. Those that cannot be used for cascade utilization can be used for regeneration. Therefore, the following can be concluded:

The profit function of power battery manufacturers is

$$\begin{array}{l}{\pi }_{\mathrm{M}}^{\mathrm{MOTR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{MOTR}}+\epsilon {\mathrm{e}}_{\mathrm{MOTR}})(w_{\mathrm{MOTR}}-C_0)-{p_m}^{\mathrm{MOTR}}(\beta {p_m}^{\mathrm{MOTR}}-h({p_v}^{\mathrm{MOTR}}+{p_t}^{\mathrm{MOTR}}))-{p_n}^{\mathrm{MOTR}}(\beta {p_v}^{\mathrm{MOTR}}-h({p_m}^{\mathrm{MOTR}}+{p_t}^{\mathrm{MOTR}}))\\ -p_n^{\mathrm{MOTR}}(\beta p_{\mathrm{t}}^{\mathrm{MOTR}}-h(p_{\mathrm{m}}^{\mathrm{MOTR}}+p_{\mathrm{v}}^{\mathrm{MOTR}}))+\theta R(\beta p_{\mathrm{m}}^{\mathrm{MOTR}}-h{p}_{\mathrm{v}}^{\mathrm{MOTR}}-h{p}_{\mathrm{t}}^{\mathrm{MOTR}}+\beta p_{\mathrm{v}}^{\mathrm{MOTR}}-h{p}_{\mathrm{m}}^{\mathrm{MOTR}}-h{p}_{\mathrm{t}}^{\mathrm{MOTR}}+\beta p_{\mathrm{t}}^{\mathrm{MOTR}}-h{p}_{\mathrm{m}}^{\mathrm{MOTR}}-h{p}_{\mathrm{v}}^{\mathrm{MOTR}})\\ -{\displaystyle \frac{1}{2}}\delta {e_{\mathrm{MOTR}}}^2+F\end{array}$$

(35)

The profit function of OEM vehicle manufacturers is

$${\pi }_{\mathrm{O}}^{\mathrm{MOTR}}=(\mathrm{a}\text{-}\alpha {\mathrm{p}}_{\mathrm{MOTR}}+\epsilon {\mathrm{e}}_{\mathrm{MOTR}})(p_{\mathrm{MOTR}}-w_{\mathrm{MOTR}})-p_v^{\mathrm{MOTR}}(\beta p_v^{\mathrm{MOTR}}-h(p_m^{\mathrm{MOTR}}+p_t^{\mathrm{MOTR}}))+p_n^{\mathrm{MOTR}}(\beta p_v^{\mathrm{MOTR}}-h(p_m^{\mathrm{MOTR}}+p_t^{\mathrm{MOTR}}))$$

(36)

The profit function of third-party recyclers is

$${\pi }_{\mathrm{T}}^{\mathrm{MOTR}}=-p_t^{\mathrm{MOTR}}(\beta p_{\mathrm{t}}^{\mathrm{MOTR}}-h(p_{\mathrm{m}}^{\mathrm{MOTR}}+p_{\mathrm{v}}^{\mathrm{MOTR}}))+p_n^{\mathrm{MOTR}}(\beta p_{\mathrm{t}}^{\mathrm{MOTR}}-h(p_{\mathrm{m}}^{\mathrm{MOTR}}+p_{\mathrm{v}}^{\mathrm{MOTR}}))$$

(37)

Theorem 4.

In the mixed-recycling mode of power battery manufacturers, OEM vehicle manufacturers, and third-party recyclers, the optimal pricing strategy for power battery manufacturers, OEM vehicle manufacturers, and third-party recyclers is

$$w_{MOTR}={\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$$

(38)

$$p_{MOTR}={\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$$

(39)

$$e_{MOTR}={\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$$

(40)

$$p_{\mathrm{v}}^{MOTR}={\displaystyle \frac{h\theta R}{2(\beta +h)}}$$

(41)

$$p_{\mathrm{n}}^{MOTR}={\displaystyle \frac{h\theta R}{2(\beta +h)}}$$

(42)

$$p_{\mathrm{t}}^{MOTR}={\displaystyle \frac{h\theta R}{2(\beta +h)}}$$

(43)

$$p_{\mathrm{m}}^{MOTR}={\displaystyle \frac{\theta R(\beta -h)}{2(\beta +h)}}$$

(44)

Substitute $w_{MOTR}$, $p_{MOTR}$, $e_{MOTR}$, $p_v^{MOTR}$, $p_{\mathrm{n}}^{MOTR}$, $p_{\mathrm{t}}^{MOTR}$, and $p_{\mathrm{m}}^{MOTR}$ into Formulas (35)–(37).

That is to say,

$${\pi }_M^{MOTR}=F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}+{\displaystyle \frac{h{\theta }^2{R}^2(\beta -h)}{\beta +h}}$$

(45)

$${\pi }_O^{OTR}={\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}$$

(46)

Theorem 4 can be proven.

Inference 1.

There is a negative correlation between $w_{MOR}$, $p_{MOR}$, $e_{MOR}$, $w_{MTR}$, $p_{MTR}$, $e_{MTR}$, $w_{OTR}$, $p_{OTR}$, $e_{OTR}$, $w_{MOTR}$, $p_{MOTR}$, and $e_{MOTR}$ and $\alpha$.

In the four mixed-recycling modes, when consumers are more concerned about the retail price of power batteries, power battery manufacturers and OEM vehicle manufacturers will, respectively, reduce wholesale and retail prices and reduce blockchain investment.

(1)

Using Formula (38) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial {\mathrm{w}}_{MOTR}}{\partial \alpha }}={\displaystyle \frac{\delta (C_0{\epsilon }^2-2a\delta )}{{(-{\epsilon }^2+2\alpha \delta )}^2}}<0$$

(2)

Using Formula (39) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial p_{MOTR}}{\partial \alpha }}={\displaystyle \frac{6\delta (C_0{\epsilon }^2-2a\delta )}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}<0$$

(3)

Using Formula (40) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial e_{MOTR}}{\partial \alpha }}={\displaystyle \frac{\epsilon (C_0{\epsilon }^2-2a\delta )}{{(-{\epsilon }^2+2\alpha \delta )}^2}}<0$$

Similarly, the relationship between wholesale prices, retail prices, blockchain investment levels, and consumer sensitivity to retail prices of power batteries under other modes can be obtained.

Inference 2.

There is a positive correlation between $w_{MOR}$, $p_{MOR}$, $e_{MOR}$, $w_{MTR}$, $p_{MTR}$, $e_{MTR}$, $w_{OTR}$, $p_{OTR}$, $e_{OTR}$, $w_{MOTR}$, $p_{MOTR}$, and $e_{MOTR}$ and $\epsilon$.

Under the four mixed-recycling modes, the wholesale and retail prices of power batteries, as well as the level of blockchain investment, are positively correlated with consumers’ sensitivity to the traceability level of power batteries. As consumers become increasingly sensitive to the traceability level of power batteries, various participants in the supply chain increase their investment in blockchain to meet consumer demand, leading to an increase in wholesale and sales prices.

(1)

Using Formula (38) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial {\mathrm{w}}_{MOTR}}{\partial \epsilon }}={\displaystyle \frac{2\delta \epsilon (a-C_0\alpha )}{{(-{\epsilon }^2+2\alpha \delta )}^2}}>0$$

(2)

Using Formula (39) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial {\mathrm{p}}_{MOTR}}{\partial \epsilon }}={\displaystyle \frac{12\delta \epsilon (a-C_0\alpha )}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}>0$$

(3)

Using Formula (40) to calculate the first partial derivative of its decision variable, we obtain

$${\displaystyle \frac{\partial e_{MOTR}}{\partial \epsilon }}={\displaystyle \frac{({\epsilon }^2+2\alpha \delta )(a-C_0\alpha )}{{(-{\epsilon }^2+2\alpha \delta )}^2}}>0$$

Similarly, the relationship between wholesale prices, retail prices, blockchain investment levels, and consumer sensitivity to retail prices of power batteries under other modes can be obtained.

Inference 3.

There is a positive correlation between $p_m^{MOR}$, $p_v^{MOR}$, $p_m^{MTR}$, $p_{\mathrm{t}}^{MTR}$, $p_{\mathrm{n}}^{OTR}$, and $p_{\mathrm{m}}^{MOTR}$ and $\beta$ and a negative correlation between $p_n^{MOR}$, $p_n^{MTR}$, $p_v^{OTR}$, $p_{\mathrm{t}}^{MTR}$, $p_v^{MOTR}$, $p_{\mathrm{t}}^{MOTR}$, and $p_{\mathrm{n}}^{MOTR}$ and $\beta$;

In the mixed-recycling mode (MOR mode) between power battery manufacturers and OEM vehicle manufacturers, and the mixed-recycling mode (MTR mode) between power battery manufacturers and third-party recyclers, when consumers pay attention to recycling prices, power battery manufacturers and OEM vehicle manufacturers/third-party manufacturers with competitive relationships will increase recycling prices to obtain larger recycling volumes. But ultimately, the power battery will flow to the power battery manufacturer for testing and undergo hierarchical utilization and recycling. The power battery manufacturer reduces the recycling price from OEM vehicle manufacturers/third-party manufacturers and controls the recycling price from OEM vehicle manufacturers/third-party manufacturers to consumers in reverse in order to achieve greater profits for themselves.

In the hybrid recycling mode (OTR mode) between OEM vehicle manufacturers and third-party recyclers, when consumers pay attention to recycling prices, both OEM vehicle manufacturers and third-party recyclers hope to maximize their profits and would rather lose some customers with high recycling prices. However, due to this consideration, power battery manufacturers receive insufficient waste batteries, resulting in a mismatch between blockchain investment costs and benefits. Therefore, increasing recycling prices is used to promote active recycling by both parties.

In the mixed-recycling mode (MOTR mode) of power battery manufacturers, OEM vehicle manufacturers, and third-party recyclers, when consumers pay attention to recycling prices and all three parties participate in recycling at the same time, OEM vehicle manufacturers and third-party recycling companies have low enthusiasm for recycling and are controlled by the recycling prices of power battery manufacturers, resulting in a negative correlation trend between the two parties unwilling to meet consumer demand.

Using Formulas (41)–(44) to calculate the first partial derivative of the decision variable, we obtain

$${\displaystyle \frac{\partial {\mathrm{p}}_v^{MOTR}}{\partial \beta }}={\displaystyle \frac{-\theta Rh}{{(\beta +h)}^2}}<0$$

$${\displaystyle \frac{\partial {\mathrm{p}}_{\mathrm{t}}^{MOTR}}{\partial \beta }}={\displaystyle \frac{-\theta Rh}{{(\beta +h)}^2}}<0$$

$${\displaystyle \frac{\partial {\mathrm{p}}_{\mathrm{n}}^{MOTR}}{\partial \beta }}={\displaystyle \frac{-\theta Rh}{{(\beta +h)}^2}}<0$$

$${\displaystyle \frac{\partial {\mathrm{p}}_{\mathrm{m}}^{MOTR}}{\partial \beta }}={\displaystyle \frac{\theta Rh}{{(\beta +h)}^2}}>0$$

Similarly, the relationship between the recycling price in other modes and the sensitivity coefficient of consumers to the recycling price of power batteries can be obtained.

4.5. Summary

The results shown as

Table 4. Results summary.

	MOR Mode	MTR Mode	OTR Mode	MOTR Mode
p	${\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$	${\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$	${\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$	${\displaystyle \frac{-2C_0{\epsilon }^2+3a\delta +\alpha C_0\delta }{2(-{\epsilon }^2+2\alpha \delta )}}$
w	${\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{-C_0{\epsilon }^2+a\delta +\alpha {\mathrm{C}}_0\delta }{-{\epsilon }^2+2\alpha \delta }}$
e	${\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$	${\displaystyle \frac{\epsilon (a-\alpha C_0)}{-{\epsilon }^2+2\alpha \delta }}$
pm	${\displaystyle \frac{\beta \theta R}{2(h+\beta )}}$	${\displaystyle \frac{\beta \theta R}{2(h+\beta )}}$		${\displaystyle \frac{\theta R(\beta -h)}{2(\beta +h)}}$
pv	${\displaystyle \frac{\beta \theta h}{2(h+\beta )}}$		${\displaystyle \frac{\beta \theta R}{6\beta -h}}$	${\displaystyle \frac{h\theta R}{2(\beta +h)}}$
pn	${\displaystyle \frac{\theta Rh}{2(h+\beta )}}$	${\displaystyle \frac{\theta Rh}{2(h+\beta )}}$	${\displaystyle \frac{(2\beta -h)\theta R}{6\beta -h}}$	${\displaystyle \frac{h\theta R}{2(\beta +h)}}$
pt		${\displaystyle \frac{\beta \theta h}{2(h+\beta )}}$	${\displaystyle \frac{\beta \theta R}{6\beta -h}}$	${\displaystyle \frac{h\theta R}{2(\beta +h)}}$
M Revenue	$\begin{array}{l}F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ -{\displaystyle \frac{{\beta }^{2}R{\theta }^2(-h+\beta R+\beta -R)}{4{(h+\beta )}^2}}\\ +{\displaystyle \frac{\beta {\theta }^2(h+R)(\beta -\mathrm{h})}{2(h+\beta )}}\end{array}$	$\begin{array}{l}F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ +{\displaystyle \frac{\beta {\theta }^{2}R(h+R)(\beta -h)}{2(\beta +h)}}\\ -{\displaystyle \frac{\beta {\theta }^2{R}^2({\beta }^2-h^2)}{4{(\beta +h)}^2}}\end{array}$	$\begin{array}{l}F-{\displaystyle \frac{{\delta }^2}{2}}+{\displaystyle \frac{{(a-\alpha C_0)}^2\alpha {\delta }^2}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ +{\displaystyle \frac{8{\beta }^2{\theta }^2{R}^2(\beta -h)}{{(6\beta -h)}^2}}\end{array}$	$\begin{array}{l}F+{\displaystyle \frac{\delta {(a-\alpha C_0)}^2(\alpha \delta -{\epsilon }^2)}{2{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ +{\displaystyle \frac{h{\theta }^2{R}^2(\beta -h)}{\beta +h}}\end{array}$
O Revenue	$\begin{array}{l}{\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ +{\displaystyle \frac{\beta {\theta }^2{h}^2(2\beta R-R^2-{\beta }^2)}{4{(\beta +h)}^2}}\end{array}$	${\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}$	$\begin{array}{l}{\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}\\ +{\displaystyle \frac{\beta {\theta }^2{R}^2{(\beta -h)}^2}{{(6\beta -h)}^2}}\end{array}$	${\displaystyle \frac{\alpha {\delta }^2{(a-\alpha C_0)}^2}{4{(-{\epsilon }^2+2\alpha \delta )}^2}}$
T Revenue		${\displaystyle \frac{\beta h^2{\theta }^2{(R-\beta )}^2}{4{(\beta +h)}^2}}$	${\displaystyle \frac{\beta {\theta }^2{R}^2{(\beta -h)}^2}{{(6\beta -h)}^2}}$

.

5. Simulation Analysis

Verifying the impact of tiered utilization rate and competition coefficient among different recyclers on the profits of supply chain members and the overall development of society through data simulation. Based on the analysis of relevant data from Tesla, a new force in electric vehicles, the company delivered a total of 1.31 million new energy vehicles in 2022. Taking the Model S as an example, the battery capacity is about 85 kWh/vehicle, and the price of the power battery system provided by CATL in 2022 is about 0.98 yuan/Wh. Therefore, the production cost of power batteries is 0.98 × 85 × 1000 = 83,300 yuan. Referring to the above data and relevant literature, assuming a = 1,310,000, α = 1.6, ε = 2, m = 0.2, β = 0.5, δ = 5, C₀ = 83,300, R = 3.5, h = 0.4 , and F = 1500.

5.1. The Impact of the Hierarchical Utilization Ratio θ on the Supply Chain

5.1.1. The Variation of Recycling Prices pm, pv, pn, and pt with the Hierarchical Utilization Ratio θ

In the four modes of mixed recycling of power batteries, namely, mixed recycling between power battery manufacturers and OEM vehicle manufacturers, mixed recycling between power battery manufacturers and third-party recyclers, mixed recycling between OEM vehicle manufacturers and third-party recyclers, and the recycling mode of all three parties jointly recycling, the recycling price is positively correlated with the utilization rate of the hierarchy. As shown in Figure 3a, the price of retired power battery recycling (from power battery manufacturers to consumers) maintains a relatively high growth rate in MOR and MTR modes, but the growth rate is slower in MOTR mode. As shown in Figure 3b, the price of retired power battery recycling (OEM vehicle manufacturer → consumer) has the fastest growth rate in the MOTR mode, followed by the OTR mode, and the slowest in the MOR mode. As shown in Figure 3c, the price of retired power battery recycling (power battery manufacturer → OEM vehicle manufacturer/third-party recycler) has the highest growth rate in the OTR mode, followed by the other three modes. As shown in Figure 3d, the price of retired power battery recycling (third-party recyclers → consumers) has the fastest growth rate in MOTR mode, followed by OTR, and MTR is the slowest.

5.1.2. The Profit of Power Battery Manufacturers Varies with the Hierarchical Utilization Ratio θ

In the four modes of hybrid recycling of power batteries, namely, hybrid recycling between power battery manufacturers and OEM vehicle manufacturers, hybrid recycling between power battery manufacturers and third-party recyclers, hybrid recycling between OEM vehicle manufacturers and third-party recyclers, and the recycling mode of all three parties jointly recycling, the profit of power battery manufacturers is positively correlated with the utilization rate. From Figure 4a,b, it can be seen that the profit of power battery manufacturers is highest in the OTR recycling mode, followed by the MOR mode, while the MTR and MOTR modes are not very ideal. In the OTR recycling mode, there is a competitive relationship between OEM vehicle manufacturers and third-party recyclers. Consumers often choose the one with the higher recycling price on the premise of consistent service and other additional conditions. In this mode, the two constrain each other and form a benign market. On the other hand, the joint recycling of both makes the recycling channels diverse, which can obtain a larger quantity of recycled batteries. Overall, for power battery manufacturers, there are both “price advantages” and “channel advantages”. Therefore, OTR mode is the most profitable recycling mode for power battery manufacturers.

5.1.3. The Profit of OEM Vehicle Manufacturers and Third-Party Recyclers Varies with the Hierarchical Utilization Ratio θ

According to Figure 5a, from the perspective of OEM vehicle manufacturers’ profits, the OTR mode is the most suitable recycling mode. In the MOR mode, there is a competitive relationship between power battery manufacturers and OEM vehicle manufacturers. Power battery manufacturers can reduce the recycling price of power batteries to OEM vehicle manufacturers, resulting in lower profits and reduced motivation for OEM vehicle manufacturers, leading to an unsatisfactory recycling situation. Figure 5b shows that from the perspective of third-party recyclers’ profits, the MTR model has greater profits than the OTR model. When OEM vehicle manufacturers join the recycling supply chain, consumers are less likely to consider third-party recyclers unless they provide more advantageous recycling prices. As a result, the profits of third-party recyclers are affected.

5.2. The Impact of Different Recycler Competition Coefficients h on the Supply Chain

5.2.1. The Variation of Recycling Prices pm, pv, pn, and pt with h

In the four modes of mixed recycling of power batteries, namely, mixed recycling between power battery manufacturers and OEM vehicle manufacturers, mixed recycling between power battery manufacturers and third-party recyclers, mixed recycling between OEM vehicle manufacturers and third-party recyclers, and the recycling mode of the three parties jointly recycling, the competition coefficient between retired power battery recycling prices (third-party recyclers → consumers and power battery manufacturers → OEM vehicle manufacturers/third-party recyclers) and recyclers is positively correlated. According to Figure 6a, in the MOTR mode, the recycling price from the power battery manufacturer to the consumer decreases the most due to the influence of the price competition coefficient among the three recyclers. According to Figure 6b, in the tripartite recycling mode, OEM vehicle manufacturers have seen a significant increase in recycling prices in order to maintain their advantageous position. From Figure 6c, it can be seen that the recycling prices of power battery manufacturers → OEM vehicle manufacturers/third-party recyclers show an increasing trend in the MOR mode, MTR mode, and MOTR mode but a decreasing trend in the OTR mode. That is, when the competition coefficient between OEM vehicle manufacturers and third-party recyclers reaches its maximum, the market has already encountered problems, which may lead to one party’s monopoly position. Manufacturers cannot obtain recycled batteries through reasonable recycling prices, so they give up hierarchical utilization and recycling. From Figure 6d, it can be seen that the recycling price of third-party recyclers → consumers increases the most in the MOTR mode, indicating that in the competition among the three parties, in order to obtain more recycled waste batteries, it is necessary to increase the price to attract consumers.

5.2.2. The Profit of Power Battery Manufacturers Changes with h

In MOR and MTR modes, the profit of power battery manufacturers is positively correlated with the competition coefficient h, that is, as the competition coefficient gradually increases, the profit of power battery manufacturers continues to increase. In the OTR mode, the profit of power battery manufacturers is negatively correlated with the competition coefficient h, that is, as the competition coefficient gradually increases, the profit of power battery manufacturers continues to decrease. In the MOTR mode, the profit of power battery manufacturers shows a trend of first increasing and then decreasing with the increase of competition coefficient h. As shown in Figure 7a,b, when power battery recycling is carried out in MOR and MTR modes, power battery manufacturers are in a more advantageous position as the competition coefficient increases, resulting in a decrease in the number of power batteries recycled by OEM vehicle manufacturers and third-party recyclers. The profit growth in MTR mode is greater than that in MOR mode; the situation of OTR recycling mode indicates that the more intense the competition between OEM vehicle manufacturers and third-party recyclers, the lower the profits of power battery manufacturers, indicating that the market order is already chaotic. One side presents a monopoly position and needs to pay a higher recycling price to obtain retired batteries, or power battery manufacturers completely abandon recycling channels and need to pay higher production costs for new power battery production, but overall it is still higher than other recycling modes. The MOTR recycling mode image indicates that appropriate competition is beneficial for power battery manufacturers to obtain optimal profits, but excessive competition coefficient will result in multiple parties suffering.

5.2.3. The Profit Changes of OEM Vehicle Manufacturers and Third-Party Recyclers with h

Shown as Figure 8, the profit of OEM vehicle manufacturers decreases continuously with the increase in competition coefficient in the MOR recycling mode. In the MTR recycling mode, the profit of third-party recyclers continues to increase with the increase in competition coefficient. In the OTR recycling mode, the profits of both OEM vehicle manufacturers and third-party recyclers show a trend of first decreasing and then increasing. When the competition coefficient is in the middle position, that is, when the market size is evenly distributed, the profits of both parties are the lowest. When there is no competition or the competition coefficient is high, the profits of both parties are relatively high. Based on the analysis of the actual situation, it can be concluded that when there is no competition, the market has a self-regulation function, making both parties in a profitable state; when the competition coefficient is high, there is a situation of monopoly or acquisition, and power battery manufacturers need to pay higher recycling costs, at which point profits will show an increasing trend.

6. Conclusions

In summary, the following conclusions can be drawn from the above research:

Firstly, consumers’ sensitivity to traceability levels is positively correlated with wholesale prices, retail prices, and blockchain investment levels. When consumers pay high attention to the traceability level of power batteries, all participants in the supply chain are willing to increase this investment, giving power battery products a competitive advantage.

Secondly, in the four modes of mixed channel recycling, the recycling price shows an increasing trend with the increase of the utilization rate of the tiers. By analyzing the profits of each member, it is found that power battery manufacturers and OEM vehicle manufacturers are more inclined to choose the OTR mode for recycling, while third-party recyclers tend to choose the MTR mode. In the OTR mode, consumers are more inclined to consider OEM vehicle manufacturers for power battery recycling. At this time, third-party recyclers can attract customers by increasing publicity, providing additional services and other forms. If power battery manufacturers hope to recycle in this mode, they can provide appropriate subsidies to jointly achieve a new pattern of win–win for all three parties.

Finally, among the four modes of mixed channel recycling, competitive factors are an undeniable influencing factor. In the case of increasing competition coefficient, most participants obtain a larger market by raising the recycling price. However, in the 0 TR mixed-recycling mode, the excessive competition coefficient can disrupt the market balance and lead to a monopoly phenomenon, which requires policy regulation. From the perspective of profit for power battery manufacturers, the OTR hybrid recycling mode is their optimal choice, but as the competition coefficient increases, their profits gradually decrease. From the perspective of OEM vehicle manufacturers’ profits, the OTR hybrid recycling model is their optimal choice, but when they share the market share equally with third-party recyclers, their profits are the lowest. From the perspective of third-party recyclers’ profits, the MTR mixed-recycling model is their optimal recycling choice.

7. Discussion and Policy Implication

Currently, some scholars have conducted research on the application of blockchain in the field of power battery recycling. However, there is still a lack of studies that simultaneously consider blockchain and competition coefficients across four hybrid recycling models. Through a review of the existing literature, it has been found that the willingness to adopt blockchain is related to its implementation costs. By introducing consumers’ sensitivity coefficient to traceability levels and the competition coefficient, this paper explores profit changes under different recycling models and identifies the preferred recycling models for different recyclers.

With the rapid increase in the number of new energy vehicles in the world, the issue of recycling power batteries for new energy vehicles has attracted widespread attention from society.

This article analyzes and simulates the model and obtains the following management insights:

• Improve the hierarchical utilization rate of power batteries.

Through analysis, it has been found that increasing the utilization rate of power batteries has many benefits. The government should actively promote the utilization of power batteries, introduce relevant policies and regulations, and vigorously promote them to increase consumers’ willingness to recycle power batteries. On the premise of safeguarding their own interests, power battery manufacturers provide partial benefits to other recycling entities to increase their enthusiasm; at the same time, they actively explore the technology of hierarchical utilization and the regeneration of power batteries to reduce resource waste. OEM vehicle manufacturers and third-party recyclers should promote the hierarchical utilization of retired batteries, provide more convenient and efficient recycling channels, and offer supporting or value-added services.

2.

Promote healthy competition and ensure market order.

By analyzing the impact of the competition coefficient on recycling prices and profits of all parties, advocating for healthy competition among all participants in the supply chain, the government and relevant departments need to strengthen supervision, intervene in vicious competition and disruptive market order behavior, provide support and assistance to competitors at a disadvantage in competition, and promote diversified market development. When power battery manufacturers collaborate with other recycling entities, they should clarify the recycling price to avoid monopoly; OEM vehicle manufacturers and third-party recyclers should abide by market order and create a good competitive environment together. All parties should work together to ensure sustainable development.