Recycling Mode Choice in a Textile and Apparel Closed-Loop Supply Chain considering Blockchain

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Introduction
With the dramatic rise in the population globally, environmental issues are becoming increasingly prominent.Te textile and apparel (T&A) industry is particularly harmful to the environment [1].Te production and transportation of T&A products consume large amounts of energy and water resources while emitting greenhouse gases and discharging wastewater, causing serious environmental pollution problems [2,3].Abbate et al. [4] demonstrated that the apparel industry annually consumes considerable quantities of water resources while emitting large amounts of carbon dioxide gas.Inevitably, continuous environmental pollution arises from the production of T&A products due to the use of dyes and microplastics.Te T&A industry has an environmental impact not only in the production process, but also in the disposal of used products which is currently not environment friendly, with most of them disposed of by incineration and landfll.Globally, the majority of used T&A products are disposed of in landflls, despite a signifcant portion being reused [5].Tus, T&A enterprises must address the environmental implications.Efective measures are necessary to reduce pollution and promote sustainability.
Currently, numerous companies in China are dedicated in reducing environmental pollution by employing environment friendly materials in the production of T&A products [1].For example, apparel manufacturers use biobased materials to reduce dependence on synthetic materials and improve environmental issues [2].However, it is not enough to consider using environmentally friendly materials.Fast fashion encourages consumers to treat clothes as disposable, thereby reducing their lifespan.Furthermore, consumers lack the concept of sustainability in apparel procurement, maintenance, and disposal.In practice, some companies mitigate environmental pollution by guiding consumers toward sustainable consumption [6,7].In recent years, the development of advanced cleaning processes for handling discarded textiles, recycling, and remanufacturing has presented companies with better options to address environmental pollution [8].Te implementation of a CLSC within the T&A industry can efectively alleviate pollution problems.Filho et al. [9] proved that the recycling of T&A products signifcantly reduces greenhouse gas emissions, chemical pollution, and eutrophication of water bodies.Recycling and remanufacturing are recognized as efective ways to enhance energy and material utilization while mitigating environmental pollution at a relatively low cost [10].
In the process of reverse recycling, various recycling modes exist.Te decision on which mode to implement is infuenced by diferent factors, including the cost of implementing the recycling channel.Manufacturers may choose to engage in direct recycling of used and end-of-life products, taking into account a multitude of factors [11].For example, Teijin Group, a Japanese enterprise engaged in fber products, fulfls its corporate social responsibility by directly recycling waste fbers and other available resources to remanufacture goods.In general, retail businesses located closest to the consumer market tend to be most efective at recycling [12].Terefore, retailers often engage in recycling used T&A products.For example, H&M, one of the largest apparel retailers globally, implemented a program for recycling used clothing to reduce its environmental impact and promote sustainable consumption [13].According to H&M's Annual Sustainability Report published in March 2023, 84% of the company's materials were either recycled or sourced sustainably as of 2022.By 2030, H&M aims to achieve 100% sustainable recycling, with a target of using 30% recycled materials by 2025.Furthermore, third-party recyclers play an important role in collecting used T&A products.For instance, "Flying Ants" is among China's largest third-party recycling platforms for used clothing, with over 50% of the recycled garments being repurposed.
While remanufactured T&A products can efectively alleviate environmental pollution, the quality of these products may raise concerns for some consumers.Traditional supply chain traceability technologies, such as barcodes, QR codes, and RFID, may not provide easily accessible product information for consumers and supply chain stakeholders, resulting in a lack of transparency and trustworthiness [14].Despite eforts to address consumer concerns regarding the quality of remanufactured T&A products, these concerns cannot be completely eliminated.Blockchain, in contrast to traditional traceability systems, serves as a distributed data ledger that provides supply chain management with traceability, transparency, and reliability [15].Blockchain can provide consumers with authentic and reliable information about products, thereby enhancing their purchase intention [16].Blockchain have been implemented into the supply chain management, with Everlane, a U.S. textile enterprise, implementing blockchain across its entire supply chain.Trough the ofcial Everlane website, consumers can conveniently access specifc information on every product, spanning the complete product cycle from manufacturing to retail.While blockchain enhances product transparency, it also entails costs.Hence, it makes sense to explore the impact of blockchain on the supply chain.
Based on the above description, we have developed three recycling modes.Tese modes are manufacturer-led and include a retailer and a third-party recycler.Furthermore, we consider the implementation of blockchain by CLSC members within these modes.In this research, we address three questions: (1) which recycling mode does the manufacturer choose when implementing or not implementing blockchain?(2) Under what conditions do the manufacturer and the retailer implement blockchain?(3) What impact does the implementation of blockchain have on the decisions of CLSC members and consumers?
Relevant research covers areas of T&A supply chains, recycling mode choice, and blockchain in supply chain management.To the best of our knowledge, there is little literature that simultaneously addresses recycling modes and blockchain within the context of the T&A CLSC.Te main contributions of this paper are summarised below.Firstly, our study ofers valuable guidance for a T&A manufacturer in choosing a recycling mode.Tat is, regardless of whether blockchain is implemented or not, the type of recycling mode a manufacturer chooses depends mainly on the recycling cost coefcient of recyclers.Secondly, this paper provides insights into the collaborative implementation of blockchain by manufacturers and retailers, specifcally that blockchain implementation can only improve the proft of the CLSC members when the cost of blockchain is below a threshold, while consumers can also beneft.Tirdly, we ofer guidance to CLSC members in the T&A industry on how to make decisions when implementing blockchain.
Te structure of this article is as follows: Section 2 is an overview of the two relevant streams of the literature.Section 3 describes the problem and presents assumptions.Section 4 formulates six models and calculates the optimal decision.Section 5 gives a sensitive and comparative analysis of equilibrium results.Section 6 summarises and draws management insights.Te appendix contains all proof procedures.

Literature Review
Tere are three relevant literature streams to this paper: T&A supply chains, recycling mode choice in CLSCs, and blockchain in supply chain management.

T&A Supply Chains.
Te existing literature has been studied mainly from the perspective of environmental sustainability.Yang et al. [17] conducted an empirical analysis to explore the infuence of corporate digitalization on the environmental performance of the T&A industry.Bubicz et al. [18] undertook a qualitative analysis to investigate the management of social sustainability in the apparel supply chains of six global corporations.Majumdar et al. [19] proposed strategies to overcome barriers and analyzed the challenges faced in the T&A supply chains.Similarly, Vishwakarma et al. [20] identifed numerous obstacles in achieving sustainability in the management of supply chains for T&A products.Tey emphasized the crucial role that technology plays in overcoming these challenges.Furthermore, Warasthe et al. [21] conducted a literature review of 127 articles on sustainability in the T&A supply chain.In addition, some scholars have examined decision-making and coordination in T&A supply chains.For instance, Cai et al. [13] conducted an investigation into recycling operations in second-hand apparel supply chains under centralized versus decentralized decision-making.In addition, they examined supply chain coordination through labor cost-sharing contracts.Adhikari et al. [22] investigated the coordination mechanism between members of the textile supply chain under diferent contracts, taking into account uncertainty on both the supply and demand sides.Adhikari and Bisi [23] proposed a cooperation mechanism for green apparel supply chains based on green cost-sharing and proft-sharing contracts.Tey evaluated the impact of various parameters on decision variables, proftability, and utility of apparel manufacturers and retailers.
Te aforementioned literature primarily explores the sustainability and coordination aspects of T&A supply chains from a theoretical perspective.Difering from previous studies, our research primarily focuses on selecting an appropriate mode for recycling and examines the infuence of blockchain on decision-making in CLSCs.

Recycling Mode Choice in CLSCs.
Previous research on CLSC recycling modes has primarily centered on the choice of the recycling agent.Savaskan et al. [12] initially compared the optimal proft of three recycling modes and discovered that the manufacturer and the retailer achieve maximum profts when the recycling agent is the retailer closest to the consumer market.On this basis, Huang et al. [24] investigated the scenario of two recyclers competing to recycle waste products under a dual-channel model.Teir fndings suggest that the optimal choice of the recycling mode is associated with the intensity of competition between recyclers.Chu et al. [25] proposed a model featuring multiple CLSCs and posited that the preference for recycling modes among manufacturers is infuenced by the market size of third-party recyclers.Furthermore, Li Xin [26] demonstrated that the most appropriate recycling mode for electric tram vehicles is based on the third-party recyclers' economies of scale.Yang et al. [27] examined the infuence of carbon trading policies on the CLSC recycling model.In addition, Yang et al. [28] noted that irrespective of cost information symmetry, manufacturers receive subsidies from the government and often outsource their recycling activities to third-party recyclers.Scholars have conducted studies on cooperative recycling modes.Zheng et al. [29] conducted a comparison of an independent recycling mode and two cooperative recycling modes.Tey discovered that cooperative recycling can tremendously enhance the recycling level.Li et al. [30] examined the most suitable joint recycling model for electric vehicle batteries.
In this study, we center our attention on the manufacturer's process of selecting recycling modes.Unlike previous research, we explore the infuence of blockchain on this process within a T&A CLSC.We aim to evaluate the impact of blockchain on recycling mode selection by the manufacturer.We provide insights on the potential benefts and drawbacks of implementing blockchain in this context.

Blockchain in Supply Chain
Management.Te transparent and traceable nature of blockchain has facilitated its widespread application in supply chain management across various industries.Paul et al. [31] analyzed the role of blockchain in the fnancial supply chain and concluded that this technology can enhance investor confdence while reducing market uncertainty.Niu et al. [32] explored the impact of blockchain in the supply chain of over-the-counter medicines and investigated the utilization of blockchain to achieve the traceability of these medicines.Li et al. [33] investigated research in the agricultural supply chain feld and stated that the implementation of blockchain may increase supply chain proftability, depending on the cost of implementing the technology.Shen et al. [34] developed a model to study the role of blockchain in the secondary market and provide insights into its implementation in sales platforms.Gong et al. [35] further identifed the prerequisites for manufacturers to implement blockchain in a competitive remanufacturing supply chain.Furthermore, numerous academic studies quantitatively analyzed the role of blockchain in supply chains using the lens of game theory.Li et al. [36] posited that blockchain can enhance customers' environmental awareness, which subsequently leads to increased profts for manufacturers and retailers.Similarly, Ma et al. [37] introduced blockchain to enhance the recycling rate and achieve triple sustainability in economic, environmental, and social areas.Likewise, Zhang et al. [16] demonstrated that manufacturers' implementation of this technology could facilitate or hinder the entry of grey marketers.Zhang et al. [38] emphasized the importance of considering blockchain costs, direct marketing costs, and demand volatility when implementing blockchain in a dualchannel supply chain.Conversely, Liu et al. [39] maintained that the implementation of blockchain not only increases consumer confdence in product quality but also raises privacy concerns.
Based on the above literature reviewed, there is limited research on the recycling mode of the T&A CLSC and the implementation of blockchain in supply chain management.To enrich the relevant research, we investigate the selection of recycling modes in the T&A CLSC, taking into account the infuence of blockchain on both recycling mode choices and decision-making within the CLSC.

Problem Description and Model Assumptions
We establish a T&A CLSC that contains a manufacturer and a retailer.Te manufacturer bears responsibility for the sale of new and remanufactured products to consumers through wholesale to the retailer.Tis paper considers three recycling modes from the perspective of the recycling agent.Te manufacturer chooses to recycle used products directly (M recycling mode) or chooses to acquire used products from the retailer (R recycling mode) or the third-party recycler (T recycling mode) by paying transfer prices [27].Following Liu et al. [39], we posit that the manufacturer and the retailer collaborate to determine the implementation of blockchain and to jointly bear the blockchain verifcation costs.We formulate six Stackelberg game models to solve the optimal decision.Consistent with Zhang et al. [40], the manufacturer acts as the leader while the retailer and the third-party recycler act as followers.Te T&A CLSC structure is shown in Figure 1.
To facilitate calculation handling, the assumptions made in our study are as follows.We consider a single consumer market and assume a consumer market size of 1 to simplify the model calculation [40].Remanufactured T&A products are visually indistinguishable from new T&A products.Hence, we assume that they are homogeneous [30].However, the recycling process of used T&A products raises concerns among consumers regarding product quality.Te level of concern has a negative impact on consumer demand.Te implementation of blockchain has the potential to mitigate these concerns and, consequently, is likely to increase consumer demand by providing greater transparency in product information.We defne the positive impact of blockchain on consumer purchase of products as α, 0 < α ≤ 1. Te level of consumer concern about products is αs with blockchain [39].We conclude that the consumer demand function when blockchain is implemented is q � 1 − p − αs.When blockchain is not implemented, α � 1 holds.
In general, the manufacturer typically allocates more resources to the production of new T&A products than to remanufactured T&A products, since the production expenses for remanufactured T&A products are generally lower than those for new T&A products, i.e., c n > c r > 0 [41].Referring to Zhang et al. [40], we assume that the recycling costs for recyclers are k i τ 2 /2, i ∈ M, R, T { }.After the retailer or the third-party recycler collects used T&A products at a price A, the manufacturer recycles these at a transfer price B above the recycling price, thus B > A > 0 [42].To make remanufacturing activities meaningful, we can obtain c n > B + c r [43].In this paper, the assumptions regarding blockchain costs were sourced from Liu et al. [39].Specifically, the manufacturer incurs the blockchain validation expenses in the production chain, while the retailer incurs these expenses in the distribution chain.Te unit validation cost of the T&A product amounts to 2b.
Based on the analysis above, the defnitions and notations given in Table 1 are used for the description in this paper.

Problem Description and Model Assumptions
In this section, we derive equilibrium results for each of the six models.For equilibrium results to be meaningful, recycling cost coefcients must be satisfed

M Recycling Mode.
Within the M Recycling mode, the manufacturer determines the wholesale price and recycling rate at the initial stage.Following this, the retailer is responsible for deciding on the retail price.When blockchain is not implemented, the optimization models for the maximization of profts are formulated as follows: ( By using reverse induction, we deduce the optimum solution for the model NM, as shown in Teorem 1.

Theorem 1. Te optimal decisions are w
Tus, the optimal consumer demand and profts are presented as When there is the implementation of blockchain, the optimization models for the maximization of profts are formulated as follows: ( Using the calculation method in Teorem 1, the optimal solution for the model YM has been derived, as demonstrated in Teorem 2.

Theorem 2. Te optimal decisions are w
Terefore, the optimal consumer demand and optimal profts are given as

R Recycling Mode.
Within the R recycling mode, the manufacturer is responsible for setting the wholesale price, while the retailer subsequently decides on both the retail price and the recycling rate.When blockchain is not implemented, the optimization models for the maximization of profts are formulated as follows: ( By using reverse induction, we deduce the optimum solution for the model NR, as illustrated in Teorem 3.

Theorem 3. Te optimal decisions are
Terefore, the optimal consumer demand and optimal profts are given as When blockchain is implemented in the CLSC, the optimization models for the maximization of profts are formulated as follows:  Discrete Dynamics in Nature and Society Using the calculation method in Teorem 3, the optimal solution for the YR model has been derived, as demonstrated in Teorem 4.

Theorem 4. Te optimal decisions are
Terefore, the optimal consumer demand and optimal profts are given as

T Recycling Mode.
Within the T recycling mode, the decision sequence is that the manufacturer determines the wholesale price frst, followed by the retailer and the thirdparty recycler to make the retail price and recycling rate, respectively.When blockchain is not implemented, the optimization models for the maximization of profts are formulated as follows: ( By using reverse induction, we deduce the optimum solution for the model NT, as shown in Teorem 5.

Theorem 5. Te optimal decisions are
Tus, the optimal consumer demand for products and optimal profts are given as When blockchain is implemented, the optimization models for the maximization of profts are formulated as follows: Using the calculation method in Teorem 5, the optimal solution for the YT model has been derived, as demonstrated in Teorem 6. Theorem 6. Te optimal decisions are w YT * � (k Tus, the optimal consumer demand and optimal profts are given as

Sensitive and Comparative Analysis of Equilibrium Results
In this part, the characterization of the equilibrium results is in Subsection 5.1.Ten, the optimal decisions of the six models are compared in Subsection 5.2.Moreover, we derive the choice of T&A CLSC member in Subsection 5.3.Finally, we examine the consumer implications of blockchain and recycling modes in Subsection 5.4.By characterizing and comparing the equilibrium results in Teorems 1-6, we can therefore conclude these propositions.

Sensitivity Analysis of T&A CLSC Members' Optimal
Decisions.Te implementation of blockchain enhances consumer utility and stimulates consumer demand.However, this also incurs additional costs.We investigate the infuence of the relevant blockchain parameters α and b on the optimal decision, as shown in Propositions 7 and 8.

Proposition .
Impacts of the parameter α on the optimal decisions are given as follows: ( Proposition 7 clarifes that if the recycling cost coefcient of the recycler falls below a threshold, both wholesale and retail prices of T&A products rise, driven by the amplifed infuence of blockchain on consumer purchases α.Te recycling rates always decrease with the amplifcation of α in the model YM, YR, and YT.Generally, the manufacturer is hesitant to raise wholesale prices to maintain consumer demand.However, when the recycling cost coefcient falls below a threshold, an increase in retail prices does not necessarily lead to a substantial decline in consumer demand.In response to an amplifcation in α, if consumer demand decreases, the manufacturer may resort to increase wholesale prices as a means to ofset losses.Accordingly, the retailer adjusts retail prices upwards in response to the manufacturer's wholesale prices' increase.A larger α decreases in consumer demand.As a result, recyclers choose to reduce the recycling rates of used T&A products.Proposition 8. Impacts of the parameter b on the optimal results are given as zw j /zb > 0, zp j /zb > 0, zτ j /zb < 0, and j ∈ YM, YR, YT { }.
Proposition 8 describes that in the models YM, YR, and YT, as the unit cost of blockchain validation b increases, both wholesale and retail prices increase, while recycling rates show a declining trend that is contrary to the rise in b.Tis implies that with a rise in the fees charged to the manufacturer and the retailer on blockchain platforms, they transfer the extra costs to consumers by boosting wholesale and retail prices to maintain their proft margins.Similar results were obtained by Zhang et al. in a dual-channel supply chain study [38].Moreover, an increase in wholesale prices can result in the retailer's increased retail prices.Consequently, this leads to diminished consumer demand for T&A products with higher prices, causing a decline in recyclers' inclination to recycle used T&A products.

Comparison of CLSC Members' Equilibrium Decisions.
By comparing the wholesale prices, retailer prices, and recycling rates with and without blockchain, we obtain Proposition 9. Proposition 9. Te optimum results are satisfactory for the following: Proposition 9(1) demonstrates that in three recycling modes, when the recycler's recycling cost coefcient exceeds a threshold, blockchain implementation will result in an increase in wholesale prices.Tis implies that a higher recycling cost coefcient limits the quantity of used T&A products that a recycler can process.Te implementation of blockchain enables consumers to access information, indicating a low percentage of remanufactured products among all T&A products.As consumer concerns regarding product quality decrease and consumer demand rises, the manufacturer responds by increasing wholesale prices.In addition, the manufacturer experiences increased production costs following blockchain implementation and compensates by adjusting wholesale prices.
Proposition 9(2) indicates that when the recycler's recycling cost coefcient exceeds a threshold, retail prices with blockchain exceed the retail prices without blockchain across the three recycling modes.Tis discrepancy is a result of higher recycling costs, which prompt the upstream manufacturer in the T&A CLSC to raise their prices, thus infating the purchase costs of the downstream retailer.In addition, the implementation of blockchain imposes supplementary expenses on the retailer.Consequently, to ofset the extra costs and maintain proftability, the retailer tends to implement retail prices, efectively transferring the expenses to consumers.
Proposition 9(3) demonstrates that the implementation of blockchain has the potential to increase recycling rates under the same recycling mode, as long as the cost of blockchain unit verifcation b is below a certain threshold.Te function of blockchain to reduce the level of consumer concern about product quality is the main attribute leading to a positive impact on consumer demand.Nevertheless, the implementation of blockchain may increase the cost of producing T&A products.To ofset this extra expense, the manufacturer and the retailer each raise their wholesale and retail prices.Higher prices may deter consumer demand.However, when b is lower than a certain threshold, the implementation of blockchain exerts a favorable infuence on consumer demand.In this case, the implementation of blockchain will increase consumer demand, which will consequently enhance recycling rates.For instance, H&M has increased consumer trust and engagement by partnering with a blockchain platform, which in turn has increased the recycling rate of T&A products.
By comparing the optimal consumer demand under diferent models, we obtain Proposition 10.

Proposition 10. Te optimal consumer demands in the six models satisfy the following:
(1) If b < (1 − α)s/2, then q YM * > q NM * , q YR * > q NR * , and then q NM * > q NR * and q YM * > q YR * ; if k R < k T F 2 /F 3 , then q NR * > q NT * and q YR * > q YT * ; if k M < k T F 1 /F 3 , then q NM * > q NT * and q YM * > q YT * .
Proposition 10(1) implies that the implementation of blockchain can increase consumer demand when the blockchain unit verifcation cost b is lower than a certain amount.Tat is to say, at b lower than a certain amount, the implementation of blockchain does not cause an excessive increase in cost.In this case, the manufacturer is unlikely to raise wholesale prices signifcantly, and the reduction in consumer demand due to blockchain costs is likely to be small.Instead, the implementation of blockchain efectively alleviates the degree of consumer concerns about product quality which can increase consumer demand.Terefore, the implementation of blockchain can increase consumer demand when b is relatively small.For example, the implementation of blockchain by H&M to increase data transparency leads to improved consumer trust and heightened consumer demand.
Proposition 10(2) indicates that customers prefer the M recycling mode the most and the T recycling mode the least when the recycler's recycling cost coefcient is relatively low regardless of whether or not the blockchain is implemented.Generally, the manufacturer has the opportunity to recycle directly when the recycling cost coefcient is relatively low.Tis corresponds to when the manufacturer has the lowest production costs.Te wholesale price is determined by the manufacturer's production cost.Terefore, in the M recycling mode, the product's price is the most afordable, which results in increased consumer demand.Similarly, the retailer has the option to lower their prices when it has a lower recycling cost coefcient, leading to higher consumer demand than in the T recycling mode.

Recycling Mode of CLSC Members.
Comparing the profts of CLSC members in the six models, we obtain Proposition 11.
Proposition 11.Te optimal profts in the six models satisfy the following: Proposition 11 (1) states that blockchain implementation can lead to increased profts for members of the A&T CLSC when the cost of verifying a unit of blockchain b is below a certain threshold.Tis is because blockchain can boost consumer demands when b falls below a certain threshold.Regardless of whether the manufacturer and the retailer choose to implement blockchain, they earn the same marginal proft per product.Tis implies that higher consumer demands lead to higher profts.Increased consumer demand leads to a rise in recycling rates for recyclers.As recycling rates increase, the third-party recycler experiences an increase in profts accordingly.Zhang et al. [41] indicate that the costs of validating blockchain units signifcantly impact the profts of supply chain participants.
Proposition 11 (2) presents that irrespective of the blockchain implementation, when the recycler's recycling cost coefcient is relatively low, the M recycling mode is the most proftable option for the manufacturer, while the T recycling mode is the least proftable.Te primary cause is the high consumer demand under the M recycling mode when the recycling cost coefcient is low.Moreover, the proft increases with the rise in consumer demand, given the similar marginal proft of T&A products.Similarly, if the recycler's recycling cost coefcient is low, consumer demand is the lowest under the T recycling mode, resulting in the manufacturer making the least proft under that mode.
To examine the impact of relevant parameters on the decision-making of T&A CLSC members, we refer to Zhang et al. [40] and set α � 0.5, s � 0.3, c n � 0.5, c r � 0.2, B � 0.25, b � 0.1, and k R � 1.Since k T � 0.5 is the threshold value for the third-party recycler and unit transfer price B is greater than the recycling price A, we set k T � 0.4, k T � 0.6, and A to vary within the range of [0, 0.2] to study the manufacturer's recycling mode selection, which is shown in Figure 2.
Figure 2 presents the manufacturer's decision regarding the recycling mode.When the manufacturer's recycling cost coefcient k M is relatively low, the third-party recycling cost coefcient k T and market recycling price A do not impact the manufacturer's selection of the direct recycling mode.Tat is to say, the M recycling mode provides the manufacturer with the opportunity to capture additional proft.However, it is worth noting that once k T rises, the manufacturer tends to avoid using the third-party recycler.Tis is because, although the third-party recycler may have efcient recycling channels, its recycling costs may become too high.When k M is relatively high, the manufacturer's decision on the mode of recycling takes A into account.In particular, when A is relatively high, the manufacturer prefers to choose the T recycling mode, and to select the R recycling mode during periods of lower A. Tis preference can be attributed to the manufacturer's stronger working relationships with the retailer, which could establish more efective recycling channels or reduce disposal expenses, thus rendering the retailer's recycling more advantageous to the manufacturer when faced with lower A.
To examine the impact of the recycling cost coefcient for the retailer on profts under three distinct recycling modes, we set A � 0.1, k M � 1.5, and k R to vary within the range of [0.015, 1].We examine how retailer's profts are afected by k R , as shown in Figure 3.
Figure 3 shows that an increase in the recycling cost coefcient k R results in a decrease in the retailer's proft under the R recycling mode.Tis is due to that a corresponding increase in recycling expenses causes a decrease in the retailer's proft.Under both the M recycling mode and the T recycling mode, the retailer does not participate in the reverse recycling process.Consequently, k R does not infuence the proft of the retailer.When the third-party recycling coefcient k T is relatively low, both the manufacturer and the retailer set lower wholesale and retail prices, which increase consumer demand and in turn, the retailer's profts.Tis trend is relatively evident in the T recycling mode.

Impact of Blockchain and Recycling Mode on Consumers.
When there is an implementation blockchain, the consumer surplus (CS) calculation formula is CS � To gain a deeper understanding of the impact of blockchain on consumers, we conduct a comparison of CS with blockchain and without blockchain in diferent recycling modes and obtain Proposition 12.

Proposition 12. Te CS in the six models satisfy when
Proposition 12 highlights the correlation between the unit verifcation cost of blockchain b and its impact on consumers.Te implementation of blockchain yields positive consequences for consumers by enhancing the transparency of product information and boosting consumers' willingness to purchase.However, if b exceed a certain value, both the manufacturer and the retailer choose to raise prices to maintain proft margins, in which the positive impact of blockchain on consumers is ofset by its negative impact, resulting in a decrease in consumer surplus.
To investigate the role of recycling mode on CS, we compare CS across the three recycling modes, presented in Figure 4.   Figure 4 shows that consumers in the R recycling mode typically derive greater benefts compared to the M recycling mode or the Trecycling mode.As the retailer engages in direct communication with consumers and serves as their closest point of contact, consumers exhibit higher levels of trust in the retailer compared to other members of the T&A CLSC.Tis enables consumers to reap greater benefts within the R recycling mode.However, it should be noted that higher recycling price A has an inverse efect on consumer benefts.As recyclers retrieve used products from consumers at higher A, the cost of remanufacturing increases.Tis can result in both the manufacturer and the retailer passing on the additional cost to consumers through higher prices, thereby compromising CS.Notably, under the R recycling mode, the impact of A on the level of CS is particularly signifcant.

Conclusions
Based on a CLSC in the T&A industry, we construct three recycling modes and consider the implementation of blockchain, developing six Stackelberg game models.For diferent models, we deduce optimal solutions.We present an in-depth analysis of manufacturer's decisions regarding recycling models in consideration of blockchain implementation.Trough a comparative examination of the optimal decisionmaking and proft of CLSC members under diferent models, our study explores the specifc conditions that infuence the manufacturer's and the retailer's decision to implement blockchain.In addition, we compare the impact of blockchain on the decision-making of CLSC members and consumers.Te results show that (1) if the manufacturer's recycling cost coefcient is relatively low, used T&A products are collected directly by the manufacturer.Otherwise, the responsibility for recycling used T&A products falls to the retailer or the thirdparty recycler.German clothing brand Puma decided to hire third-party recyclers to handle their used products, as creating a new recycling business themselves would have been more expensive.It is noteworthy that the manufacturer's choice of recycling mode remains unchanged whether or not blockchain is implemented.(2) Blockchain can lead to increased profts and benefts consumers when the cost of validating blockchain units remains below a certain threshold.Terefore, CLSC members should implement blockchain when the cost of blockchain is relatively low.(3) When the recycling cost coefcient exceeds a threshold, the implementation of blockchain results in a price increase.Meanwhile, it consistently enhances the recycling rate of T&A products.Nike and Adidas have successfully implemented blockchain into their supply chains, thereby enhancing transparency and trustworthiness.Tis implementation has efectively mitigated consumer concerns about product quality, subsequently boosting consumer demand and driving higher profts.
Combined with the above analysis, this paper presents some management implications for the T&A CLSC.Firstly, when selecting a recycling mode for used products, manufacturers should prioritize the cost of establishing recycling channels as the key consideration.Te implementation of blockchain does not infuence the choice of recycling model.Secondly, manufacturers and retailers primarily prioritize the cost per unit of validation when implementing blockchain, as high costs can negatively impact the profts of supply chain members.Finally, when implementing blockchain, companies should only consider implementing a high-price strategy if they face relatively high recycling expenses.Besides, with the implementation of blockchain, companies typically can enhance their recycling rates.
Tis paper has certain limitations due to incomplete consideration of the problem.Firstly, blockchain expenses incurred during production and distribution processes are shared between the manufacturer and retailer.However, dominant and follower entities bear diferent proportions of blockchain validation costs.Secondly, this paper exclusively examines the positive impact of blockchain on consumer demand.Te implementation of blockchain may potentially decrease consumer demand due to concerns over consumer privacy.In addition, this paper discusses the use of a single recycling entity in the recycling model, whereas manufacturers can directly recycle products while authorizing thirdparty recyclers to collect used T&A products.respect to w YM and τ YM .It can be obtained from zπ YM M / zw YM � 0 and zπ YM M /zτ YM � 0 that w YM * � (2k Substituting w YM * and τ YM * into p YM , we have 2 ).In order to make the results meaningful, it is necessary to ensure that the recycling rate τ YM * is positive, and then we have s + c n + 2b < 1.

C. Proof of Theorem 3
Proof of Teorem 3. Te Hessian matrix of π NR R in terms of p NR and τ NR is By substituting p NR and τ NR into π NR M , the second derivative of By substituting w NR * into p NR and τ NR , we have R is strictly concave with respect to p YR and τ YR .It can be obtained from zπ YR R /zp YR � 0 and By substituting p YR and τ YR into π YR M , the second derivative of π By substituting w YR * into p YR and τ YR , we have p Substituting p NT and τ NT into π NT M and fnding the second derivative of w NT for π NT M , we have By substituting p YT and τ YT into π YT M and fnding the second derivative of w YT for π YT M , we have and by examining the impacts of α on the optimal decisions in the models YM, YR, and YT, it is easily verifed that Discrete Dynamics in Nature and Society

Figure 2 :Figure 3 :
Figure 2: Impact of A and k M on the manufacturer's profts: (a) k T � 0.4 and (b) k T � 0.6.

Table 1 :
Parameters and decision variables.
TProft of the T in models NT and YT CS jConsumer surplus in the model j, j ∈ NM, YM, NR, YR, NT, YT { } 2. Under this assumption, π NR R is strictly concave with respect to p NR and τ NR .It can be obtained from zπ NR R /zp NR � 0 and zπ NR R /zτ NR � 0 that,