Optimal Return Freight Insurance Policies in a Competitive Environment

Abstract

In recent years, return freight insurance (RFI) has emerged as a solution to the problem of returns of goods purchased online. However, although RFI reduces the return costs of both parties and increases the purchase intention of consumers, it also increases the rate of returns and reduces retailers’ profits. Therefore, some online retailers have looked at increasing their service effort as a means of improving the service level and reducing the rate of returns. Considering the impact of retailers’ service efforts on consumer returns, the retailers’ choice of RFI strategy is very important for its profit. It is worth studying how retailers choose RFI policies and the pricing and service effort level in different market environments. In this study, we examine the retailers’ RFI decision-making process, including the influence of retail service effort on consumer returns, by developing three duopolistic-competition game models based on three RFI markets. In this case, we analyze and compare the retailers’ optimal pricing decisions, optimal service effort decisions, and optimal profits in each RFI market, and identify the relationship between the retailers’ optimal decisions and the degree of competition. The result shows that under the market where RFI is provided by the retailer, the retailers’ optimal pricing and optimal service effort level both increase with the increase of market competition. In addition, retailers should consider the impact of market competition and return compensation on consumer demand when making the decision of whether to offer freight insurance.

1. Introduction

Since the outbreak of COVID-19, many countries and regions have introduced different quarantine policies to curb the growth of the epidemic, and many people have chosen to minimize travel for the sake of their health. At the same time, many supermarkets were forced to close their stores and residents were limited to go shopping during the outbreak. In this context, the demand for online shopping surges, however, due to the virtual nature of online shopping, it is difficult for consumers to ascertain whether a product fully meets their requirements (that is, there is matching uncertainty), which reduces their enthusiasm for online purchasing. More than 70% of customers evaluate a retailer’s returns policy before deciding to purchase through an online channel [1]. The 2018 China E-commerce User Experience and Complaint Monitoring Report released by the E-commerce Research Center revealed that refunds, returns, and exchanges topped the list of online consumer complaints [2]. In addition, about 42% of disputes involved return freight costs [3]. The COVID-19 pandemic has seen the demand for return management services continue to increase. In 2020, the top three types of insurance purchased online were health insurance, auto insurance, and other insurance (mainly return freight insurance), with a cumulative premium income of 65.67 billion-yuan, accounting for 82.30% of all online insurance purchases. Statistics published by the Insurance Industry Association showed that in 2021, of the top 60 online insurance products other than auto insurance, the majority were for return freight insurance (RFI), the premiums for which accounted for 9% of the year-on-year increase.

In general, RFI is divided into two categories: RFI provided by the retailer and RFI purchased by the customer. The former is provided by the retailer for all products, while the latter is purchased by the customer at the time of purchasing the product. If the level of claims by either the retailer or customers becomes excessive, the insurance company will suspend their RFI service until the level of claims returns to the normal level, at which point the insurance company will reinstate the service [4]. Under the influence of the COVID-19 pandemic, some consumers who return goods may encounter the situation that the express delivery is returned and cannot return goods normally. At this time, they will fail to return goods even though the RFI has been used. Insurers and retailers need to think about this, who is responsible when this happens, and insurance companies and retailers need to evaluate whether they can offer consumers RFI again. To sum up, on the one hand, RFI reduces the return costs of both parties and increases consumers’ willingness to buy, while on the other hand, it increases the product return rate and reduces retailers’ profits. Thus, RFI has a significant impact on retailers’ pricing decisions and profitability. In an effort to reduce inventory costs, resale costs, and other costs caused by returns, some online retailers have begun to increase their service effort with the aim of improving service quality, which plays an extremely important role in a competitive sales environment. By increasing their service effort, retailers can significantly affect the consumer’s shopping experience, which in turn affects their purchase and return decisions.

In summary, although RFI solves the problem of return freight costs in relation to returns of goods purchased online, these returns still result in costs to retailers and consumers. Due to the COVID-19 pandemic, online shopping is increasingly becoming an indispensable way to shop. However, due to the virtual nature and unavailability of online shopping, it is difficult for consumers to fully understand whether the products meet their requirements. Most shopping platforms require merchants to have a seven-day return policy without an excuse. In this context, the choice of RFI policy is crucial for retailers. Thus, in this study, we investigate how retailers choose the RFI policy and how to set the optimal service effort level to maximize their own profits under the background of different market competition by answering the following research questions: When retailers adopt different RFI strategies? What is the relationship between their optimal pricing decisions and the level of competition? What is the relationship between the optimal service level and optimal pricing? Which RFI strategy should a retailer pursue to maximize total profits? What decision should retailers make regarding RFI when there is competition? We concluded that when retailers are operating in a competitive environment, they should analyze the likely impact of RFI decisions on both demand and returns. If increased return compensation has a greater impact on returns than demand, they should not introduce RFI. If the impact of return compensation on demand is significantly greater than that on returns, they should provide RFI. If the impact of return compensation on demand is greater than that on returns but the difference is within a normal range, retailers should make their RFI decisions based on the level of competition.

2. Literature Review

In this study, we focus on return strategies, RFI, service effort, and duopoly competition.

(1) Return Strategies. Previous theoretical studies on return strategies have focused on product heterogeneity, product pricing, inventory issues, and supply chain coordination. Shang et al. [5] studied the impact of speculative return behavior on the design of retailers’ return strategies, while Hu et al. [6] studied the effectiveness of dynamic pricing strategies in coping with higher return rates through online shopping channels. Altug et al. [7] studied the impact of strategic customer behavior on online retailers’ return strategies, while Su [8] found that consumer return policies can distort incentives under common supply contracts (such as manufacturer buybacks) and proposed strategies to coordinate supply chains in response to consumer returns. Zhao et al. [9] studied the online shopping situation where retailer faces uncertain demand and uncertain consumer valuations and they compared the suitability and effectiveness of two return freight policies, consumer affording return freight and retailer paying return freight. In this study, we focus on return strategies, but also consider the impacts of service effort and RFI on consumer returns.

(2) Return Freight Insurance. Lin et al. [10] examined retailers’ optimal pricing, return strategies, and freight insurance decisions in the context of heterogeneous consumers, while He [11] examined the impact of the introduction of seller-provided RFI on retailers’ pre-sale strategies. Chen et al. [12] studied whether the e-seller should provide RFI under two online sales formats: the reselling format and the agency selling format. Chen et al. [13] developed a duopoly model to investigate how this new practice (introducing RFI) affects the pricing strategies and demand of two e-sellers with different qualities and their RFI decisions. In this study, we also consider the impact of service effort on RFI.

(3) Service Effort. Previous studies on service effort (or service inputs) have focused on the effects of service effort on the return rate, optimal pricing, consumer loyalty, supply chain coordination, and dual-channel pricing. Bellos and Kavadias [14] studied the impact of service effort on the customer experience, while Chen et al. [15] analyzed the influence of service effort on retailers’ optimal pricing and inventory ordering strategies using alternative models involving discounted and non-discounted products. Ji et al. [16] studied the impact of retailers’ value-added service effort on cross-channel competition strategies based on strategic consumer behavior, while Liu et al. [17] studied the optimal retail price and service level of the supply chain, and deduced the boundary conditions related to the services provided by retailers. In this study, we focus on the interactions among service effort, RFI, and returns.

(4) Competitive Environment. Sinh et al. [18] examined the impact of price competition on the coordination of two-stage supply chains, while Zhong et al. [19] studied the influence of three types of competition between two retailers on the optimal profits of supply chain members. Yi et al. [20] constructed an asymmetric dual-retailer evolutionary game model to study the stability of bounded rational retailers’ pursuit of maximum revenue and profits. Ji et al. [21] explored when manufacturers should introduce blockchain technology and their optimal pricing decisions in a competitive manufacturer environment. Chen et al. [22] investigated a manufacturer’s online selling strategy choice between wholesale selling and agency selling, and discuss its impact in the presence of spillovers from online to offline sales. In this study, we examine retailers’ RFI decisions in a competitive environment.

In summary, previous studies have mainly focused on the impact of retailers’ RFI decisions on pricing, inventory, and profits, and focused less on customers’ RFI decision-making. In addition, these studies have focused on the introduction of RFI and separately analyzed its impact on retailers and dual-channel supply chain coordination, while failing to address the impact of factors such as service effort and retail competition. Thus, in this study, we explore the relationship between retailer decisions regarding service effort, RFI, and pricing strategies, and consumer behavior in terms of demand and returns in the context of retail competition. By analyzing the optimal decision-making and optimal profits under different RFI markets, we identify the optimal freight insurance decisions for retailers.

3. Problem Description

Consider two online retailers (retailer i and retailer j) who offer consumers a heterogeneous and yet substitutable product. Both retailers offer no-questions-asked returns and full refunds. The retailers’ RFI decisions are to either not use it, provide it at their expense, or offer it at the customer’s expense. The decision sequence in the different freight insurance models is as follows. First, both retailers set the product price and service effort levels before the start of the selling period. Next, consumers decide to buy the desired product based on factors such as product attributes and service experience. If the consumer places an order and does not initiate a return application after receiving the product, the transaction is completed. If the consumer initiates a return application after receiving the product, the transaction fails. After the retailer receives the returned product, it can be placed into secondary sales after simple processing and repacking. The decision-making sequence is shown in Figure 1.

In the absence of RFI, when consumers return products, they must bear the return freight cost. When the retailer provides RFI, if a consumer submits a return application, the insurance takes effect, and the consumer will be compensated by the insurance company for the return freight. For orders that are not returned, the freight insurance automatically lapses. When the consumer purchases RFI, if they choose to return the product, they initiate the insurance claim process, and the insurance company pays for the return freight. Again, for orders that are not returned, the freight insurance automatically lapses.

In this study, we make the following assumptions.

(1) No-defect returns. The issue of who bears the return cost of non-defective goods is often the subject of disputes. This assumption is similar to the study conducted by Hu. et al. [23]. That is even if the product does not have functional or appearance defects, the seller allows the customer to return the product within a certain period of time after purchase. In this study, we focus on how to reduce the non-defective return rate and how to solve the problem of whether the customer or the retailer should pay the return freight costs when non-defective returns occur.

(2) Full refund. At present, most large e-commerce platforms such as Taobao, Tmall, JD.com, Suning.com, and Amazon have a 7-day, no-questions-asked full-refund policy.

(3) Retailer costs. In this study, we focus on the retailer’s service effort costs and RFI costs. Similar to Hu et al. [23], they also considered the retailer’s service effort costs. Chen et al. [11] also considered the retailer to bear return-freight insurance premium.

(4) Retail competition model. In this study, we focus on retailers selling similar products of different quality, that is, there is substitutability between products. This situation is abundant in reality. For example, both Carrefour and Walmart sell similar products such as air conditioners and refrigerators, which may have different quality and fungible. The game between retailers is Bertrand’s game, that is, price is the competitive factor. We explore the impact of competition on retailers’ decision-making under different return freight policies.

(5) Return freight insurance. In practice, the unit cost of RFI provided by the retailer is not the same as the unit cost of RFI purchased by the customer, but both are less than the return freight cost. To simplify the calculation, it is assumed that the cost of purchasing RFI for both retailers is equal, and the compensation amount is equal to the return freight cost.

Retailer $x$ sells its product at retail price $p_x$ and its service effort level is $s_x$, where $x\in \left\{i,j\right\}$. The service effort level $s_x$ mainly refers to the comprehensive service quality level including the authenticity of the product description, logistics speed, and service attitude, which directly affect the consumer’s return decision. In general, the higher the retailer’s service effort level, the better its service quality, and the higher the cost-of-service quality improvement. Similar to Li et al. [24], we assume that the cost of the service effort is $C_x={\lambda }_x{s}_x{}^2$, where ${\lambda }_x>0$. The retailer chooses the service effort level with decision $s_x$.

Suppose the unit cost of the RFI provided by the retailer is $\overline{h}$. When the RFI is activated, the consumer receives the insurance company’s compensation of $h$, otherwise the insurance lapses. In the case where the retailer pays for the RFI, the retailer’s cost function is the sum of the service effort cost and the RFI cost. In the case where the consumer purchases RFI, they pay a premium of $\widehat{h}$, and if a return occurs, they receive compensation of $h$. If they do not purchase RFI, they must pay the freight return cost of $h$ if they return the goods. Assume that the proportions of consumers who do and do not purchase RFI are $\theta$ and $1-\theta$, respectively. Other parameters and values are shown in Appendix A.

4. The Model

4.1. No Freight Insurance Market

4.1.1. Consumer Demand Analysis

Referring to [4,25], in the market where full refunds are provided but RFI is not available, consumers are required to bear the return freight costs, and their return compensation is the difference between the refunded price of the goods and the return freight cost. Use $\xi$ to denote the sensitivity of consumer demand to return compensation. In addition to the impact of the retailer’s decisions on consumer demand, demand for the retailer’s products in a competitive market is influenced by their competitors’ pricing strategies. Referring to [26], the demand for the products of retailer $i$ affected by the pricing of retailer $j$ is defined as $\gamma p_j$, where $\gamma$ represents the degree of competition between the two retailers. Therefore, the demand function of retailer $i$ is a function of product price, return compensation, and competitor product price, that is, $D_i^0=a-\beta p_i+\gamma p_j+\xi t_0$, where $a>0$ represents the fixed consumer demand that is not affected by the product price, $\beta >0$ represents the coefficient of consumer demand sensitivity to the product price, $\gamma$ represents the coefficient of consumer demand sensitivity to competitor pricing, $\xi$ represents the coefficient of consumer demand sensitivity to return compensation, and $t_0$ represents the return compensation of consumers in the market without RFI (product price minus return freight, $t_0=p_x-h$). In addition, $\beta >\xi >0$, $\beta >\gamma >0$.

4.1.2. Consumer Returns Analysis

In the market without RFI, assuming that the coefficient of consumer returns sensitivity to service effort is $\delta$ and the coefficient of consumer returns sensitivity to return compensation is $\phi$, the consumer returns function is $R_i^0=b-\delta s_i+\phi t_0$, where $b>0$ represents consumer returns that are not affected by the retailer’s service effort and return compensation, and $\delta$ indicates that for each unit increase in the retailer’s service effort, consumer returns decrease by $\delta$ units. $\phi$ indicates that for each additional unit of return compensation, consumer returns increase by $\phi$ units. The return compensation for consumers in the market without RFI is given by $t_0=p_x-h$.

4.1.3. Optimal Retailer Decision Analysis

In a competitive market where retailers do not introduce RFI, they do not have to pay RFI costs. Retailers make decisions on product prices and service effort levels with the goal of maximizing profits. The profit functions of retailers $i$ and $j$ are as follows:

$${\pi }_i^0=\left(D_i^0-R_i^0\right)p_i-C_i^0,{\pi }_j^0=\left(D_j^0-R_j^0\right)p_j-C_j^0.$$

After substituting the demand function and the returns function, the profit function of retailers $i$ and $j$ is obtained as follows:

$${\pi }_i^0=\left\{\left. [a-\beta p_i+\gamma p_j+\xi \left(p_i-h\right)\right]-\left. [b-\delta s_i+\phi \left(p_i-h\right)\right]\right\}{p}_i-{\lambda }_i{s}_i{}^2$$

(1)

$${\pi }_j^0=\left\{\left. [a-\beta p_j+\gamma p_i+\xi \left(p_j-h\right)\right]-\left. [b-\delta s_j+\phi \left(p_j-h\right)\right]\right\}{p}_j-{\lambda }_j{s}_j{}^2$$

(2)

Theorem 1.

When $4\lambda \left(\beta -\xi +\phi \right)-{\delta }^2>0$, the profit function of retailer $x$ is concave and has a unique maximum value of ${\pi }_0^{*}$.

The proof of Theorem 1 is shown in Appendix B.

Based on Theorem 1, the retailers’ optimal service effort level and optimal product price without RFI can be obtained as follows:

$$p_i^{*}=-\frac{2{\lambda }_i\left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_i^{*}=-\frac{\delta \left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$p_j^{*}=-\frac{2{\lambda }_j\left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_j+{\lambda }_i\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_j^{*}=-\frac{\delta \left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_j+{\lambda }_i\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}.$$

Theorem 2.

In the market without freight insurance, when $\xi -\phi <\frac{a-b}{h}$, the optimal price $p_x$ of retailer $x$ decreases with the increase in the degree of competition $\gamma$, and when $\xi -\phi \ge \frac{a-b}{h}$, $p_x$ increases as $\gamma$ increases.

The proof of Theorem 2 is shown in Appendix B.

Theorem 2 shows that the relationship between the retailer’s product pricing and the degree of competition is related to the impact of return compensation on demand and returns. When $\xi -\phi <\frac{a-b}{h}$, return compensation has a greater impact on demand, and the benefits from product sales are greater than the costs of returns. Thus, retailers should increase the prices of their products to obtain higher profits. Given the increase in competition, the benefits obtained from the increase in product prices are sufficient to offset the losses caused by the reduction in sales. Conversely, when $\xi -\phi \ge \frac{a-b}{h}$, return compensation has a greater impact on returns. As the level of competition increases, the reduction in demand as a result of the increased prices is greater than the increased demand for return compensation, and thus retailers should lower the prices of their products.

Theorem 2 also shows that the difference between the impact of return compensation on demand and its impact on returns has a significant impact on sales. From the analysis of the demand function, when the difference exceeds a critical value, the impact of return compensation on demand exceeds the impact of the coefficient of cross-price elasticity on demand. In this case, the higher the price, the higher the demand. When the difference is lower than the critical value, the coefficient of cross-price elasticity has a greater impact on demand, and thus reducing the price increases demand. Additionally, the higher the cost of returns to consumers, the lower this threshold, which means that retailers should lower their prices. This is because when the return cost that consumers must bear increases, return compensation decreases and its impact on demand is reduced. Therefore, retailers should reduce their prices to attract more consumers and obtain greater profits.

Theorem 3.

In the market without freight insurance, when $\xi -\phi \le \frac{a-b}{h}$, the degree of competition $\gamma$ is enhanced, and retailer $x$ should simultaneously increase their product price $p_x$ and service effort level $s_x$. When $\xi -\phi \ge \frac{a-b}{h}$, the degree of competition $\gamma$ is reduced, and retailer $x$ should simultaneously reduce their product price $p_x$ and service effort level $s_x$.

The proof of Theorem 3 is shown in Appendix B.

Theorem 3 shows that when retailers make different freight insurance decisions, the effects of return compensation on their optimal product pricing and optimal service effort level are consistent. On the one hand, consumer return compensation encourages consumers to buy, so retailers can set a higher price, and on the other hand, improving service efforts can reduce consumer return rates, both of which work together to maximize retailer profits.

4.2. Market Where RFI Is Provided by the Retailer

4.2.1. Consumer Demand Analysis

When a retailer provides RFI, consumers do not have to bear the cost of returns, which are borne by the insurance company. Therefore, the return compensation in this market is reflected in the product price. Use $t_1$ to represent the consumer’s return compensation in the market where the retailer provides RFI, that is, $t_1=p_x$. Referring to the demand function in the market without RFI, consumer demand is affected by the product price, return compensation, and the competitor’s product price, and thus retailer $i$’s demand is given by:

$$D_i^1=f\left(p_i,t_1,p_j\right)=a-\beta p_i+\gamma p_j+\xi t_1,$$

(3)

where $a$ $(a>0)$ represents fixed consumer demand that is not affected by product prices, $\beta$ $(\beta >0)$ represents the coefficient of consumer demand sensitivity to product prices, and $\gamma$ represents the degree of competition. $\beta$ and $\xi$ satisfy $\beta >\xi >0$, and $\beta$ and $\gamma$ satisfy $\beta >\gamma >0$. $t_1$ represents the return compensation of consumers in the market without freight insurance, that is, $t_1=p_i$.

4.2.2. Consumer Returns Analysis

In the case where the retailer provides RFI, consumers do not need to consider the cost of returns, which to a certain extent encourages them to return goods. By improving their service effort, retailers can effectively reduce the proportion of non-matching transactions and reduce the return rate. Conversely, by providing consumers with RFI, retailers increase return compensation and return rates. Therefore, for retailer $i$, the consumer’s return function is $R_i^1=f\left(s_i,t_1\right)=b-\delta s_i+\phi t_1$, where $b(b>0)$ represents the volume of returns that are not affected by the retailer’s service effort and return compensation, $\delta$ represents the sensitivity of consumer returns to the retailer’s service effort, and $\phi$ indicates that for each unit of return compensation, consumer returns increase by $\phi$ units. In the market where the retailer provides RFI, the return compensation is equal to the product price, that is, $t_1=p_i$.

4.2.3. Optimal Retailer Decision Analysis

For retailers, providing consumers with RFI not only encourages consumers to buy, but also exacerbates consumer returns, thereby increasing the retailers’ costs. Let $C_i^1$ be the retailer’s RFI cost. Next, $C_i^1=D_i^1\overline{h}$. Referring to the consumer demand function and returns function presented above, the profit function of retailer $x$ can be obtained by:

$${\pi }_i^1=\left(D_i^1-R_i^1\right)p_i-C_i^1-D_i^1\overline{h},{\pi }_j^1=\left(D_j^1-R_j^1\right)p_j-C_j^1-D_j^1\overline{h}.$$

After substituting the demand function, the returns function, and the cost function, the profit functions of retailers $i$ and $j$ are obtained as follows:

$${\pi }_i^1=\left(a-\beta p_i+\xi t_1+\gamma p_j-b+\delta s_i-\phi t_1\right)p_i-(a-\beta p_i+\xi t_1+\gamma p_j)\overline{h}-{\lambda }_i{s}_i{}^2$$

(4)

$${\pi }_j^1=\left(a-\beta p_j+\xi t_1+\gamma p_i-b+\delta s_j-\phi t_1\right)p_j-(a-\beta p_j+\xi t_1+\gamma p_i)\overline{h}-{\lambda }_j{s}_j{}^2$$

(5)

The retailers’ optimal service effort levels and optimal product prices can be obtained as follows:

$$p_i^{*}=-\frac{2{\lambda }_i\left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2+2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_i^{*}=-\frac{\delta \left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2+2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$p_j^{*}=-\frac{2{\lambda }_j\left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2\pm 2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_j+{\lambda }_i\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_j^{*}=-\frac{\delta \left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2+2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_j+{\lambda }_i\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}.$$

Theorem 4.

In the market in which the retailers provide RFI, as competition increases, the retailers’ optimal product pricing and service effort level also increase. As the level of competition decreases, the retailers’ optimal product pricing and service effort level decrease.

The proof of Theorem 4 is shown in Appendix B.

Theorem 4 shows that in the case where retailers provide RFI, when competition is fierce, to offset the cost of purchasing RFI, retailers can set higher prices by increasing their level of service effort to reduce the return rate. When competition is weak, they can offset the cost of RFI by reducing prices and increasing sales without incurring additional service effort costs.

Theorem 5.

In the market in which the retailers provide RFI, when $\gamma <\overline{\gamma }$, the retailer’s selling price increases with $\overline{h}$, and when $\gamma \ge \overline{\gamma }$, the retailer’s selling price decreases as $\overline{h}$ increases, where $\overline{\gamma }=\frac{\sqrt{\left. [{\delta }^2-4{\lambda }_i\left(\beta -\xi +\phi \right)\right]\left. [{\delta }^2-4{\lambda }_j\left(\beta -\xi +\phi \right)\right]}}{2\sqrt{{\lambda }_i{\lambda }_j}}$

The proof of Theorem 5 is shown in Appendix B.

Theorem 5 shows that when competition is weak, the RFI cost increases the retailer’s costs, and the retailer can recoup some of their costs by raising prices. When competition is fierce, the loss caused by increasing product prices is greater than the cost of providing RFI. Therefore, retailers can only offset the cost of providing RFI by reducing prices in an effort to increase sales.

4.3. Market Where RFI Is Provided by the Customer

4.3.1. Consumer Demand Analysis

In the case where the customer can choose to purchase RFI, they need to make two decisions: whether to purchase the product and whether to purchase RFI. As noted above, the consumer demand function is affected by the product price, the service effort level, and the competitor’s price. The consumer demand function in the market in which the customer purchases RFI is $D_i^2=f\left(p_i, t_2,p_j\right)=a-\beta p_i+\gamma p_j+\xi t_2$, where $a(a>0)$ represents fixed consumer demand that is not affected by the product price, $\beta (\beta >0)$ represents the coefficient of consumer demand sensitivity to the product price, and $\gamma$ represents the degree of competition. $\beta , \xi$ satisfy $\beta >\xi >0$, and $\beta , \gamma$ satisfy $\beta >\gamma >0$. $t_2$ represents the average return compensation consumers receive.

4.3.2. Consumer Returns Analysis

In the market in which customers purchase RFI, customers who decide to purchase RFI indicate that they have certain expectations regarding the risk of return and are prepared to bear an additional cost if the product does not have to be returned. Overall consumer demand in the market where customers purchase RFI has increased compared to the market without RFI, but the return rate has also increased. Overall consumer demand in the market where customers purchase RFI has increased compared to the market without RFI, but the return rate has also increased. If the consumer chooses to purchase RFI, they need to pay the premium of $\widehat{h}$. When consumers return products, they can acquire the return cost $h$ paid by the insurance company. Therefore, at this time, the return compensation is $p_x-\widehat{h}$. If the consumer does not purchase RFI, a return cost of $h$ needs to be paid if the product is returned. In this case, the return compensation is $p_x-h$. Similar to the previous case, the proportion of consumers who purchase freight insurance is $\theta$ and the proportion of consumers who do not purchase freight insurance is $1-\theta$. Therefore, the average return compensation of consumers is $t_2=\theta \left(p_x-\widehat{h}\right)+\left(1-\theta \right)\left(p_x-h\right)$. The consumer returns function is $R_i^2=f\left(s_i,t_2\right)=b-\delta s_i+\phi t_2$, where $b(b>0)$ represents consumer returns that are not affected by the retailer’s service efforts and return compensation, $\delta$ indicates that for each unit increase in retailer service effort, consumer returns decrease by $\delta$ units, and $\phi$ indicates that for each unit increase in return compensation, consumer returns increase by $\phi$ units.

4.3.3. Optimal Retailer Decision Analysis

Overall, the purchase of RFI by consumers will not affect the retailers’ costs, but might stimulate demand and increase returns. Referring to the previous consumer demand function and returns function, the profit function of retailer $x$ can be obtained as follows:

$${\pi }_i^2=\left(D_i^2-R_i^2\right)p_i-C_i^2,{\pi }_j^1=\left(D_j^1-R_j^1\right)p_j-C_j^1-D_j^1\overline{h}.$$

After substituting the demand function, the returns function, and the cost function, the profit functions of retailers $i$ and $j$ are obtained as follows:

$${\pi }_i^2=\{a-\beta p_i+\xi \left. [p_i-\theta \widehat{h}-\left(1-\theta \right)h\right]+\gamma p_j-b+\delta s_i-\phi [p_i-\theta \widehat{h}-\left(1-\theta \right)h]\}{p}_i-{\lambda }_i{s}_i{}^2,$$

$${\pi }_j^2=\{a-\beta p_j+\xi \left. [p_j-\theta \widehat{h}-\left(1-\theta \right)h\right]+\gamma p_i-b+\delta s_j-\phi [p_j-\theta \widehat{h}-\left(1-\theta \right)h]\}{p}_j-{\lambda }_j{s}_j{}^2.$$

The retailers’ optimal service effort levels and optimal product prices can be obtained as follows:

$$p_i^{*}=-\frac{2{\lambda }_i\left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_i^{*}=-\frac{\delta \left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$p_j^{*}=-\frac{2{\lambda }_j\left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)},$$

$$s_j^{*}=-\frac{\delta \left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_i\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}.$$

Theorem 6.

For the case in which customers purchase RFI, when $\xi -\phi \ge \frac{\theta \left(a-b\right)}{1-\theta +\theta \widehat{h}}$, the retailer’s optimal pricing increases as competition increases, and when $\xi -\phi \le \frac{\theta \left(a-b\right)}{1-\theta +\theta \widehat{h}}$, the retailer’s optimal pricing decreases as competition increases.

The proof of Theorem 6 is shown in Appendix B.

Theorem 6 shows that in the market in which customers purchase RFI, the return compensation of consumers who have purchased RFI is greater than that of consumers who have not purchased RFI. Therefore, parameter $\theta$ is introduced into the model to represent the proportion of consumers purchasing freight insurance. From $\theta$, the average return compensation of consumers in this market can be obtained.

In summary, in the market without RFI and the market in which consumers purchase RFI, the optimal pricing and service effort level decisions of retailers are affected by the degree of competition, consumer demand, and the sensitivity of returns to return compensation. In the market in which the retailers provide RFI, the retailer’s optimal decisions are only affected by the degree of competition. Therefore, return compensation affects consumer demand and returns, and thus retailers’ decision-making.

5. Comparative Analysis of the Three RFI Models

5.1. Comparative Analysis of Optimal Decisions

From the preceding analyses, the optimal decision of retailer $i$ in the three RFI markets can be obtained, as shown in

Table 1. Optimal decision of retailer i in different freight insurance markets.

Different Freight Insurance Markets	Optimal Decisions
No freight insurance market	$p_i^0=-\frac{2{\lambda }_i\left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$
	$s_i^0=-\frac{\delta \left. [a-b+h\left(\phi -\xi \right)\right]\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$
Market where RFI is provided by the retailer	$p_i^1=-\frac{2{\lambda }_i\left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2+2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$
	$s_i^1=-\frac{\delta \left. [a-b+\overline{h}\left(\beta -\xi \right)\right]\left. [-{\delta }^2+2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$
Market where RFI is provided by the customer	$p_i^2=-\frac{2{\lambda }_i\left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$
	$s_i^2=-\frac{\delta \left\{a-b+\left. [h\left(\theta -1\right)-\theta \widehat{h}\right]\left(\xi -\phi \right)\right\}\left. [{\delta }^2-2{\lambda }_j\left(2\beta +\gamma -2\xi +2\phi \right)\right]}{{\delta }^4-4{\delta }^2({\lambda }_i+{\lambda }_j\left(\beta -\xi +\phi \right)+4{\lambda }_i{\lambda }_j\left(2\beta -\gamma -2\xi +2\phi \right)\left(2\beta +\gamma -2\xi +2\phi \right)}$

.

Theorem 7.

When $\xi >\phi$, the optimal pricing of retailer $x$ satisfies $p_i^1>p_i^2>p_i^0$.

The proof of Theorem 7 is shown in Appendix B.

Theorem 7 shows that when the impact of return compensation on demand is greater than its impact on returns, retailers have the lowest product pricing in the market without RFI and the highest product pricing in the market in which they provide RFI. It also shows that when the impact of return compensation on consumers’ purchase intention is higher than that on returns, in the market where the retailers provide RFI with high return compensation, demand increases and returns decrease. Therefore, in this market, when retailers adopt a generous RFI strategy in an effort to stimulate demand, they should increase product prices to offset the cost of the RFI. In addition, in the market in which the customers purchase RFI, return compensation is not directly related to the retailer’s decision, but rather depends on the proportion of consumers purchasing RFI. Compared with the market without RFI, the improvement in return compensation in the market in which customers purchase RFI encourages consumers to purchase more products, and given that return compensation has a higher impact on demand than on returns, retailers can raise prices.

Theorem 8.

When $\xi >\phi$, the optimal service effort level of retailer $x$ satisfies $s_i^1>s_i^2>s_i^0$.

The proof of Theorem 8 is similar to the proof of Theorem 7.

It can be seen from Theorem 7 and Theorem 8 that when retailers make different freight insurance decisions, the trends in which retailers’ optimal product pricing and optimal service level are affected by the return compensation are consistent. That is, retailers have the lowest service effort level in the market without RFI and the highest service effort level in the market in which they provide RFI. This is because in different RFI markets, as return compensation increases, both demand and returns also increase. Increased return compensation encourages consumers to purchase, and thus the retailer can increase prices, while improving the level of service effort can reduce returns.

Theorem 9.

When $\phi >\xi +\frac{\beta -\xi }{h-h\theta +\widehat{h}\theta }$, the optimal pricing of retailer $x$ satisfies $p_i^1<p_i^2<p_i^0$.

The proof of Theorem 9 is similar to the proof of Theorem 7.

Theorem 9 shows that the retailer’s optimal pricing decreases with the increase in return compensation when the impact of return compensation on returns is greater than that on demand. That is, retailers have the highest product pricing in the market without RFI and the lowest product pricing in the market in which they provide RFI. Thus, retailers should offset the cost of returns by reducing product prices to stimulate demand when return compensation is insufficient to increase demand but results in a high level of returns.

5.2. Comparative Analysis of Optimal Profits

5.2.1. Parameter Settings

The assignment of return freight $h$ and the premium of RFI $\widehat{h}$ is mainly determined according to the situation in real life.

Figure 2 shows the retailer’s optimal decision and optimal profit under the combined influence of $\xi$ and $\phi$. The column numbers in Figure 2 correspond to the column numbers in

Table 2. Parameter assignment range.

	1	2	3	4	5	6	7	8
$\xi$	0.6	0.5	0.4	0.35	0.1	0.2	0.3	0.34
$\phi$	0.1	0.2	0.3	0.34	0.6	0.5	0.4	0.35

and represent graphs under different assignments of $\xi$ and $\phi$. On the basis of relevant research (Chen et al. [11]), without loss of generality, the parameters are $a=5$, $b=0.5$, $\beta =0.7$, $\delta =0.2$, $h=5$, $\overline{h}=0.8$, $\widehat{h}=0.9$, ${\lambda }_i=6$, and ${\lambda }_j=4$. The assignment range of the other parameters is shown in Table 2.

In Figure 2, orange represents the market without RFI, blue represents the market in which the retailer provides RFI, and green represents the market in which the customer purchases RFI. Figure 2a shows that the retailers’ optimal decisions and optimal profits under different market models when $\xi >\phi$. Figure 2b shows that the retailers’ optimal decisions and optimal profits under different market models when $\xi <\phi$.

Conclusion 1. When $\xi <\phi$, the retailer should not introduce RFI, when $\xi >\phi$ and the difference is large, the retailer should provide RFI, and when $\xi >\phi$ and the difference is small, the retailer should enable customers to purchase RFI. When $\xi >\phi$ and the difference is moderate, retailers should enable customers to purchase RFI when competition is weak, and provide RFI when competition is strong.

Comparing columns 1–4 and columns 5–8, it can be seen that when $\xi >\phi$, regardless of the level of competition, the retailer’s profit is higher when it provides RFI, and when $\xi <\phi$, profit is maximized when RFI is not provided. Comparing columns 1–4, it can be seen that the greater the difference between $\xi$ and $\phi$, the greater the retailers’ profit in the market in which they provide RFI, and thus the more beneficial it is for them to provide RFI. When the difference between $\xi$ and $\phi$ is close to zero, the impact of return compensation on demand is no longer significantly greater than that on returns. In this case, it is optimal for retailers to enable customers to purchase RFI.

When $\xi >\phi$, it can be seen from column 3 that when the difference between $\xi$ and $\phi$ is maintained within an appropriate range, the retailer’s profit level will be dependent on the level of competition. When the level of competition increases, profits will be higher when retailers provide RFI than when consumers purchase RFI. In this case, the retailer’s optimal pricing and optimal service level are higher than the case in which customers purchase RFI, and thus it is optimal for the retailer to provide RFI.

When $\xi <\phi$, in columns 5–7, the retailer’s optimal pricing is highest in the market without RFI, lower in the market in which the customer purchases RFI, and the lowest in the market in which they provide RFI. When the difference between $\xi$ and $\phi$ is almost zero, the optimal pricing in column 8 is the same as when $\xi >\phi$, which verifies the existence of the threshold in Theorem 9. In this case, the retailer’s optimal pricing is highest in the market in which they provide RFI, lower in the market in which the customer purchases RFI, and lowest in the market without RFI. However, because of the high volume of returns in the two RFI markets, the retailer’s profit is optimal in the market without RFI.

Conclusion 2. When $\xi$ is greater than $\phi$ and the difference is large, the retailers’ profits increase as the level of competition increases regardless of their RFI decision. However, when the level of competition reaches a specific threshold, the retailers’ profits will suddenly decrease. It can be seen from columns 1 and 2 that when the impact of return compensation on demand is greater than that on returns, within a certain range of competition, retailers can maximize their profits by providing RFI. However, when the level of competition exceeds a specific threshold, the retailers’ pricing and service levels drop sharply, as do their profits. The market in which the retailer provides RFI remains more profitable than the other markets, but in this case a generous returns policy is not the optimal strategy.

Conclusion 3. When $\xi <\phi$, the retailers’ profits are maximized when RFI is not provided, but the smaller the difference between $\xi$ and $\phi$, the lower the profits. Comparing columns 5–7, it can be seen that when the impact of return compensation on returns is higher than that on demand, retailers should not introduce any type of RFI. As the impact of return compensation on returns decreases, both the market in which the customer purchases RFI and the market in which the retailer provides RFI become more profitable. When the impact of return compensation on returns is less than that on demand, it is optimal for retailers to provide RFI. From the above comparison of columns 5–7, it can be seen that when $\xi <\phi$ changes to $\xi >\phi$, it is inevitable that the retailer’s optimal decision and optimal profit graph will be transformed from columns 5–8 to columns 1–4, which shows that it is feasible to use the difference between $\xi$ and $\phi$ to determine the retailer’s optimal profit and RFI decisions.

Existing studies have mainly focused on the impact of retailers’ RFI decisions on pricing, inventory, and profits, and focused less on customers’ RFI decision-making. Based on the existing research, we consider the case of consumers purchasing RFI by themselves, and we analyze its impact on retailers and dual-channel supply chain coordination, while failing to address the impact of factors such as service effort and retail competition. It has made a theoretical contribution to the current research field. The conclusion shows that it is feasible to use the difference between sensitivity coefficient of consumer demand to return compensation and sensitivity coefficient of return volume to return compensation to determine the retailer’s optimal profit and RFI decisions.

5.2.2. Parameter Analysis

• The retailer’s RFI cost $\widehat{h}$ and the customer’s RFI cost $\overline{h}$

The previous analysis assumed that $\overline{h}<\widehat{h}$. In practice, there are also situations in which $\overline{h}>\widehat{h}$. Figure 3 shows the changes in the retailer’s optimal decisions and profits in the situation where $\overline{h}>\widehat{h}$. The parameters are $a=5$, $b=0.5$, $\beta =0.7$, $\delta =0.2$, $h=5$, ${\lambda }_i=6$, and ${\lambda }_j=4$. The other parameters are shown in

Table 3. Control group for $\overline{h}>\widehat{h}$.

			$\mathit{\xi }$	$\mathit{\varphi }$	$\overline{\mathit{h}}$	$\widehat{\mathit{h}}$				$\mathit{\xi }$	$\mathit{\varphi }$	$\overline{\mathit{h}}$	$\widehat{\mathit{h}}$
$\xi >\phi$	$\overline{h}<\widehat{h}$	(1)	0.6	0.1	0.8	0.9	$\xi <\phi$	$\overline{h}<\widehat{h}$	(9)	0.1	0.6	0.8	0.9
		(2)	0.5	0.2	0.8	0.9			(10)	0.2	0.5	0.8	0.9
		(3)	0.4	0.3	0.8	0.9			(11)	0.3	0.4	0.8	0.9
		(4)	0.35	0.34	0.8	0.9			(12)	0.34	0.35	0.8	0.9
	$\overline{h}>\widehat{h}$	(5)	0.6	0.1	0.9	0.8		$\overline{h}>\widehat{h}$	(13)	0.1	0.6	0.9	0.8
		(6)	0.5	0.2	0.9	0.8			(14)	0.2	0.5	0.9	0.8
		(7)	0.4	0.3	0.9	0.8			(15)	0.3	0.4	0.9	0.8
		(8)	0.35	0.34	0.9	0.8			(16)	0.34	0.35	0.9	0.8

.

There are four groups A, B, C and D. Group A is $\xi >\phi$ and $\overline{h}<\widehat{h}$. Group B is $\xi >\phi$ and $\overline{h}>\widehat{h}$. Group C is $\xi <\phi$ and $\overline{h}<\widehat{h}$. Group D is $\xi <\phi$ and $\overline{h}>\widehat{h}$. Since the graphs of each group show the same trend and draws consistent conclusions, here we take (3) and (7), (11) and (15) as examples to explore the changes in the retailer’s optimal decisions and optimal profits when $\overline{h}>\widehat{h}$, as shown in Figure 3.

It can be seen from Figure 3 that the relationship between the retailer’s RFI cost and the customer’s RFI cost does not affect the retailer’s optimal pricing and service level, nor the retailer’s profit in the three RFI decision markets. Furthermore, it does not affect the absolute value of the retailer’s optimal decisions and optimal profit. In addition to (3), (7), (11) and (15), the results of other control groups are consistent with this conclusion. This indicates that the relative unit costs of the retailer’s RFI and the customer’s RFI do not affect the retailer’s optimal decisions and optimal profit in the different RFI markets and at different competition levels. In Figure 3, orange represents the market without RFI, blue represents the market in which the retailer provides RFI, and green represents the market in which the customer purchases RFI.

• Sensitivity coefficient $\delta$ of consumer returns to service effort level

The case where $\delta =0.2$ was discussed above. Next, we discuss whether the retailer’s optimal decisions and optimal profit are the same when $\delta =0.6$ (as shown in Figure 4). The parameters are $a=5$, $b=0.5$, $\beta =0.7$, $h=5$, $\overline{h}$ = 0.8, $\widehat{h}$ = 0.9, ${\lambda }_i=6$, and ${\lambda }_j=4$. The other parameters are shown in

Table 4. Parameter assignment range.

	I	II	III	IV
$\xi$	0.5	0.4	0.2	0.3
$\phi$	0.2	0.3	0.5	0.4

. The row numbers in Figure 4 correspond to the column numbers in Table 4 and represent graphs under different assignments of $\xi$ and $\phi$. In Figure 4, orange represents the market without RFI, blue represents the market in which the retailer provides RFI, and green represents the market in which the customer purchases RFI.

In Group III, the impact of return compensation on demand is lower than that on returns, and thus retailers offering RFI might increase returns more than they increase demand. In this case, it is optimal for the retailer not to provide RFI. Based on the control group in group III, it can be seen that when the coefficient of sensitivity of consumer returns to the retailer’s service effort level increases, retailers can reduce the rate of returns by improving their service effort level, therefore the retailer’s optimal service effort level increases in the control group. However, the retailer’s pricing, demand, returns, and optimal profit are unchanged, indicating that when return compensation has a significant impact on returns, the improvement in the retailer’s service effort level has little effect on the retailer’s pricing and profits. Therefore, the change in $\delta$ does not affect the retailer’s optimal pricing strategy and returns strategy in different RFI markets.

• Service effort cost coefficient $\lambda$

Previously, it was assumed that ${\lambda }_i=6,{\lambda }_j=4$, that is, the service effort cost of the two retailers is similar. To confirm the validity of the previous results, here we make the opposite assumption regarding the retailers’ service effort costs, and take a large value of $\lambda$ to check whether this affects the retailers’ optimal decisions and profits (as shown in Figure 5). The parameters are $a=5$, $b=0.5$, $\beta =0.7$, $\delta$= 0.6 $h=5$, $\overline{h}$ = 0.8, $\widehat{h}$ = 0.9, ${\lambda }_i=80$, and ${\lambda }_j=100$. The rest of the parameters are shown in Table 4. The row numbers in Figure 5 correspond to the column numbers in Table 4 and represent graphs under different assignments of $\xi$ and $\phi$

Similar to the previous analysis, here we take Group II and Group IV as examples to compare the optimal decisions and optimal profits of retailers under the two service effort cost coefficient assumptions. It can be seen from Figure 5 that the service effort cost coefficients of retailer $i$ and retailer $j$ have no effect on the retailers’ pricing strategy and returns strategy in the different freight insurance markets. When the retailer’s service effort cost coefficient is significantly increased (i.e., costs increase), the retailer’s optimal service effort level is significantly reduced regardless of which RFI market it is in, which indicates that the increase in the service effort cost coefficient leads to an increase in the retailer’s service effort costs. Therefore, retailers will not choose to increase their service effort in an effort to reduce the rate of returns. Changes in the service effort cost coefficients of retailer $i$ and retailer $j$ have no effect on the retailers’ decisions. In Figure 5, orange represents the market without RFI, blue represents the market in which the retailer provides RFI, and green represents the market in which the customer purchases RFI.

Therefore, when return compensation has a significant impact on demand, regardless of the level of competition, retailers who either provide or offer RFI are more profitable than those who do not introduce RFI, and when return compensation has a significant impact on returns, the retailer’s profit is optimal when they do not introduce RFI.

6. Conclusions

From the perspective of retailers’ RFI decisions, in this study, we analyzed the impact of retailers’ service efforts on returns, established a duopoly competition game model using three RFI markets, and determined the retailers’ optimal pricing decisions, optimal service effort level decisions, and optimal profits in each RFI market. We then compared the retailers’ optimal decisions and optimal profits under the three RFI markets, and identified the relationship between the retailers’ optimal RFI decision and the degree of competition.

Our findings were as follows. First, in the market in which the retailer provides RFI, the retailer’s optimal pricing and optimal service effort level increase with increasing competition and decrease with decreasing competition. The fact that retailers provide consumers with RFI is a generous returns policy, and thus the rate of returns will remain relatively high. When competition intensifies, it is unwise for retailers to reduce product prices in an effort to stimulate demand. In this case, retailers should increase their service effort to reduce returns and maintain prices at a high level. Therefore, when retailers choose to provide consumers with RFI, as competition intensifies, they should increase both their service effort and prices to maximize profits. Second, when the retailer is deciding whether to provide RFI, it is necessary to evaluate whether the return compensation has a greater impact on demand or returns. For products with high return costs and complicated return processes, retailers can choose to provide RFI to increase consumers’ willingness to buy. For products whose increasing return compensation will lead to an increase in returns, retailers should raise the return thresholds and increase return hassle costs in an effort to reduce the impact of return compensation on returns. Third, when retailers are making RFI decisions, they should consider the impact of competition and return compensation on demand. In a market environment with relatively flexible pricing power, providing RFI will increase both return compensation and profits. For example, in 2020 Alipay announced that their RFI had been upgraded. In the past, when consumers returned goods, they had to pay in advance to express freight the goods back to Alipay, and only received reimbursement after Alipay confirmed that the goods had been received. Furthermore, in some cases the amount they were reimbursed was lower than the return freight fee they had paid. Following the change, once Alipay had agreed to provide a refund, consumers were able to use the free freight insurance return service, and goods weighing up to 3 kg were able to be returned using SF Express’s door-to-door service at no cost.

6.1. Managerial Insights

In conclusion, when retailers are operating in a competitive environment, they should analyze the likely impact of RFI decisions on both demand and returns. If increased return compensation has a greater impact on returns than demand, they should not introduce RFI, and should force consumers to bear the cost of returns. However, if the impact of return compensation on demand is significantly greater than that on returns, they should provide RFI. If the impact of return compensation on demand is greater than that on returns but the difference is within a normal range, retailers should make their RFI decisions based on the level of competition. When the level of competition is low, they should enable consumers to purchase RFI, and when the level of competition is high, they should provide RFI to maximize profits.

The conclusion of this paper provides theoretical guidance for whether and when retailers should introduce return freight insurance. Meanwhile, retailers can know more clearly under what circumstances it is beneficial for them to increase service efforts to reduce the return rate. For insurance companies, different insurance pricing can be carried out according to different introduction strategies of freight insurance in the market. For example, when retailers purchase insurance, due to the large purchase quantity and long-term cooperation relationship, insurance companies can appropriately reduce the insurance price to enhance user stickiness, so as to facilitate long-term cooperation.

6.2. Limitations and Future Research

This study has some limitations that provide opportunities for future research. First, the duopoly retailer competition model used in this study does not involve upstream suppliers, and these should be considered in future studies to enrich our understanding of the implications for the supply chain. The impact of retailers’ attitudes to risk on their RFI decisions, pricing, and profits should also be investigated. Finally, this study only considered linear functions of demand and returns. Future studies should consider other functions to analyze more complex real-world problems.