Dual-Channel Decisions under Blockchain and Returns

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Introduction
Online retail sales of physical goods reached 13.1 trillion yuan in 2021, up to 14.1% year over year, and accounted for 24.5% of all retail sales of social consumer goods, according to the 49th China Internet Development Statistics Report [1]. Online shopping has become a habit due to the rise in its consumption, but unlike traditional ofine physical store purchases, consumers cannot physically experience or cognitively comprehend the goods they are purchasing online; instead, they must rely on the merchant's promotional videos and pictures to understand how the products work and look. Statista estimates that by 2020, the costs of returns will have increased to $550 billion in the U.S. alone, with at least 20% of all online purchases being returned. Tis rate is nearly twice as high as that of traditional brick-and-mortar retailers. Due to information asymmetry, which results in consumers' difering perceptions of products in online channels and a high return rate, as well as the costs associated with returns (such as packing and mailing), consumers' shopping preferences are infuenced. It is therefore practically crucial to assist consumers in learning more about products in order to enhance the shopping experience and, in turn, decrease product returns in order to support the steady growth of the supply chain.
Online shopping is also a common occurrence when it comes to customer returns, in addition to ofine brick-andmortar establishments. Tis is due to the difculty in identifying product information, such as fraudulent statements on food labels or ingredients, or imitations of the food itself, which causes consumers to lose faith in their purchases and negatively afects corporate reputation and customer satisfaction [2]. For instance, the practice of passing of conventional foods as having a green food label undermines customer confdence in the designation and harms the organic market [3]. Manufacturers, sales platforms, etc., will conduct product traceability to identify the issue as a result. Consumers' trust in products and purchase intent can be increased, purchase barriers can be reduced, and the rate of customer returns can all be decreased with the support of the traceability system [4]. Te typical supply chain traceability system, on the other hand, has issues with easy data manipulation, a lack of openness and reliability, and inefective transmission [5]. Blockchain technology ofers an information platform based on openness, transparency, neutrality, reliability, and security for all participants in the supply chain, including authorities and regulators [6]. It is a distributed ledger with the two key characteristics of decentralization and difculty of tampering [7].
Blockchain technology can be used to trace the information of products quickly and accurately, create a credible environment for consumers, and reduce return behavior [8]; realize real-time information sharing for enterprises, improve the operation and management of enterprises, and maintain the interests and development of the supply chain [9]. For instance, Limousin, the company in charge of the French beef brand Blason Prestige, participated in the "2nd China International Import Expo" and highlighted the usage of a blockchain solution built on the Foodgates platform. In order to achieve full traceability of goods and reduce the risk of COVID-19 and other bacteria, fungi, and parasites in the meat supply chain, consumers can learn the geographic location of the source of goods, logistics process time, inspection, and testing reports, and other detailed information through QR codes [10].
Te use of blockchain technology in the supply chain is a topic that is well worth researching because it has many benefts. Many academics think that using blockchain technology will help the supply chain evolve [11]. But will the adoption of blockchain technology be taken into account in certain situations, and whether it will inevitably be advantageous for the supply chain? Tere has not been much study on how using blockchain technology afects supply chain returns in the literature up to this point. As a result, we look into the following topics in our study: (1) How does the dual-channel supply chain price under diferent return modes and what factors will afect the pricing decisions of enterprises? (2) In what situations and to what extent could supply chain participants beneft from the deployment of blockchain technology? (3) How does the use of blockchain technology afect market demands and pricing decisions and is it good for consumers ? We build a two-stage supply chain with a manufacturer and a retailer in order to better comprehend the problems driving these inquiries. Without the use of blockchain technology, we were able to reach the equilibrium results for several return models. Ten, we compare the equilibrium results under various models and study the trend of the equilibrium fndings under various models. Te frm may then implement blockchain technology and carry out the previous process once more. Numerical analysis is used to confrm the model's validity before discussing how the inclusion of blockchain technology may afect supply chain performance.
Te contributions of our study are as follows: frst, we investigate consumers' decisions to return products from various channels and analyze the infuence of this on supply chain decisions, which is rarely covered in existing research. Second, to enhance the use of blockchain technology in the supply chain, our study combines blockchain technology with the return issue. Last but not least, a theoretical and numerical analysis of the infuence of blockchain technology on supply chain performance enables businesses to make informed decisions.
Te remainder of the paper is organized as follows. Section 2 presents a review of the relevant literature. Section 3 describes the problem and model assumptions. Section 4 gives the equilibrium results under diferent return models without blockchain and analyzes and compares them. In Section 5, we have the manufacturer introduce blockchain technology and repeat this work in Section 4. Section 6 verifes the conclusions we obtained with numerical analysis. Section 7 summarizes the conclusions and gives the limitations of the study and future research directions.

Literature Review
Tis paper is related to supply chain management with the blockchain technology application and returns in the supply chain.

Applications of Blockchain Technology in Supply Chains.
Blockchain technology has attracted global attention and has the potential to revolutionize supply chain management and sustainable development achievements [12]. Many scholars have specifcally studied the stages, methods, benefts, and scenarios of blockchain applications in supply chains. Cao et al. [13] found that the application of blockchain platforms can increase production and total surplus and stimulate green investments, but care needs to be taken to control operational costs. Wu et al. [14] found that the leader of the fresh product supply chain should implement blockchain under the coordination of a two-part tarif contract to maximize profts. Ye et al. [15] found that early adoption of blockchain in the agri-food supply chain will yield more benefts than subsequent adoption, and blockchain does not always beneft the consumer surplus and the social welfare. However, Liu et al. [16] found that the adoption of blockchain can reduce consumers' concerns about food safety and increase their surplus. Behnke and Janssen [17] identifed key boundary conditions for the successful use of blockchain to ensure information sharing and traceability through a template analysis of interviews. Liu et al. [18] found that the application of blockchain prompted retailers to ofer more lenient return policies and enhanced consumer surplus. Liu et al. [19] constructed a game theory model based on the use of blockchain to solve the fraudulent returns problem, and the study showed that the adoption of blockchain depends on the efciency of investment in product innovation and the return losses. Diferently, we construct four gametheoretic models considering three diferent return methods to study the impact of return methods and blockchain on optimal decision-making and consumers.
However, some studies have pointed out that blockchain technology cannot be widely applied to all scenarios in supply chains. Tat is to say, the use of blockchain technology is subject to certain restrictions. Ji et al. [20] proposed that manufacturers should only adopt blockchain technology if consumers are sensitive to it beyond a certain level, and the unit verifcation fee paid by the retailer to the manufacturer is subsidized by the manufacturer to the retailer in the form of a lower wholesale price. Choi [21] found that blockchain-enabled supply chains generate lower operational risk than traditional supply chains if the cost of the bank's services is high enough, and it can result in higher expected profts and lower risk for the supply chain and its members. Choi and Luo [22] pointed out that the implementation of blockchain technology can help improve social welfare but can be detrimental to supply chain proftability. Xu et al. [23] used the Stackelberg game approach to study remanufacturing with blockchain, and they found that without the cap-and-trade regulation, using blockchain would instead shrink market share. Although the implementation of blockchain has many benefts, it inevitably encounters many challenges and difculties during the implementation process. Liu et al. [24] proposed that applying blockchain technology in maritime supply chains will face technical, applied, regulatory, and secure challenges in specifc implementation and application. Mirabelli and Solina [25] found that factors such as lack of standards, stakeholder resistance, and insufcient scalability will hinder the spread of blockchain technology. Li et al. [26] proposed that blockchain is benefcial to food safety, operations, and sustainability in the food supply chain but will encounter challenges in technology, cost, government regulation, and awareness.
We review the methods, stages, scenarios, benefts, obstacles, and challenges of blockchain applications in supply chains. Tere is relatively little literature studying the impact of diferent return methods and blockchain on supply chain operations decisions and consumers from an operations management perspective. Also, we propose a cost threshold for the manufacturer to introduce blockchain through numerical simulation analysis, aiming to make better decisions for companies to introduce blockchain.

Returns in Supply
Chains. It has been found that consumers' consumption decisions are often infuenced by merchants' return policies, with 82% of consumers indicating that an overly cumbersome return process would discourage them from making a purchase, and the average return rate for online shopping has reached 22% [27,28]. As an important after-sales service, the study of returns in the supply chain has received more and more attention. Liu et al. [29] considered the hassle costs of consumer returns and analyzed the impact of return losses on retailers' optimal pricing and profts across diferent channels from three diferent return methods. Ma et al. [30] considered two return policies, allowing and disallowing returns, and applied the Stackelberg game approach to analyze the impact of return policies on retail prices, commission rates, and profts in a two-stage supply chain consisting of a retailer and a P2P platform. Wang and He [31] used the Stackelberg game to study the return policies of a mass customization dualchannel supply chain under a retailer selling two products (standard and customized products) directly or through an agent. Jena and Meena [32] analyzed test-in-store-and-buyonline retailing strategies in the absence and presence of product return policies and their impact on supply chain proftability and price competition among manufacturers. Huang and Jin [33] found that in a monopolistic environment, buy-online-and-return-in-store (BORS) can hurt retailers; however, a competitive environment can make both types of retailers willing to ofer BORS under almost all conditions, benefting both the supply chain and its members. Cao and Choi [34] examined the impact of companies ofering both full-trade-in-return and partial-trade-inreturn policies on company decisions and consumer surplus. Te study fnds that which return policy a company chooses depends on the residual value of the product and the satisfaction rate of the new product.
Current research related to returns in supply chains has focused on the impact of return policies and supply chain performance, with little consideration of return costs and different return methods from the consumer's perspective. Terefore, we introduce blockchain technology by considering the costs of consumer returns and diferent return methods to study whether blockchain technology should be introduced and how it afects pricing decisions and supply chain performance.
In summary, in the literature related to the application of blockchain technology in the supply chain, there is less literature discussing how blockchain technology afects consumer channel choice. While most of the relevant literature on return factors focuses on dual-channel or omnichannel sales, and some of the literature considers return policies or pricing strategies, there is little coverage on how blockchain technology afects dual-channel return methods and supply chain performance. We construct a dual-channel supply chain consisting of a manufacturer and a traditional retailer. Based on the assumption that consumers have diferent perceptions of products in diferent channels, considering such parameters as consumers' hassle costs, product validation time, probability of quality products, and blockchain technology costs, the impact of diferent channel return methods without blockchain technology and the adoption of blockchain technology on pricing decisions are investigated. In Table 1, we summarize the main diferences between our study and the relevant literature.

Problem Description and Assumptions.
We develop a supply chain with a manufacturer and a retailer as the leader and follower, respectively. Te manufacturer controls the online channel, and the retailer owns and operates the ofine brick-and-mortar store. According to whether blockchain technology is adopted or not and the various return methods chosen by customers, it is divided into original return models without blockchain technology (model NO), online return models without blockchain technology (model NM), ofine return models without blockchain technology (model NR), and dual-channel models with blockchain technology (model B), as shown in Figure 1.
Discrete Dynamics in Nature and Society Consumers' willingness to pay for products through various channels is taken into account, and it is assumed that their willingness to pay for products through online and ofine channels difers because consumers through ofine channels can actually experience the features of the products, whereas consumers through online channels can only understand the products through information such as pictures and videos released by online stores, which is uncertain.
According to Chiang et al. [37], it is assumed that the customer's willingness to pay for the product v is uniformly distributed between [0, 1]. Due to the uncertainty of online customers' purchases, their product value perception discount percentage is θ ∈ (0, 1), where 1 − θ is the expected value loss of products from online customers, online customers' willingness to pay for products is θv, and their willingness to give up purchase or return is 0. Similar to Gong et al. [38], in order to simplify the analysis, it is assumed that the manufacturer's unit production cost is 0, the wholesale price is w, and the sales price is p 1 in the online channel. Te retailer sells the products to consumers at retail price p 2 .
Referring to Choi [39], it is assumed that the time spent by consumers to verify the products without the blockchain technology is t i (i � 1, 2), and the time spent to verify the products with blockchain technology is Te consumer's sensitivity coefcient for time loss is η, then the consumer's loss in verifying products is ηt. Assuming that the return hassle cost of products purchased online by consumers is a 1 , such as consumers need to package products for mailing; the return hassle cost of products purchased ofine by consumers is a 2 , such as consumers need to specifcally go to the store to return products [29]. When blockchain technology is not used, consumers cannot trace the source of products and may purchase counterfeit products, then consumers will return products, and the manufacturer and the retailer will get zero profts. Referring to Liang and Xiao [35] and Xu and Choi [36], the adoption of blockchain technology can ensure that consumers buy quality products, i.e., β � 1, they will not return products. At the same time, we assume that the potential market demand is 1, and each consumer can purchase at most one product.
Te return hassle cost and verifcation time brought to consumers by online and ofine channels may be diferent [40], that is, the return hassle cost and verifcation time of products purchased through online channels are less than those purchased through ofine channels.
Without blockchain technology, consumers are unable to verify the authenticity of products and may end up buying counterfeit goods, i.e., β ∈ [0, 1); as a result, consumers will return goods, leaving the manufacturer and the retailer with no proft. With the introduction of blockchain technology, consumers will be more likely to purchase high-quality goods and not return them. Assume that there is a one-unit maximum purchase per consumer and that the potential market demand is one. We consider the potential diferences in return hassle costs and verifcation time between the online and ofine channels. So we assume that a 1 ≤ a 2 , t 1 ≤ t 2 , and T 1 ≤ T 2 , that is, that products bought online have a lower return hassle cost and shorter verifcation times than those bought ofine [40].
If consumers do not have a preference between products sold through online and ofine channels, the choice of the channel depends on how much value they will ultimately receive. Based on the above assumptions, the consumer's total utility function is equal to the consumer's willingness to pay minus the cost of time lost in verifying the product and the cost of hassle in returning the product. Te utility U 1 and U 2 obtained by consumers through online and ofine channels are as follows: (1) Equation (1) indicates that consumers use the original channel return mode. In this paper, consumers will employ additional return modes in addition to the initial channel return method. Tis paper frst examines the original channel return mode chosen by consumers in the absence of blockchain technology, then examines the cross-return mode where consumers choose exclusively online returns or exclusively ofine returns, and fnally examines the efects  Discrete Dynamics in Nature and Society of the manufacturer adoption of blockchain technology on supply chain pricing and members' profts. Table 2.

NO Model: Consumers Return Products through Original
Channels. According to the previous assumptions, consumers choose which channel to purchase products based on the overall utility of the two channels. According to equation (1), consumers will choose to buy online products when consumers will choose to buy ofine products when U 2 ≥ U 1 and there is no diference in the utility obtained by consumers when purchasing products from online or ofine channels. From this, we can get the demand functions of two channels as follows: , otherwise, consumers will only buy from a single channel, there is no dual channel, and we only study the dual-channel scenario. Terefore, in the NO model, the optimization models of the manufacturer and the retailer are as follows: In the NO model, the manufacturer and the retailer play a Stackelberg game: the manufacturer is the leader, frst deciding on the wholesale price and online direct sales price; the retailer is the follower, then deciding on the ofine retail price. Solving by the reverse induction, we have the optimal results for the NO model, which are described in the following Teorem 1.

Theorem 1.
In the NO model, the optimal retail prices and wholesale price are as follows: Furthermore, the demands for online and ofine products can be obtained as follows: Te optimal profts for the manufacturer and the retailer are as follows: 6 Discrete Dynamics in Nature and Society Te proof is displayed in Appendix A. Teorem 1 shows that the optimal sales volume in the online (ofine) channel is decreasing in the online (ofine) return hassle cost and increasing in the ofine (online) return hassle cost. While this fnding is intuitive, it reveals an important insight: the cost of return hassles to consumers brought about by the manufacturer or retailer developing a return policy can have an impact on other channels. Specifcally, many previous studies only found that diferences in channel pricing or costs afect demands in the respective channels [30,31,41]. In contrast, our study considers the return hassle costs for both channels and interestingly fnds the impact of return policies on the other channels. According to our observation, this is widespread in practice. For example, among online platforms, clothing merchants on Taobao.com often provide return insurance for consumers, which undoubtedly alleviates the cost of return hassles for consumers, making sales of the same clothing often greater than on JD.com, which does not provide return insurance.
Proposition . In the NO model, the change trends of the retail prices, wholesale price, and demands of the two channels with parameters θ, η, and β are as follows.
Te proof is displayed in Appendix B. According to Proposition 2 (1), the wholesale price is unrelated to how consumers perceive the value of an online product, and as consumer perception of the value of an online product rises, so do online retail price and demand, whereas ofine retail price and demand decline. It suggests that when consumers' perceptions of online products improve, some of them may switch from using physical channels to making purchases online. As a result, the manufacturer would raise the price at which online products are sold in order to make more money. It suggests that some consumers may switch from making ofine purchases to making purchases online when the perceived value of online products rises. As a result, the manufacturer will raise the selling price of online products to enhance profts.
According to Proposition 2 (2), as the consumer time loss sensitivity coefcient rises, the wholesale price, retail price, and demand of ofine channel fall. Te total utility gained by consumers from buying products declines as the time loss sensitivity coefcient rises, which causes Discrete Dynamics in Nature and Society a corresponding decline in demand for ofine products. As a result, the manufacturer and the retailer will actively lower retail prices to stimulate consumer demands in order to prevent losses. However, when the verifcation time for online products is much less than that for ofine products, a higher time loss sensitivity coefcient will increase the demand for online channels. In this case, consumers who are sensitive to time loss will shift from ofine channels to online channels, leading to an increase in demand for online channels.
According to Proposition 2 (3), the wholesale price, retail price, and demand of ofine channel all rise as the likelihood that consumers would buy high-quality products rises. Consumer demands for ofine products increase as the likelihood of buying a quality product rises, consumers are less likely to return the product, and the overall utility gained from their purchase rises. As a result, prices rise to allow both the manufacturer and the retailer to make more money. However, when the cost of return hassle is much lower in the online channel than in the ofine channel, a higher rate of quality products will instead reduce the demand for the online channel. When the rate of quality products is high, consumers' return rates are low, and the low return hassle cost is not enough to attract them to buy online products. In this case, the lower return hassle cost is not enough to make up for the discount in willingness to buy, so consumers are still more willing to purchase ofine products.
Consumer demands for ofine products increase as the likelihood of buying a quality product rises, consumers are less likely to return the product, and the overall utility gained from their purchase rises. As a result, prices rise to allow both the manufacturer and the retailer to make more money.

NM Model: Consumers All Return Products through
Online Channel. Assuming that every client opts for the online return option, this has the efect of raising the cost of return hassle for customers who shop both online and ofine while remaining constant for those who shop online. When consumers all returns goods through online channels, the following are the utility functions of customers: Which channel to buy the product for consumers still depends on the size of the total utility obtained. Similar to the analysis method in 4.1, the demand functions of the two channels can be obtained as follows: where (p 1 + ηt 1 + a 1 (1 − β)/p 2 + ηt 2 + a 1 (1 − β)) ≤ θ ≤ 1 − p 2 + p 1 + η(t 1 − t 2 ), otherwise, consumers will only buy from a single channel, there is no dual channel, and we only study the dual-channel scenario. Terefore, in the model NM, the optimization models of the manufacturer and the retailer are as follows: Solving by the reverse induction, we have the optimal results for the model NM, which are described in the following Teorem 3.

Theorem 3.
In the model NM, the optimal retail prices and wholesale price are as follows: Furthermore, the demands for online and ofine products can be obtained as follows: Te optimal profts for the manufacturer and the retailer are as follows: Teorem 3 shows that the optimal sales volume of the online channel increases only with the increase in the online return hassle cost, and the optimal sales volume of the ofine channel is not afected by the return hassle cost. Tis fnding difers from Teorem 1 due to the fact that all consumers choose to return goods from the online channel in the model NM. Tis phenomenon is also common in practice, for example, Chinese law provides consumers with a right to return goods without reason within 7 days of online shopping, which cannot be used for ofine stores. Obviously, whether a merchant has a seven-day no-excuse return policy will not afect the sales of its ofine stores. Tis fnding contains an interesting management insight: the choice of sales channel may difer for demand-driven companies, which do not need to consider the impact on ofine stores to develop online return policies when consumers can only return goods online. 8 Discrete Dynamics in Nature and Society Proposition 4. In the model NM, the change trends of the retail prices, wholesale price, and demands of the two channels with parameters θ, η, and β are as follows.
Te proof is displayed in Appendix C. Some of the conclusions in Proposition 4 are similar to Proposition 2 and will not be repeated here. Te diference is that under the model NM, consumers' demand for ofine products is independent of the probability that the product is quality, and the demand for ofine products is the same when consumers use online and ofine return modes ), so the retailer will raise the price of ofine products to make more proft.

Model NR: Consumers All Return Products through Ofine
Channel. Assuming that consumers all choose the ofine return mode, it means that the return hassle cost for consumers in both channels becomes a 2 , thus afecting the return hassle cost for consumers who purchase products in the online channel, but not changing the utility for consumers who purchase products in the ofine channel. Terefore, when all consumers return products through ofine channels, the utility functions of consumers are as follows: Which channel to buy the product for consumers still depends on the size of the total utility obtained, and the demand functions for both channels can be obtained as follows: where (p 1 + ηt 1 + a 2 (1 − β)/p 2 + ηt 2 + a 2 (1 − β)) ≤ θ ≤ 1 − p 2 + p 1 + η(t 1 − t 2 ); otherwise, consumers will only buy from a single channel, there is no dual channel, and we only study the dual-channel scenario. Terefore, in the model NR, the optimization models of the manufacturer and the retailer are as follows: Solving by the reverse induction, we have the optimal results for the model NR, which are described in the following Teorem 5.

Theorem 5.
In the model NR, the optimal retail prices and wholesale price are as follows: Furthermore, the demands for online and ofine products can be obtained as follows: Te optimal profts for the manufacturer and the retailer are as follows: Discrete Dynamics in Nature and Society 9 Teorem 5 shows that the optimal sales in the online channel increase only with the decrease of the ofine return hassle cost, and the optimal sales in the ofine channel are not afected by the return hassle cost. Tis fnding difers from Teorem 3 due to the fact that consumers all choose to return products from the ofine channel in the model NR. Although this fnding is not very intuitive, we can fnd corresponding examples in practice. Many retailers have implemented omnichannel strategies, and one of the key strategies is to ofer buy-online-and-return-in-store (BORS) services to consumers, such as Uniqlo, Hewlett-Packard, Walmart, and other well-known retail brands. During the COVID-19 epidemic, BORS reduced the cost of return hassles for consumers, which could efectively reduce the high return rate online and increase in-store purchases [33,42]. From this fnding, we can learn that the return of goods is an important after-sales service. When consumers choose to return goods ofine, companies still need to consider the impact of their return hassle costs on online channel purchases. If the ofine return hassle costs are too high, it will reduce sales in the online channel.

Proposition 6.
In the model NM, the change trends of the retail prices, wholesale price, and demands of the two channels with parameters θ, η, and β are as follows. Te proof is displayed in Appendix D. It is clear from Proposition 6 that consumer demand for ofine products under the model NR is also independent of the probability that the product is quality. Te other conclusions are similar to Proposition 2 and will not be repeated here.

Comparative Analysis of Model NO, Model NM, and
Model NR Proposition 7. Te following relationships can be obtained for the three return models without blockchain: Te proof is displayed in Appendix E. Proposition 7 presents the fndings of a comparison of three return models' optimal pricing and requests in the absence of blockchain technology. Te NM model has the greatest wholesale price, ofine demand, and retail price of the two channels; the model NR has the lowest wholesale price, online retail price, and demand; the NO model has the highest online retail price and demand, and the lowest ofine retail price and demand. Due to the lower hassle costs associated with online returns compared to ofine returns, consumers will beneft more overall from returning products online, which will increase demands for both online and ofine channels and provide the manufacturer and the retailer with an incentive to raise prices to increase profts. Instead, if all returns are made through ofine channels, consumers would receive less overall value from the products, and the manufacturer and the retailer will have to lower their prices in order to retain a proft. Diferent consumers' perceptions of online products mean that the method of returning goods entirely through online channels cannot entirely make up for the decline in demand for online channels brought on by these perceptions. As a result, when customers return goods through the original channels, demand for the online channel is at its maximum, and the manufacturer will boost the online retail price to increase his proft.
When compared to physical channels, the inconvenience associated with product returns for customers via online channels is comparatively low. Online returns can lower the amount of inventory in ofine locations and minimize costs for ofine merchants, while consumers who buy things ofine and prefer to return them online may receive additional benefts. In contrast, choosing to return goods through an ofine route causes the retailer to sufer bigger losses when the additional revenue brought in by customer returns is minimal. Te demands and retail prices of the NM model are always higher than the NR model for both channels, as shown by Propositions 7 (2) and (3). Trough advertising and live commerce, the manufacturer can raise online product awareness, which can further raise the product's price and enhance the manufacturer's ideal proft. To encourage customers to choose to return goods more frequently via online channels, the manufacturer can also work with logistics frms to introduce value-added services such as freight insurance.

Dual-Channel Return Model with Blockchain Technology
Te retailer joining the blockchain platform can achieve information exchange and let customers rapidly trace the source of products, decreasing the returns. Te manufacturer introducing blockchain technology can enable enterprises to have both product traceability and sales functions. For instance, the JD.com blockchain anticounterfeit monitoring technology syncs GIA diamond grade data with the Everledger blockchain network, which ofers clients independently certifed diamond certifcates and provenance information through the JD.com app, cell phone, and desktop website [39]. By using blockchain technology, consumers can authenticate products without having to go through additional channels (e.g., third-party authentication agencies), which lowers the cost of doing so. Terefore, in the case of the manufacturer introducing blockchain technology, we have T i ≤ t i (i � 1, 2), β � 1, and consumer returns that do not occur. In this paper, the manufacturer establishes the blockchain information platform, assuming that the fee paid by the manufacturer is a fxed value F. Te retailer, as a member of the blockchain system, can share information with consumers in order to enhance the utility of purchased products by using blockchain technology, assuming that the retailer needs to pay a unit verifcation fee (f) to use the blockchain platform established by the manufacturer. Te utility functions for the consumer in the case of adopting blockchain technology are as follows: Which channel to buy the product for consumers still depends on the size of the utility obtained from both channels. Similarly, the demand functions for both channels can be obtained as follows: where ( otherwise, consumers will only buy from a single channel, there is no dual channel, and we only study the dual-channel scenario. Terefore, the optimization models for the manufacturer and the retailer under the introduction of blockchain technology by the manufacturer are as follows: Solving by the reverse induction, we have the optimal results for the model B, which are described in the following Teorem 8.

Theorem 8.
In the model B, the optimal retail prices and wholesale price are as follows: Furthermore, the demands for online and ofine products can be obtained as follows: Te optimal profts for the manufacturer and the retailer are as follows: From Teorem 8, it is clear that the unit verifcation fee f only afects the wholesale price w B * . Te unit verifcation fee f is equivalent to a decrease of f in the wholesale price of the manufacturer. Terefore, in the model B, we can consider w B * + f as the wholesale price of the manufacturer, that is, w B * + f � (1 − ηT 2 /2). Tis means that the manufacturer subsidizes the retailer in the form of a lower wholesale price, that is, the size of f has no efect on the manufacturer or the retailer.
Proposition 9. In model B, the change trends of the retail prices, wholesale price, and demands of the two channels with parameters θ, η, f, and F are as follows.
(1) (zw B * /zθ) � 0, and then Te proof is displayed in Appendix F. Te use of blockchain technology, as demonstrated by Proposition 9, demonstrates that the unit validation fee only impacts the wholesale price. Tis is due to the fact that the unit verifcation fee is paid by the retailer to the Discrete Dynamics in Nature and Society manufacturer in exchange for a lower wholesale price, which has no impact on either party's profts as it boosts and decreases their earnings. Te larger the unit validation fee, the larger the manufacturer's subsidy to the retailer. Tus, the retailer always benefts from the use of blockchain technology. Te manufacturer's proft will be impacted by the blockchain set charge, but not the wholesale pricing, retail prices, requests, or retailer's proft. Te manufacturer's proft declines when the fxed blockchain platform charge goes up. Tis is because the manufacturer creates the blockchain platform, and the retailer can only implement information sharing by paying the unit verifcation fee. Proposition 10. Te following relationships can be obtained by comparing the impact of adopting blockchain technology or not on pricing strategy and demands: Te proof is displayed in Appendix G.
Proposition 10 (1) shows that the wholesale price with blockchain is highest when the time loss sensitivity coefcient is high; when the time loss sensitivity is low, the wholesale price with blockchain is lowest. A large time loss sensitivity coefcient means that consumers care about the time it takes to verify products, and for this reason, consumers are willing to pay a higher price in exchange for faster service. As a result, the manufacturer has an incentive to raise wholesale prices to make greater profts.
We defne t 1 − T 1 (t 2 − T 2 ) as the level of blockchain technology in the online (ofine) channel. Intuitively, t 1 − T 1 (t 2 − T 2 ) is the reduced verifcation time of online (ofine) products after adopting blockchain, and the larger the reduced verifcation time is, the higher the level of blockchain technology. Propositions 10 (2) and (3) indicate that the online retail price is the highest with blockchain. Te manufacturer has to pay costs associated with adopting blockchain technology, so it has to increase the price of online products to compensate for blockchain costs. When the level of blockchain technology in the online channel is greater, consumers will increase their purchases even if the price of online products is the highest. For example, according to a survey by CEIBS and JD.com, sales of nutritional supplements increased by 29.4% after the traceability service was provided [16]. However, when the level of blockchain technology in the online channel is low, then the online channel sales depend on the time loss sensitivity. If the time loss sensitivity coefcient is high, then consumers will shift from the online channel to the ofine channel to buy.
When the level of blockchain technology in the ofine channel is high, the consumers will increase their ofine product purchases and the retailer will raise the price of ofine products to make more profts. And when the level of blockchain technology in the ofine channel is low and the time loss sensitivity coefcient is high, then consumers will shift from ofine channels to buy online, and the retailer will have to reduce the price of ofine products to increase the sales. In this case, the manufacturer squeezes the retailer's proft margin by raising the wholesale price. Overall, the higher the level of blockchain technology in the online (ofine) channel, the more popular the online (ofine) products will be with the consumers. Otherwise, it depends on the time loss sensitivity coefcient.

Numerical Analysis
In this section, we did numerical analyzes to support the strategic decision to implement blockchain technology based on the size of the fxed blockchain charge as well as the change in pricing and profts of supply chain participants under various return models. According to the study of Jin and Guo [43], we use the following settings: a 1 � 0.2, a 2 � 0.3, t 1 � 0.3, t 2 � 0.4, T 1 � 0.15, T 2 � 0.25, β � 0.7, and f � 0.09. We have taken F, η, and θ as independent variable parameters. To ensure the validity of the model and the ease of analysis, let F ∈ [0, 0.15], η ∈ [0, 1], and θ ∈ [0.2, 0.8].

Comparison of Supply Chain Pricing Decisions.
Regardless of the return mode, Figure 2 demonstrates that the wholesale and retail prices of both channels decline when the consumer time loss sensitivity coefcient rises. Online direct sales prices rise as consumer perceptions of the value of the products rise, whereas ofine retail prices are the exact opposite. Figure 2(a) shows that the wholesale price with blockchain decreases at a slower rate as the time loss sensitivity coefcient increases than when blockchain is not used. If consumers are more sensitive to time loss, they are prepared to pay more for better and faster service. Te manufacturer will raise the wholesale price for greater proftability. Figure 2(b) shows that the online retail price with blockchain is consistently greater than the online retail price without the blockchain. Figure 2(c) shows that when the level of blockchain technology in the ofine channel is greater, the online direct prices have the following relationships: . Figure 2(d) shows that when the level of blockchain technology in the ofine channel is very small, the ofine price with blockchain decreases at a faster rate as the time loss sensitivity coefcient increases than when blockchain is not used. In this case, blockchain technology cannot attract consumers to purchase, and the retailer has to lower the ofine retail price to increase demand.

Te Impact of Blockchain Fixed Fee on Manufacturer's Proft.
We established the parameters η � 0.5 and θ � 0.7 to examine how blockchain fxed fees afect the proft of the manufacturer. Figure 3 illustrates how the manufacturer's proft falls when the blockchain fxed charge rises after the manufacturer adopts blockchain technology. Tis is because the manufacturer's proft with blockchain technology is strictly decreasing with F when other parameters are determined, while the manufacturer's proft without blockchain technology is independent of F. When F < 0.0876, the manufacturer's proft after adopting blockchain technology is greater than the case without blockchain technology, and when F > 0.0945, the manufacturer's proft after adopting blockchain technology is less than the case without blockchain technology. Tis demonstrates that a crucial consideration in a manufacturer's decision to adopt blockchain technology is the fxed blockchain fee.

Comparison of Supply Chain Members' Profts.
Te manufacturer's proft declines as η grows, as shown in Figure 4. When blockchain technology is implemented, the manufacturer's proft increases, but not when it is not implemented. As seen in Figure 4(a), the manufacturer's proft is better without blockchain technology only when η is larger and θ is smaller with a modest blockchain fxed charge. In most cases, adopting blockchain technology may boost a manufacturer's proft. To strengthen consumer perception of online goods and increase sales, the manufacturer can improve product advertising online. Te manufacturer using blockchain technology is least proftable when the blockchain fxed fee is higher, as indicated in Figure 4(b). Te manufacturer must consider the blockchain fxed fee while deciding whether to implement blockchain technology and should reasonably control the fxed cost of blockchain.
Contrary to what is seen in Figure 5, the retailer's proft decreases with the increase of θ, as opposed to the manufacturer's. Tis is so because the online channel is within the manufacturer's control. With the growth, some customers will switch from ofine to online shopping, lowering the retailer's proft. Te store always makes more money after using blockchain technology than those who do not, proving that the retailer always benefts when a manufacturer introduces blockchain technology. Tis is so that the manufacturer, who pays the blockchain fxed charge, can subsidize the retailer's unit validation fee at a reduced wholesale cost while the retailer is responsible for paying the unit validation fee. Discrete Dynamics in Nature and Society Figure 6 shows that the total supply chain proft decreases as η increases. As shown in Figure 6(a), with a small blockchain fxed fee, the total supply chain proft is higher without blockchain technology only when η is larger and θ is small. Under most conditions, the adoption of blockchain technology can increase total supply chain proft. As shown in Figure 6(b), the supply chain with blockchain technology is the least proftable in the case of a larger blockchain fxed fee. Terefore the manufacturer has to control the blockchain cost reasonably so that the total proft of the supply chain is maximized.

Comparison of Consumer Surplus.
According to Liu et al. [44], Te consumer surplus for NO model is CS NO Similarly, the consumer surplus can be calculated for the other three models. As shown in Figure 7, it shows the impact of η and θ values on consumer surplus. It is clear that with the increase of θ, the consumer surplus also increases. Te consumer surplus without blockchain technology is greater than with blockchain technology only for a specifc value, that is to say, only when the value of η is larger and the value of θ is smaller. Under most conditions, consumer surplus is higher with blockchain technology than without blockchain technology, indicating that the adoption of blockchain technology can increase the total consumer utility and consumers are willing to pay higher prices in exchange for better services and therefore will reduce the return rate to promote the stability of the supply chain.

Conclusions
Based on the hypothesis that consumers perceive products diferently when they are purchased through diferent channels, we created a dual-channel supply chain. We then investigated the efects of return modes through various channels, both with and without the use of blockchain technology, on the profts and channel pricing of supply chain members, taking into account factors such as the cost of consumer return hassle, the amount of time it takes to verify the products, and the likelihood that a product will be defective. Te conclusions of the paper indicate as follows: (1) Te wholesale price, retail prices, and demand of ofine channel, whether or not blockchain technology is used, are inversely related to the customer time loss sensitivity coefcient; when the online product validation time is small, the online channel demand increases with the time loss sensitivity coefcient; the online retail price is directly proportional to the online product value perception, while the ofine retail price is the exact reverse. Only the wholesale price will be impacted by the retailer's unit verifcation cost.
(2) While the retailer pays a unit validation fee, the manufacturer actually subsidizes this fee to the retailer at a lower wholesale price; therefore, the retailer always benefts from the deployment of blockchain technology. Te fxed blockchain cost, the consumer time loss sensitivity coefcient, and the perceived worth of the goods online will all infuence whether the manufacturer adopts blockchain technology. (3) Both customers and the retailer proft when consumers return goods online even when blockchain technology is not involved. Te wholesale price, retail price, and demand with blockchain are infuenced by the level of blockchain technology and the time loss sensitivity coefcient. A high level of blockchain technology and a high time loss sensitivity coefcient will make consumers willing to spend more money to shorten the verifcation time. When the level of blockchain technology in the ofine channel is very low and the consumer sensitivity coefcient is large, the manufacturer will raise the wholesale price while the retailer lowers the ofine retail price, resulting in the manufacturer squeezing the retailer's proft margins. Te implementation of blockchain technology can typically result in a larger consumer surplus.
Only buy offline products Buy offline products Buy online products We provide some management considerations based on these fndings. (1) Consumers' choice of purchase channel is infuenced by the costs of return hassle, thus businesses should design fair return policies to lower consumers' return costs for increased proftability. More than 146,000 businesses in Jiangsu Province, China, have joined the return alliance since the province began testing a no-reason return policy for brick-and-mortar establishments in 2020. Consumers gain from this decision, and it also makes brick-andmortar establishments more competitive with regard to Internet retailers. (2) Te manufacturer adopts blockchain technology only when the blockchain fxed fee is high, indicating the potential for free-rider behavior in the supply chain, but the retailer adopts blockchain technology at all times. In order to use the blockchain technology that the manufacturer has ofered, supply chain participants should set up the proper contracts. Tis is the greatest option for supply chain participants, supply chain systems, and consumers. (3) Te arrival of the blockchain 3.0 era has made blockchain widely used in various industries [45]. Te manufacturer should improve the level of blockchain technology and balance the technological diferences between the two channels to avoid competitive conficts between the two channels. Te application of blockchain makes consumers willing to spend more money for better service and better quality products, which also allows the manufacturer and retailer to gain more profts from raising prices, but they need to pay attention to the control of blockchain costs.
Future research may expand on our work in a number of ways. In a dual-channel supply chain, the impact of blockchain technology and various return models on return selection and pricing decisions is taken into account. After using products ofine, some customers may really compare the two channels' worth, which can afect the demand for the other channel. Tis infuence might be positive or negative, therefore it is a topic worth further research. Our study can be further expanded in the future. For example, examining how blockchain technology afects social welfare when government subsidies are used.
Ten, we solve the model by backward induction. We know that the second order derivative of π r NO with respect to p 2 NO is − 2β/(1 − β) < 0 and π r NO is concave on p 2 NO . It can be obtained from (zπ r NO /p 2 NO ) � 0 that p 2 NO � ((1 − β)(a 1 − a 2 ) + η(t 1 − t 2 ) + p 1 + w + 1/2). Substituting p 2 NO into π m NO , we know that the Hessian matrix of π m NO in terms of w NO and p 1 NO is

Data Availability
Te data used to support the fndings of this study are included within the paper and available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.