Research on Optimal Promotion Strategies of Remanufactured Products in a Dual-Channel Supply Chain

Abstract

As an important way to realize the circular economy, remanufacturing faces the problem of low consumer recognition of remanufactured products. Given that factor, this study formulates a model that integrates offline direct sales with online distribution led by remanufacturers, assuming that consumers perceive differences between channels. We develop a Stackelberg game model to represent cases of remanufactured channel promotion and generic promotion and analyze the optimization of pricing and the level of promotion effort decisions for remanufactured products. Furthermore, considering the market conditions, such as the difference coefficient of consumer channel perception and the spillover effect in generic promotion, we investigate the selection of the optimal promotion strategy for remanufacturers. The research findings reveal the following: (i) Under channel promotion, the level of promotion effort and the prices of online and offline products are positively correlated with the difference coefficient of consumer value perception. Conversely, under generic promotion, the level of promotion effort and the prices of online and offline products initially decrease and then increase with the difference coefficient of consumer value perception. (ii) Under the generic promotion, the differences in prices between online and offline products are significantly smaller compared to channel promotion. (iii) The remanufacturer’s profit from channel promotion is higher when the difference in consumer channel perception is either small or large. Conversely, when the difference in consumer channel perception is moderate, the optimal strategy for remanufacturers is generic promotion, thereby achieving a mutually beneficial outcome with retailers. This study provides a theoretical foundation for remanufacturers to formulate effective pricing and promotion strategies in dual-channel marketing, thereby enhancing the market recognition and sales of remanufactured products.

1. Introduction

With the progress of industrialization and the advancement of technology, products are being updated at an accelerating pace, resulting in the abandonment of many products that still retain significant utility. Compared to manufacturing new products, remanufactured products offer substantial economic and environmental advantages, including a 50% reduction in costs, 60% savings in energy, 70% conservation of materials, and over 80% reduction in carbon emissions [1]. Remanufacturing has thus emerged as a crucial measure for extracting residual value from these abandoned end-of-life products and lowering unit production costs. Therefore, numerous well-known enterprises (such as Apple, Canon, HP, Lenovo, Panasonic, etc.) have incorporated remanufacturing practices into their operational frameworks to expand their market share and enhance brand reputation through the production of remanufactured products. Moreover, the role of the Internet in trade activities has been increasingly important, and the advent of e-commerce has significantly changed consumer purchasing patterns. According to Statista, it is predicted that the total sales across the world will reach USD 5.8 trillion in 2023 and are expected to grow to over USD 8 trillion by 2027. As a result, numerous manufacturers are adopting dual-channel supply chain structures that integrate direct sales with online distribution to attract more potential consumers.

However, influenced by traditional consumer attitudes, consumers often believe new products to be of higher quality than remanufactured ones, restricting the application and market share of remanufactured products. Some surveys have indicated that only a mere 9.6% of remanufactured products online were purchased during the second half of 2022 (CNNIC, [2]). Customer recognition and acceptance of remanufactured products are essential to the circular economy. How can remanufacturers and even the entire supply chain break through this operational dilemma to increase consumer recognition and expand the market size of their products? Establishing appropriate promotion strategies for remanufactured products is a crucial measure. According to the different influences on the sales of channels, the product promotion strategies of remanufactured products are divided into two types. The first type is channel promotion, aimed at increasing the sales volume of products in the distribution channel. For instance, brands like iPhone and Xiaomi are actively involving consumers in product recycling initiatives such as “trade-in for remanufactured” alongside the establishment of physical experience stores offline to enhance consumer acceptance and propensity to purchase remanufactured products. The second type is generic promotion, emphasizing the unique advantages of remanufactured products, such as their environmental benefits and superior performance. For example, BMW has launched advertising campaigns on prominent television networks featuring the slogan “Transformation of Parts Brings New Life”, which is aimed at promoting the distinctive features of its remanufactured components, including transmissions, air conditioning compressors, and vehicle hosts.

As the primary entities in the production and operation of remanufactured products, remanufacturers often face the challenge of determining optimal promotion strategies. Within the dual-channel supply chain framework discussed in this paper, encompassing both offline direct sales and online distribution, remanufacturers that implement channel promotion strategies can utilize the offline experiential advantage to generate a “siphon effect” in demand, thereby improving the efficiency of promotions. However, this strategy incurs higher promotional costs, resulting in less competitive product pricing relative to other channels. Conversely, remanufacturers adopting generic promotion strategies can boost overall supply chain sales through a “spillover effect”. Nevertheless, this approach may induce “free-riding” behavior among online retailers, thereby diminishing promotional incentives. Therefore, it is imperative for remanufacturers to formulate appropriate pricing and promotion strategies that align with the specific characteristics of remanufactured products and market demand within dual-channel marketing. Such strategies are vital for improving the market recognition and sales performance of remanufactured products.

To summarize, within a dual-channel supply chain where remanufacturers conduct offline direct sales and retailers distribute remanufactured products online, our study considers the demand expansion effect of remanufacturer-led channel promotion and the demand spillover effect of generic promotion. It investigates product pricing and the level of promotional effort under these two distinct promotion types, systematically analyzing the effectiveness of each promotional strategy. Therefore, our research seeks to investigate the following questions:

RQ1: What is the impact of the different promotion strategies on the optimal price and sales volume of remanufactured products? How should this impact be described?

RQ2: How will the difference in consumer value perception of channels for remanufactured products affect the decisions and profits of supply chain members?

RQ3: Faced with different promotion strategies for remanufactured products, what is the optimal decision for remanufacturers? Is there a win–win situation?

To address the above questions, we first establish a theoretic game model of two members, a dominant remanufacturer and a retailer, competing in the market by selling remanufactured products while there is a cooperative relationship between the two in the distribution channel. We consider two promotion strategies: channel promotion and generic promotion, and assume the demand expansion effect from the implementation of channel promotion and the demand spillover effect from generic promotion. Then, we obtain the pricing decision, the level of promotion effort, and the profit of supply chain members of remanufactured products under each promotion strategy, respectively. Finally, we obtain the relevant factors that affect the profits of the remanufacturer and the retailer and the applicable conditions of the promotion strategies through the equilibrium analysis.

Our study has the following three main contributions: Firstly, it analyzes the influence of generic promotion strategies on the pricing strategies employed by remanufacturers. For conventional research on product promotion, the main attention has been focused on the influence of remanufacturer channel promotion on consumer utility, while the research on the pricing complexity of remanufacturer generic promotion is relatively unexplored. Consequently, this research focuses on the pricing decisions undertaken by both remanufacturers and retailers within the context of a dual-channel supply chain model, particularly when the manufacturer implements generic promotion. Secondly, this research investigates the dynamics of a dual-channel supply chain for remanufactured products that integrates both online and offline channels. Given the biggest consumer perception gap regarding remanufactured products and the differences in the online and offline shopping experiences, we recognize that online channels offer unparalleled convenience and efficiency, while offline channels provide consumers with tangible interactions with remanufactured products, thereby enhancing their appeal. To capture this subtle consumer behavior, we incorporate the parameter of difference in consumer channel perception, making our model more closely related to realistic scenarios. Finally, we capture not only the impact of remanufacturers’ promotion efforts on remanufacturer’s promotion strategies but also the impact of cost and market expansion effects on promotion strategies.

In addressing the areas of dual-channel supply chains, remanufactured products, and promotion strategies, we conducted a research gap analysis, which outlines the contributions of this study in filling these research gaps.

(i).

There are many studies that extensively review the pricing strategies of both retailers and manufacturers within dual-channel supply chains, covering advancements in the operations of retailers and manufacturers separately. However, a significant limitation of the existing research is its reliance on deterministic demand models. This study addresses this gap by analyzing pricing strategies for remanufactured products in dual-channel supply chains under conditions of uncertain demand.

(ii).

Through our investigation of the literature on remanufactured products, we found that there is limited research on the impact of consumer perception differences between online and offline channels on the sales of remanufactured products in dual-channel supply chains. Therefore, this paper focuses particularly on this area, further exploring the differences in consumer perception between different channels and their impact on the sales of remanufactured products.

(iii).

Existing studies often overlook the promotion strategies for remanufactured products and rarely address generic promotion. Our study introduces an innovative approach by examining the optimal decisions for channel and generic promotion, providing a thorough analysis of the most effective promotion strategies for remanufactured products.

This structured review highlights the research gaps and presents the unique contributions of our study in addressing these gaps, thus enhancing the academic discourse on dual-channel supply chains, remanufactured products, and promotional strategies.

The rest of this study is organized as follows. Section 2 provides a literature review. Section 3 introduces hypotheses and models. Section 4 analyzes the pricing decisions of retailers and remanufacturers under channel promotion and generic promotion strategies, respectively. Section 5 investigates the remanufacturer’s optimal promotion strategy, utilizing numerical studies to acquire further managerial insights. Section 6 presents the conclusions and suggests future research directions. All proofs are given in Appendix A.

2. Literature Review

To reflect the novelty and contribution of the present study compared to the existing literature, a contribution table is provided in

Table 1. Comparison of literature reviews.

Relevant Work	Online Channel in a Dual-Channel Supply Chain		Green Product	Uncertain Demand	Channel Promotion	Generic Promotion
	Manufacturer-Owned	Retailer-Owned
Chen et al. [3]	√				√
Li et al. [4]		√	√
Datta et al. [5]		√			√
Taleizadeh et al. [6]	√		√			√
Qian et al. [7]		√	√	√	√
Mandal et al. [8]	√		√		√
Tran et al. [9]		√		√
Berman et al. [10]	√		√
Sun et al. [11]		√		√
Kumar et al. [12]			√		√
Pu et al. [13]	√				√
This study	√		√	√	√	√

.

2.1. Dual-Channel Supply Chain

Over the past few decades, an increasing number of studies have analyzed effective operational strategies within supply chains. Initially, Anderson et al. [14] underscored the significant economic reasons for different channels serving distinct customer segments. Subsequently, Kacen et al. [15] found that dual channels not only facilitate companies in expanding their market reach but also enhance customer awareness and loyalty toward products. In recent years, researchers have concentrated on pricing strategies within various structures of dual-channel supply chains. The structure of a dual-channel supply chain can encompass retailers operating both offline and online or manufacturers distributing online while selling directly through offline stores. Luo et al. [16] have investigated the impact of channel information asymmetry and supply chain coordination strategies on retailers’ dual-channel operations. Tran et al. [9] examined the optimal pricing strategies for retailers selling a single product to consumers through both channels by constructing a cross-channel effect attractiveness model. Sun et al. [11] explored the dual-channel management issues faced by retailers selling multiple products to customers. On the other hand, when manufacturers implement dual-channel strategies, there is a heightened focus on the pricing and competitive dynamics between direct sales channels and traditional retail channels. Li and Mizuno [17] explored the power structure of manufacturers within a dual-channel context, investigating the competitive interactions between traditional retail and direct sales channels. Zhang et al. [18] examined a dual-channel supply chain where manufacturers produce both high- and low-quality products. Their findings indicate that when the product is cost-driven, manufacturers prefer to sell low-quality products through direct channels and high-quality products through retail channels. Conversely, when the product is demand-driven, manufacturers tend to sell high-quality products through direct channels and low-quality products through retail channels. Mandal et al. [8] studied a closed-loop supply chain for green products, recommending that manufacturers should sell remanufactured products directly to consumers online.

However, most of the aforementioned literature is based on deterministic demand models. Diverging from these studies, our model considers a dual-channel supply chain in which suppliers distribute products through both their direct offline channels and online retailers (Yan, Liu, Xu, and He [19] and Chen, Zhao, Yan, and Zhou [3]), integrating a nonlinear uncertain demand function. This methodology enables our research to more accurately capture the complex demand dynamics present in realistic scenarios.

2.2. Remanufactured Products

With the rising awareness of environmental protection, incorporating remanufactured products into supply chains has become an effective strategy for improving environmental quality and reducing pollutant emissions. Within this framework, the existing literature predominantly concentrates on remanufactured product pricing, sales channel selection, and the influence of consumer behavior on remanufactured product sales. Firstly, regarding the pricing of remanufactured products, Miao et al. [20] investigated the optimal production and pricing decisions of new and remanufactured products under government subsidies. Zhu et al. [21] studied the pricing problem of new/remanufactured products under different decision scenarios by constructing a two-stage supply chain of duopoly manufacturers and e-commerce platforms. Taking into account both endogenous and exogenous wholesale prices, Zhou et al. [22] examined the impact of three types of authorization contracts on manufacturer pricing strategies for both new and remanufactured products. Barman et al. [10] developed a three-tier green supply chain framework, encompassing suppliers, manufacturers, and retailers within a dual-channel structure, to evaluate the influence of product greenness and government subsidies on pricing determinations and supply chain member profitability. Their findings indicated that government subsidies can alleviate the costs associated with green products and confer benefits upon both manufacturers and suppliers. In contrast to the methodology employed in the referenced study, which utilizes consistent pricing strategies across online and offline channels to minimize channel conflicts, this paper, based on a sequential game framework, proposes that retailers establish distribution prices after observing the prices set independently by manufacturers for each channel. This approach better reflects real-world dynamics.

Furthermore, concerning the selection of sales channels for remanufactured products, Yan et al. [4] analyzed the environmental implications associated with different sales channels for remanufactured products. Their findings suggest that establishing direct sales channels for remanufactured products is more environmentally sustainable than relying on third-party sales. He et al. [23] delineated the criteria dictating when manufacturers should opt to distribute remanufactured products through third-party entities or platforms to become eligible for government subsidies. Liang et al. [24] concluded that in scenarios where the establishment cost of direct channels is high, manufacturers exhibit a preference for retail channels to sell remanufactured products. Lastly, regarding the impact of consumer behavior on the sales of remanufactured products, the study by Li et al. [25] delved into the strategies employed by supply chain members for direct sales and distribution of new/remanufactured products under varying competitive conditions. Additionally, Ma et al. [26] investigated the dual reference behavior of consumers in the context of selecting remanufactured products within a two-period model in which manufacturers employ a “trade-in” strategy. Wang et al. [27] investigate the optimal pricing problem of remanufactured products under three different power structures of consumer behavior and find supply chain members should adopt lower pricing strategies to expand demand when consumer preference differences and sensitivity coefficients of consumer regret expectations are high.

2.3. The Effectiveness of Sales Promotion Strategies

The effectiveness of promotion in attracting potential consumers’ interest and influencing them to develop favorable purchasing tendencies has attracted significant attention from both marketing practitioners and scholars [12,28]. For instance, Khouja et al. [29] found that the implementation of promotion is always favorable to the manufacturers. Rainer [30] extended the aforementioned model into a market decision-making environment characterized by multi-period stochastic demand, corroborating the finding that manufacturers’ implementation of promotion increases their own revenue. Yu et al. [31], through the establishment of a manufacturer-dominated Stackelberg game model, analyzed promotion decisions on a network platform, revealing that the platform’s channel promotion engenders an expansion in the sales of both manufacturers and the platform. However, some scholars argue that product promotion in a competitive market environment may reduce the profits of the supply chain and its members. Qian et al. [7], employing a game model involving a manufacturer, a retailer, and a remanufacture to investigate the impact of digital promotion, found that when product substitutability is high, manufacturers’ implementation of promotion results in a reduction of retailers’ profits. In the analysis of a supply chain comprised of two manufacturers and one retailer, Salma and Guiomar [32] explored manufacturers’ generic promotion strategies for differentiated products. Their findings reveal a rise in the prices of differentiated products with increasing promotion efforts, with retailers consistently benefiting from manufacturers’ promotion strategies.

It is worth noting that recent scholarly work has expanded to analyze the effectiveness of joint channel promotions by supply chain members. For instance, Tsay and Agrawal [33] found that joint promotion by two channels can generate positive demand externalities, achieving complementary advantages between online and offline channels. Zhang et al. [34] examined the impact of joint promotion on supply chain profits, concluding that when manufacturers implement brand differentiation strategies, cooperative promotion can enhance profitability. Pietro et al. [35] discovered that joint promotions by retailers can achieve a “win-win-win” scenario for channel members and consumers. The aforementioned literature considers the positive impact of multichannel joint promotions on consumer utility and the amplification effect on total demand. However, they generally assume that product demand networks are relatively independent or treat them as a whole in their studies. In contrast, this paper simultaneously considers the expansion effect of channel promotion on the demand of the implementing party and the spillover effect of generic promotion on other channels. It examines the impact of these two promotion strategies on product pricing decisions in the context of perception differences between online and offline channels.

A comprehensive review of the literature reveals that most existing studies on promotional strategies primarily focus on their impact on consumer purchasing decisions for traditional products (Datta et al. [5], Pu et al. [13], Cao and Li [36], and Min et al. [37]). However, the relationship between promotional strategies and remanufactured products has been less explored. Some research has examined the effects of sales efforts within green supply chains, with Codini and Liang [38] demonstrating that promotional efforts have a significantly positive impact on green consumption. Yang et al. [39] incorporated quotas and transaction regulations into dual-channel supply chains, finding that promotions for remanufactured products consistently enhance profits for manufacturers and the entire supply chain. Taleizadeh et al. [6] further identified that joint promotion by manufacturers and retailers in closed-loop green supply chains can increase total supply chain profits. Therefore, further research is required to investigate how different types of promotional strategies can more effectively stimulate the consumption of remanufactured products. Our study addresses this gap by considering the spillover effect of generic promotion on remanufactured products, thereby enriching the literature on promotion and remanufactured products.

3. Definition of Model and Hypotheses

3.1. Problem Definition

We consider a two-stage supply chain system involving a remanufacturer (denoted as $d$) and a retailer (denoted as $r$). In the production and sale of remanufactured products, remanufacturers serve as the pivotal enterprises in the remanufacturing production line. Consequently, we assume that the remanufacturer is the dominant player in the Stackelberg game and sells products through offline direct channels at a price denoted as $p_d$. Simultaneously, the remanufacturer wholesales the products to the retailer at a price denoted as $w$. Subsequently, the retailer resells the wholesale products through an online channel at a price denoted as $p_r$. This supply chain model is quite common in the production and sale of remanufactured products. For example, Greencitizen is a company dedicated to remanufacturing and recycling electronic products. They offer remanufactured electronic products, such as computers, photography equipment, and other electronic devices, in their offline channel. Additionally, they also collaborate with online retailers such as Newegg to distribute their products. This system is illustrated in Figure 1.

The remanufacturer is confronted with two distinct promotion types: one is channel promotion, which is strategically designed to augment sales volume through its proprietary channel. Based on the media richness theory, the execution of channel promotion by the remanufacturer is posited to enhance consumers’ utility for offline channel purchases. The increased part is expressed as $k_{1}s$ [40], where $k_1$ signifies the demand elasticity coefficient for channel promotion, $s$ denotes the level of effort for remanufacturers to implement promotion strategies, and $s\in [0,1]$. The alternative promotion type is generic promotion, which is characterized by the promotion of the advantages of the remanufactured product itself, such as being environmentally friendly and being no less advantageous than the performance of the new product. In consonance with media richness theory and spillover effect theory, the market feedback engendered by the remanufacturer’s generic promotion is anticipated to elevate consumers’ utility in procuring products across diverse channels. The increased components are delineated as $r_{2}s$ and $k_{2}s$ [41], with $r_2$ and $k_2$ representing the demand elasticity coefficients for online and offline channels, respectively. To discriminate between the two promotion strategies, decision variables under channel promotion and generic promotion are designated by superscripts “M” and “N”, respectively. The implementation of promotion by the remanufacturer incurs associated costs (including labor costs, maintenance costs, etc.), which manifest as quadratic functions of the effort level of promotion. This is expressed as $C(s)=\frac{1}{2}{\eta }_i{s}^2$ [30], $i=1,2$, where ${\eta }_1$ and ${\eta }_2$ denote the cost coefficient for implementing channel promotion and generic promotion, respectively. In congruence with the assumptions made by Chen [42] and Ali et al. [43], it is posited that ${\eta }_1<{\eta }_2$.

3.2. Abbreviation Part

The abbreviations in

Table 2. Abbreviation list.

Abbreviattion	Related Description
Indices
$i$	Index of firms’ channel: remanufacturer, $i=d; retailer, i=r$
$j$	Index of promotion strategy, $j=M, N$
$M$	Channel promotion
$N$	Generic promotion
Parameters
$k_1$	The demand elasticity coefficient for offline channels under channel promotion
$k_2$	The demand elasticity coefficient for offline channels under generic promotion
$r_2$	The demand elasticity coefficient for online channels under generic promotion
${\eta }_1$	The cost coefficient under channel promotion
${\eta }_2$	The cost coefficient under generic promotion, ${\eta }_1<{\eta }_2$
Decision variables
$p_i^j$	The selling price of the firms’ channel $i=d,r$
$w^j$	Wholesale price of remanufacturer under promotion strategy $j=M, N$
$s^j$	The level of promotional effort of remanufacturer under promotion strategy $j=M, N$,$s\in [0,1]$
Dependent variables
$C(s)$	Promotion cost
$D_i^j$	Demand of the firms’ channel $i$ under the promotion strategy $j$,$i=d,r;$$j=M, N$
${\Pi }_i^j$	Profit of the firms $i$ under the promotion strategy $j$,$i=d,r;$$j=M, N$

are used to establish the model.

3.3. Hypotheses

The hypotheses to establish the model are explained as follows:

Hypothesis 1. 

The perceived value of consumers regarding products in offline channels is denoted as V, following a uniform distribution. Acknowledging the distinct shopping experiences between online and offline channels, as in the introduction of Chen et al. [44], which describes the valuation difference brought to consumers by online and offline channel shopping experience, it is defined as the difference coefficient of consumer value perception. It represents the differences in consumers’ channel perception values. When consumers choose online purchases, they are deprived of the offline experience, trial services, and the ability to perceive product attributes through tangible interaction. Consequently, the perceived value for products in the online channel is expressed as $\beta v$ and $\beta \in [0,1]$. A higher value signifies that consumers attribute a greater value to the online channel, leading to enhance acceptance of the retailer’s online channel.

Hypothesis 2. 

The expected utility for consumers engaging in product purchases is linear with price. In the context of the remanufacturer implementing channel promotion, the anticipated utility for consumers engaging in offline purchases is denoted as $v-p_d^M+k_1{s}^M$. Similarly, in the case of the remanufacturer implementing generic promotion, the utility for consumers making online channel purchases is represented as $v-p_r^N+r_2{s}^N$, while the utility for offline channel purchases is $v-p_d^N+k_2{s}^N$. Consumers make purchasing decisions and choose their preferred channel based on a utility comparison. Additionally, it is posited that the demand for offline and online is denoted by $D_d^j$ and $D_r^j$, and $j=M,N$, respectively.

Hypothesis 3. 

The remanufacturer’s promotion decision satisfies “incentive compatibility” [45]. This implies that the remanufacturer will only implement a promotion decision when $D_d^j>0$. In instances where there are no consumer purchases subsequent to the promotion implementation ($D_d^j=0$), the remanufacturer will cease the promotion.

This study constructs a dynamic game model under demand uncertainty. The sequential stages of the game are as follows: (1) The remanufacturer, who is the dominant player, decides on the promotion strategy. (2) The remanufacturer decides the offline channel product price, wholesale price, and the level of promotion effort. (3) After observing the remanufacturer’s pricing decision, the retailer decides the online channel product price. (4) The consumers decide whether to make a purchase and specific channel for the transaction. This decision sequence is shown in Figure 2.

4. Models Analysis and Results

4.1. Pricing Decision under Channel Promotion Strategy

Under the remanufacturer’s channel promotion strategy, consumers purchasing products through offline channels must satisfy the following conditions: $v-p_d^M+k_1{s}^M\ge 0$ and $v-p_d^M+k_1{s}^M\ge \beta v-p_r^M$, with which we can obtain: $v\ge \max \left\{\left.p_d^M-k_1{s}^M,\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }\right\}\right.$. And only if $p_r^M\ge \beta (p_d^M-k_1{s}^M)$, $p_d^M-k_1{s}^M\ge \frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }$ is met. Similarly, consumers purchasing products through online channels need to satisfy the following conditions: $\beta v-p_r^M\ge 0$ and $\beta v-p_r^M\ge v-p_d^M+k_1{s}^M$, we can get $\frac{p_r^M}{\beta }\le v\le \frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }$. And then we find only $P_r^M\le \beta (p_d^M-k_1{s}^M)$, this case exists. If $\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }>1$, only the online channel has a positive demand. In summary, $D_d^M$ and $D_r^M$ in channel promotion can be obtained as shown in Equations (1) and (2):

$$D_d^M=\left\{\begin{array}{c}1-p_d^M+k_1{s}^M,p_r^M\ge \beta (p_d^M-k_1{s}^M)\\ \begin{array}{l}1-\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta },p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)\\ 0,p_r^M\le p_d^M-k_1{s}^M-1+\beta \end{array}\end{array}\right.$$

(1)

$$D_r^M=\left\{\begin{array}{c}0,p_r^M\ge \beta (p_d^M-k_1{s}^M)\\ \begin{array}{l}\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }-\frac{p_r^M}{\beta },p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)\\ 1-\frac{p_r^M}{\beta },p_r^M\le p_d^M-k_1{s}^M-1+\beta \end{array}\end{array}\right.$$

(2)

4.1.1. Analysis of the Retailer’s Decision

According to the previous assumption, the remanufacturer is the dominant player in the Stackelberg game, so the reverse induction method is adopted to solve the problem starting from the pricing strategy of the retailer. From (1) and (2), we can obtain the following.

(1).

When $p_r^M\le p_d^M-k_1{s}^M-1+\beta$, the retailer’s profit is ${\Pi }_r^M=(p_r^M-w^M)D_r^M=(p_r^M-w^M)(1-\frac{p_r^M}{\beta })$.

Given $p_d^M$, $s^M$ and $w^M$, by solving $\frac{\partial {\Pi }_r^M}{\partial p_r^M}=(p_r^M-w^M)D_r^M=(p_r^M-w^M)(1-\frac{p_r^M}{\beta })=0$, subject to the constraint $\frac{{\partial }^2{\Pi }_r^M}{\partial {(p_r^M)}^2}=-\frac{2}{\beta }<0$, the retailer’s price response function is obtained: $p_r^{M*}=\frac{\beta +w^M}{2}$. Substituting $p_r^{M*}$ into $p_d^M\ge p_r^{M*}+k_1{s}^M+1-\beta$, followed by simplification, yields $p_d^M\ge \frac{2k_1{s}^M+w^M+2-\beta }{2}$.

Following Hypothesis 3, it can be deduced that in the absence of remanufacturer demand, there is no motivation for the implementation of channel promotion by the remanufacturer. Consequently, this paper does not contemplate such a scenario.

(2).

When $p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)$, the retailer’s profit is

$${\Pi }_r^M=(p_r^M-w^M)D_r^M=(p_r^M-w^M)(\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }-\frac{p_r^M}{\beta })$$

(3)

Given $p_d^M$, $s^M$ and $w^M$, through the resolution of the equation $\frac{\partial {\Pi }_r^M}{\partial p_r^M}=(p_r^M-w^M)(\frac{p_d^M-p_r^M-k_1{s}^M}{1-\beta }-\frac{p_r^M}{\beta })=0$, simultaneously fulfilling $\frac{{\partial }^2{\Pi }_r^M}{\partial {(p_r^M)}^2}=-\frac{2}{\beta (1-\beta )}<0$, the price response function for the retailer can be derived:

$$p_r^{M*}=\frac{\beta (p_d^M-k_1{s}^M)+w^M}{2}$$

(4)

Then, substituting $p_r^{M*}$ into $p_d^M-k_1{s}^M-1+\beta \le p_r^{M*}\le \beta (p_d^M-k_1{s}^M)$, followed by simplification, yields $\frac{\beta k_1{s}^M+w^M}{\beta }\le p_d^M\le \frac{k_1{s}^M(2-\beta )+w^M+2(1-\beta )}{2-\beta }$.

(3).

When $p_r^M\ge \beta (p_d^M-k_1{s}^M)$, we obtain $p_d^M\le \frac{p_r^M+\beta k_1{s}^M}{\beta }$. Then, we can let $g(p_r^M)=\frac{p_r^M+\beta k_1{s}^M}{\beta }$, and by solving $p_d^M\le g_{\min }(p_r^M)=g(\frac{\beta (p_d^M-k_1{s}^M)+w^M}{2})$, we can obtain $p_d^M\le \frac{\beta k_1{s}^M+w^M}{\beta }$; thus, the demand for the online channel is 0.

4.1.2. Analysis of the Remanufacturer’s Decision

The remanufacturer’s decision must satisfy the conditions $0<p_d^M<1$ and $0<w^M<1$. As expounded above, the viable area for the remanufacturer’s pricing is depicted in Figure 3.

• Region I: $p_d^M\le \frac{\beta k_1{s}^M+w^M}{\beta }$, $(p_d^M,w^M)\in R_1^M$;
• Region II: $\frac{\beta k_1{s}^M+w^M}{\beta }\le p_d^M\le \frac{k_1{s}^M(2-\beta )+w^M+2(1-\beta )}{2-\beta }$, $(p_d^M,w^M)\in R_2^M$;
• Region III: $\frac{k_1{s}^M(2-\beta )+w^M+2(1-\beta )}{2-\beta }\le p_d^N\le \frac{2k_1{s}^M+w^M+2-\beta }{2}$, $(p_d^M,w^M)\in R_3^M$;
• Region IV: $p_d^M\ge \frac{2k_1{s}^M+w^M+2-\beta }{2}$, $(p_d^M,w^M)\in R_4^M$;

In Region IV, when $(p_d^M,w^M)\in R_4^M$, the demand for the offline channel is 0. In accordance with the assumption of incentive compatibility, the remanufacturer lacks the incentive to carry out promotion strategies. In Region III, when $(p_d^M,w^M)\in R_3^M$, the retailer’s optimal price is attained at the boundary. Comparative analysis of profit values in the two boundary regions indicates higher profits when $p_r^{M*}=\frac{\beta +w^M}{2}$. As a result, the remanufacturer continues to lack the incentive to implement promotions in this region. Consequently, the subsequent analysis exclusively concentrates on the decision-making processes in Regions II and I. In addition, since all data in this paper have been normalized, the dashed lines represent the maximum range of $p_d^M$ and $w^M$.

(1).

When $p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)$, we obtain $p_r^{M*}=\frac{\beta (p_d^M-k_1{s}^M)+w^M}{2}$. Hence, the profit for the remanufacturer can be expressed as follows:

$${\Pi }_d^M=p_d^M(1-\frac{p_d^M-p_r^{M*}-k_1{s}^M}{1-\beta })+w^M(\frac{p_d^M-p_r^{M*}-k_1{s}^M}{1-\beta }-\frac{p_r^{M*}}{\beta })-\frac{1}{2}{\eta }_1(s^M{)}^2$$

(5)

Lemma 1 can be deduced from Equation (5).

Lemma 1. 

When $p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)$, ${\Pi }_d^M$ exhibits strict joint concavity concerning $p_d^M$ and $w^M$, while it is not jointly concave concerning $p_d^M$, $w^M$, and $s^M$.

The proof of Lemma 1 is given in Appendix A. From Lemma 1, the direct application of first-order optimality conditions to obtain optimal solutions $p_d^M$, $w^M$, and $s^M$ is not feasible. Consequently, a two-stage optimization approach is employed. Initially, the offline channel selling price $p_d^{M*}$ and the wholesale price $w^{M*}$ are determined to maximize the remanufacturer’s profit function. Following this, the obtained values of $p_d^{M*}$ and $w^{M*}$, which are substituted into ${\Pi }_d^M$ to derive the remanufacturer’s profit function in terms of $s^M$, thereby determining the optimum.

Lemma 2. 

When $p_d^M-k_1{s}^M-1+\beta \le p_r^M\le \beta (p_d^M-k_1{s}^M)$, the offline channel price and wholesale price are determined as follows:

$$p_d^{M*}=\frac{k_1{s}^M+1}{2}$$

(6)

$$w^{M*}=\frac{\beta }{2}$$

(7)

The proof of Lemma 2 is given in Appendix A.

Theorem 1. 

Under the channel promotion strategy, when $1-\frac{k^2}{4{\eta }_1-k_1^2}<\beta <1$, the optimal pricing for the online channel and offline channel, the optimal level of promotional effort for the remanufacturer, the remanufacturer’s profit, and the retailer’s profit, respectively, can be provided as follows:

$$p_r^{M*}=\frac{\beta k_1^2(3-2\beta )-4\beta {\eta }_1(1-\beta )}{2\left[k_1^2(2-\beta )-4{\eta }_1(1-\beta )\right]}$$

(8)

$$p_d^{M*}=\frac{\beta k_1^2-4{\eta }_1(1-\beta )}{2\left[k_1^2(2-\beta )-4{\eta }_1(1-\beta )\right]}$$

(9)

$$s^{M*}=\frac{2k_1(1-\beta )}{2\left[k_1^2(2-\beta )-4{\eta }_1(1-\beta )\right]}$$

(10)

$${\Pi }_d^{M*}=\frac{4{\eta }_1(1-\beta )-\beta k_1^2}{4[4{\eta }_1(1-\beta )-k_1^2(2-\beta )]}$$

(11)

$${\Pi }_r^{M*}=\frac{\beta k_1^4(1-\beta )}{4{[4{\eta }_2(1-\beta )-k_1^2(2-\beta )]}^2}$$

(12)

The proof of Theorem 1 is given in Appendix A.

(2).

When $p_r^M\ge \beta (p_d^M-k_1{s}^M)$, the profit for the remanufacturer can be expressed as follows:

$${\Pi }_d^M=p_d^M(1-p_d^M+k_1{s}^M)-\frac{1}{2}{\eta }_1{s}^{M^2}$$

(13)

Lemma 3 can be deduced from Equation (13).

Lemma 3. 

When $k_1^2<2{\eta }_1$,  ${\Pi }_d^M$ exhibits strict joint concavity concerning $p_d^M$ and $s^M$.

The proof of Lemma 3 is given in Appendix A. Consequently, Theorem 2 can be deduced.

Theorem 2. 

Under the channel promotion strategy when $0<\beta <1-\frac{k^2}{4{\eta }_1-k_1^2}$.

(a)

If $k_1^2<2{\eta }_1$, the optimal pricing for the offline channel, the optimal level of promotional effort for the remanufacturer, and the remanufacturer’s profit are, respectively, as follows:

$$p_d^{M*}=\frac{{\eta }_1}{2{\eta }_1-k_1^2}$$

(14)

$$s^{M*}=\frac{k_1^2}{2{\eta }_1-k_1^2}$$

(15)

$${\Pi }_d^{M*}=\frac{{\eta }_1}{4{\eta }_1-2k_1^2}$$

(16)

(b)

If $k_1^2>2{\eta }_1$, then

$$p_d^{M*}=\frac{k_1+1}{2}$$

(17)

$$s^{M*}=1$$

(18)

$${\Pi }_d^{M*}=\frac{1}{4}+\frac{k_1^2-2{\eta }_1+2k_1}{4}$$

(19)

The proof of Theorem 2 is given in Appendix A. Theorems 1 and 2 elucidate that within the framework of channel promotion, the optimal decisions made by the remanufacturer are linked to the perceived value difference among consumers across distinct channels. When $\beta$ is comparatively small, the consumers display a heightened inclination towards accessing the offline channel. Consequently, the remanufacturer’s optimal decision entails exclusively conducting direct sales through the offline channel. Conversely, when $\beta$ is larger, consumers ascribe a heightened perceived value to the online channel, resulting in a diminished proclivity to access the offline channel. In such circumstances, the remanufacturer’s optimal strategy involves collaborating with retailers for online product sales while concurrently pursuing direct sales through the offline channel.

4.2. Pricing Decision under Generic Promotion Strategy

Under the remanufacturer’s generic promotion strategy, consumers purchasing products through offline channels must satisfy the following conditions: $v-p_d^N+k_2{s}^N\ge 0$ and $v-p_d^N+k_2{s}^N\ge \beta v-p_r^N+r_2{s}^N$, we can obtain $v\ge \max \left\{\left.p_d^N-k_2{s}^N,\frac{p_d^N-p_r^N+r_2{s}^N-k_2{s}^N}{1-\beta }\right\}\right.$. And only if $p_r^N-r_2{s}^N\ge \beta (p_d^N-k_2{s}^N)$, $p_d^N-k_2{s}^N\ge \frac{p_d^N-p_r^N+r_2{s}^N-k_2{s}^N}{1-\beta }$ is met. Similarly, consumers purchasing products through online channels need to satisfy the following conditions: $\beta v-p_r^N+r_2{s}^N\ge 0$ and $\beta v-p_r^N+r_2{s}^N\ge v-p_d^N+k_2{s}^N$. Thus, it can be derived that $\frac{p_r^N-r_2{s}^N}{\beta }\le v\le {\frac{p_d^N-p_r^N+r_2{s}^N-k_{2}s}{1-\beta }}^N$. Furthermore, this case exists only when $p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)$. If ${\frac{p_d^N-p_r^N+r_2{s}^N-k_{2}s}{1-\beta }}^N>1$, only the online channel has a positive demand. In summary, $D_d^N$ and $D_r^N$ in generic promotion can be obtained as shown in (20) and (21):

$$D_d^N=\left\{\begin{array}{c}1-p_d^N+k_2{s}^N,p_r^N-r_2{s}^N\ge \beta (p_d^N-k_2{s}^N)\\ \begin{array}{l}1-\frac{p_d^N-p_r^N+r_{2}s-k_2{s}^N}{1-\beta },p_d^N-k_2{s}^N-1+\beta \le p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)\\ 0,p_r^N-r_2{s}^N\le p_d^N-k_2{s}^N-1+\beta \end{array}\end{array}\right.$$

(20)

$$D_r^N=\left\{\begin{array}{c}0,p_r^N-r_2{s}^N\ge \beta (p_d^N-k_2{s}^N)\\ \begin{array}{l}\frac{p_d^N-p_r^N+r_2{s}^N-k_2{s}^N}{1-\beta }-\frac{p_r^N-k_2{s}^N}{\beta },p_d^N-k_2{s}^N-1+\beta \le p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)\\ 1-\frac{p_r^N-k_2{s}^N}{\beta },p_r^N-r_2{s}^N\le p_d^N-k_2{s}^N-1+\beta \end{array}\end{array}\right.$$

(21)

4.2.1. Analysis of the Retailer’s Decision

(1).

When $p_r^N-r_2{s}^N\le p_d^N-k_2{s}^N-1+\beta$, the retailer’s profit function is

$${\Pi }_r^N=(p_r^N-w^N)D_r^N=(p_r^N-w^N)(1-\frac{p_r^N-r_2{s}^N}{\beta })$$

Given $p_d^N$, $s^N$, and $w^N$, the retailer’s first ordered condition for profit maximization is $\frac{\partial {\Pi }_r^N}{\partial p_r^N}=(p_r^N-w^N)(1-\frac{p_r^N-r_2{s}^N}{\beta })=0$. Moreover, the second ordered derivative concerning price is $\frac{{\partial }^2{\Pi }_r^N}{\partial {(p_r^N)}^2}=-\frac{2}{\beta (1-\beta )}<0$; thus, the retailer’s optimal price response function is obtained following $p_r^{N*}=\frac{\beta +w^N+r_2{s}^N}{2}$. Then, substituting $p_r^{N*}$ into $p_r^N-r_2{s}^N\le p_d^N-k_2{s}^N-1+\beta$, followed by simplification, yields $p_d^N\ge \frac{2k_2{s}^N+w^N+r_2{s}^N+2-\beta }{2}$.

(2).

When $p_d^N-k_2{s}^N-1+\beta \le p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)$, the retailer’s profit is

$${\Pi }_r^N=(p_r^N-w^N)D_r^N=(p_r^N-w^N)(\frac{p_d^N-p_r^N+r_2{s}^N-k_2{s}^N}{1-\beta }-\frac{p_r^N-r_2{s}^N}{\beta })$$

(22)

Given $p_d^N$, $s^N$, and $w^N$, by solving $\frac{\partial {\Pi }_r^N}{\partial p_r^N}=(p_r^N-w^N)(\frac{p_d^N-p_r^N+r_2{s}^N-k_2{s}^N}{1-\beta }-\frac{p_r^N-r_2{s}^N}{\beta })=0$, subject to $\frac{{\partial }^2{\Pi }_r^N}{\partial {(p_r^N)}^2}=-\frac{2}{\beta (1-\beta )}<0$, we can obtain the retailer’s optimal price response:

$$p_r^{N*}=\frac{\beta (p_d^N-k_2{s}^N)+w^N+r_2{s}^N}{2}$$

(23)

Substituting $p_r^{N*}$ into $p_r^N-r_2{s}^N\le p_d^N-k_2{s}^N-1+\beta$, followed by simplification, yields $\frac{\beta k_2{s}^N+w^N-r_2{s}^N}{\beta }\le p_d^N\le \frac{k_2{s}^N(2-\beta )+w^N+2(1-\beta )-r_2{s}^N}{2-\beta }$.

(3).

When $p_r^N-r_2{s}^N\ge \beta (p_d^N-k_2{s}^N)$, the offline channel’s price satisfies the following condition: $p_d^N\le \frac{p_r^N+r_2{s}^N}{\beta }+k_2{s}^N$. Let $h(p_r^N)=\frac{p_r^N+r_2{s}^N}{\beta }+k_2{s}^N$, by solving $p_d^N\le h_{\min }(p_r^N)=h(\frac{\beta (p_d^N-k_2{s}^N)+w^N+r_2{s}^N}{2})$, we obtain $p_d^N\le \frac{\beta k_2{s}^N+w^N-r_2{s}^N}{\beta }$, and the demand for the online channel is 0.

4.2.2. Analysis of the Remanufacturer’s Decision

Similarly, the remanufacturer’s decision must satisfy $0<p_d^N<1$, $0<w^N<1$, and then we can obtain $\frac{\beta k_2{s}^N+w^N-r_2{s}^N}{\beta }\le \frac{k_2{s}^N(2-\beta )+w^N+2(1-\beta )-r_2{s}^N}{2-\beta }\le \frac{2k_2{s}^N+w^N+r_2{s}^N+2-\beta }{2}$.

Consequently, the viable area for the remanufacturer’s pricing can be depicted, as indicated in Figure 4, where

• Region I: $p_d^N\le \frac{\beta k_2{s}^N+w^N-r_2{s}^N}{\beta }$, $(p_d^N,w^N)\in R_1^N$;
• Region II: $\frac{\beta k_2{s}^N+w^N-r_2{s}^N}{\beta }\le p_d^N\le \frac{k_2{s}^N(2-\beta )+w^N+2(1-\beta )-r_2{s}^N}{2-\beta }$, $(p_d^N,w^N)\in R_2^N$;
• Region III: $\frac{k_2{s}^N(2-\beta )+w^N+2(1-\beta )-r_2{s}^N}{2-\beta }\le p_d^N\le \frac{2k_2{s}^N+w^N+r_2{s}^N+2-\beta }{2}$, $(p_d^N,w^N)\in R_3^N$;
• Region IV: $p_d^N\ge \frac{2k_2{s}^N+w^N+r_2{s}^N+2-\beta }{2}$, $(p_d^N,w^N)\in R_4^N$;

Figure 4. Viable areas of remanufacturers’ offline channel prices and wholesale prices under generic promotion.

Figure 4. Viable areas of remanufacturers’ offline channel prices and wholesale prices under generic promotion.

In Region IV, i.e., $(p_d^N,w^N)\in R_4^N$, the demand for the offline channel is 0, and the remanufacturer lacks the motivation to implement generic promotion. In Region III, i.e., $(p_d^N,w^N)\in R_3^N$, the optimal pricing for the retailer is achieved at the boundary. A comparison of profit values in the two boundary regions reveals that profits are higher at $p_r^{N*}=\frac{\beta +w^N+r_2{s}^N}{2}$. Consequently, the remanufacturer also refrains from implementing generic promotion. Thus, this section focuses on Regions I and II. In addition, since all data in this paper have been normalized, the dashed lines represent the maximum range of $p_d^N$ and $w^N$.

(1).

When $p_d^N-k_2{s}^N-1+\beta \le p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)$, we obtain $p_r^{N*}=\frac{\beta (p_d^N-k_2{s}^N)+w^N+r_2{s}^N}{2}$. Hence, the profit function for the remanufacturer can be expressed as follows:

$${\Pi }_d^N=p_d^N(1-\frac{p_d^N-p_r^{N*}+r_2{s}^N-k_2{s}^N}{1-\beta })+w^N(\frac{p_d^N-p_r^{N*}+r_2{s}^N-k_2{s}^N}{1-\beta }-\frac{p_r^{N*}-r_2{s}^N}{\beta })-\frac{1}{2}{\eta }_2(s^N{)}^2$$

(24)

Based on (24), Lemma 4 can be deduced.

Lemma 4. 

Under the condition of the remanufacturer implementing generic promotion, the remanufacturer’s profit is strictly concave concerning both $p_d^N$ and $w^N$. While it does not exhibit joint concavity concerning $p_d^N$, $w^N$, and $s^N$.

The proof of Lemma 4 is given in Appendix A. From Lemma 4, it is obvious that the optimal solutions for $p_d^N$, $w^N$, and $s^N$ cannot be directly obtained using the first ordered optimality conditions. As a result, a two-stage optimization approach is employed. Initially, the offline and wholesale prices are determined to maximize the remanufacturer’s profit. Subsequently, the values of $p_d^{N*}$ and $w^{N*}$ obtained in the first stage are substituted into ${\Pi }_d^N$ to formulate the remanufacturer’s profit function concerning $s^N$, ultimately leading to the determination of the optimal.

Lemma 5. 

When $p_d^N-k_2{s}^N-1+\beta \le p_r^N-r_2{s}^N\le \beta (p_d^N-k_2{s}^N)$, the offline channel selling price and wholesale price are determined as follows:

$$p_d^{N*}=\frac{k_2{s}^N+1}{2}$$

(25)

$$w^{N*}=\frac{r_2{s}^N+\beta }{2}$$

(26)

The proof of Lemma 5 is given in Appendix A.

Theorem 3. 

Under the generic promotion strategy, when $\underset{¯}{\mathsf{\Phi }}<\beta <\overline{\mathsf{\Phi }}$, we obtain the optimal pricing for the online channel and offline channel, the optimal level of promotional effort for the remanufacturer, the remanufacturer’s profit, and the retailer’s profit, respectively, as follows:

$$p_r^{N^{*}}=\frac{\beta k_2{r}_2(3-\beta )+4{\beta }^2{\eta }_2(1-\beta )-{\beta }^2{k}_2^2(3-2\beta )-\beta r_2^2}{4\beta (k_2{r}_2+2\beta -2\beta {\eta }_2)-2\beta k_2^2(2-\beta )-2r_2^2}$$

(27)

$$p_d^{N*}=\frac{4\beta {\eta }_2(1-\beta )+\beta k_2(2r_2-\beta k)-r_2^2}{4\beta (k_2{r}_2+2\beta -2\beta {\eta }_2)-2\beta k_2^2(2-\beta )-2r_2^2}$$

(28)

$$w^{N*}=\frac{4{\beta }^2{\eta }_2(1-\beta )-{\beta }^2{k}_2^2(2-\beta )+\beta r_2(2k_2-\beta )}{4\beta (k_2{r}_2+2\beta -2\beta {\eta }_2)-2\beta k_2^2(2-\beta )-2r_2^2}$$

(29)

$$s^{N*}=\frac{2\beta k_2(1-\beta )}{2\beta (k_2{r}_2+2{\eta }_2-2\beta {\eta }_2)-\beta k_2^2(2-\beta )-r_2^2}$$

(30)

$${\Pi }_d^{N*}=\frac{4\beta {\eta }_2(1-\beta )+\beta k_2(2r_2-\beta k_2)-r_2^2}{16\beta {\eta }_2(1-\beta )+4r_2(2\beta k_2-r_2)-4\beta k_2^2(2-\beta )}$$

(31)

$${\Pi }_r^{N*}=\frac{\beta k_2^2(1-\beta ){(\beta k_2-r_2)}^2}{{[4\beta {\eta }_2(1-\beta )+r_2(2\beta k_2-r_2)-\beta k_2^2(2-\beta )]}^2}$$

(32)

where

$$\underset{¯}{\mathsf{\Phi }}=\frac{2{\eta }_2+k_2{r}_2-k_2^2-\sqrt{4{\eta }_2({\eta }_2-r_2^2-k_2^2+k_2{r}_2)+k_2^2(k_2^2-2k_2{r}_2+2r_2^2)}}{4{\eta }_2-k_2^2};\overline{\mathsf{\Phi }}=\frac{2{\eta }_2+2k_2{r}_2-k_2^2+\sqrt{4{\eta }_2({\eta }_2-r_2^2-k_2^2+k_2{r}_2)+k_2^2(k_2^2-2k_2{r}_2+2r_2^2)}}{4{\eta }_2-k_2^2}$$

The proof of Theorem 3 is given in Appendix A.

(2).

when $p_r^N-r_2{s}^N\ge \beta (p_d^N-k_2{s}^N)$, $(p_d^N,w^N)\in R_1$, the profit for the remanufacturer can be expressed as follows:

$${\Pi }_d^N=p_d^N(1-p_d^N+k_2{s}^N)-\frac{1}{2}{\eta }_2{s}^{N^2}$$

(33)

Theorem 4 can be deduced from Equation (33).

Theorem 4. 

Under the generic promotion strategy, $\beta \in \left\{[0,\min (0,\underset{¯}{\mathsf{\Phi }})]\right.\cup \left.[\overline{\mathsf{\Phi }},\max (\overline{\mathsf{\Phi }},1)]\right\}$.

(a)

If $k_2^2<2{\eta }_2$, then

$$p_d^{N*}=\frac{{\eta }_2}{2{\eta }_2-k_2^2}$$

(34)

$$s^{N*}=\frac{k_2^2}{2{\eta }_2-k_2^2}$$

(35)

$${\Pi }_d^{N*}=\frac{{\eta }_2}{4{\eta }_2-2k_2^2}$$

(36)

(b)

If $k_2^2>2{\eta }_2$, then

$$p_d^{N*}=\frac{k_2+1}{2}$$

(37)

$$s^{N*}=1$$

(38)

$${\Pi }_d^{N*}=\frac{1}{4}+\frac{k_2^2-2{\eta }_2+2k_2}{4}$$

(39)

The proof of Theorem 4 is given in Appendix A. Under the context of generic promotion, it is obvious that with sufficiently small values $\beta$, the consumers show a preference for purchasing through offline channels. As a result, the remanufacturer’s optimal strategy is to distribute products exclusively through the offline channel. When $\beta$ attains a moderate magnitude, the remanufacturer’s optimal strategy shifts towards collaboration with retailers for remanufactured product sales, concurrently incorporating direct sales through the online channel. Currently, the remanufacturer’s demand encompasses both the retailer’s online channel and direct sales through the offline channel. As $\beta$ becomes sufficiently large, the high cost associated with generic promotion hinders the remanufacturer. Consequently, the optimal strategy for the remanufacturer is to focus on direct sales through the offline channel.

5. The Optimal Promotion Strategy of Remanufacturers

Expanding on the theoretical analysis delineated earlier, this section aims to elucidate the influence of the difference coefficient of consumer value perception $\beta$ on sales prices in both online and offline channels, the profits of remanufacturer and retailer and to investigate the optimal promotion strategy of the remanufacturer. To achieve this purpose, a numerical simulation will be conducted for comprehensive analysis, and we have normalized the data to simplify the interpretation and analysis of the results (Li et al. [46], He et al. [47]). Given the condition $k_i^2>2{\eta }_i$ ($i=1,2$), the remanufacturer’s promotional effort remains consistently set at one. The prices and profits within the offline channel exhibit an upward trend with increasing values $k_i$, and they remain unaffected by the difference coefficient of consumer value perception. For illustrative purposes, this section employs the specific case of $k_i^2<2{\eta }_i$ ($i=1,2$), with the following parameter settings: $k_1=k_2=0.5$, $r_2=0.8$, ${\eta }_1=0.3$, and ${\eta }_2=0.8$; the results are shown in

Table 3. Impact $\beta$ on price and profit under remanufacturer’s channel promotion.

$\mathit{\beta }$	The Level of Promotion Effort	Offline Channel Price	Online Channel Price	Remanufacturer’s Profit	Retailer’s Profit	Profit of the Supply Chain
0.1	0.435	0.609	-	0.304	0	0.304
0.2	0.435	0.609	-	0.304	0	0.304
0.3	0.435	0.609	-	0.304	0	0.304
0.4	0.469	0.617	0.177	0.309	0.002	0.311
0.5	0.488	0.622	0.221	0.311	0.004	0.315
0.6	0.520	0.630	0.261	0.315	0.006	0.321
0.7	0.582	0.644	0.330	0.322	0.012	0.334
0.8	0.612	0.692	0.333	0.346	0.037	0.383
0.9	0.657	0.783	0.405	0.391	0.113	0.504
1	0.706	0.802	0.423	0.413	0.164	0.577

and

Table 4. Impact $\beta$ on price and profit under remanufacturer’s generic promotion.

$\mathit{\beta }$	The Level of Promotion Effort	Offline Channel Price	Online Channel Price	Remanufacturer’s Profit	Retailer’s Profit	Profit of the Supply Chain
0.1	0.370	0.592	-	0.296	0	0.296
0.2	0.370	0.592	-	0.296	0	0.296
0.3	0.370	0.592	-	0.296	0	0.296
0.4	0.833	0.708	0.658	0.354	0.065	0.419
0.5	0.671	0.668	0.611	0.334	0.034	0.368
0.6	0.603	0.651	0.617	0.325	0.024	0.349
0.7	0.583	0.646	0.645	0.323	0.020	0.342
0.8	0.588	0.647	0.694	0.324	0.022	0.346
0.9	0.626	0.657	0.734	0.329	0.027	0.356
1	0.370	0.592		0.296	0	0.296

. It is important to note that within this range $k_i^2<2{\eta }_i$, other valid values exhibit similar effects on prices, profits, and other related factors as the results presented herein. Due to space constraints, these additional results are not included in this paper.

As can be seen from the table:

(1).

In a case where demand exists in both online and offline channels, the implementation of channel promotion by the remanufacturer leads to an increase in product prices in both online and offline channels as the difference coefficient of consumer value perception rises. In contrast, the adoption of generic promotion initially causes a decline in prices in both channels, followed by an increase in response to an escalation in the difference coefficient of consumer value perception. A comparative analysis of the price differential between the two promotion strategies reveals an apparent elevation in the online channel price after the implementation of generic promotion, notably surpassing that of channel promotion. Furthermore, the observed reduction in price disparities between online and offline channels signifies that the spillover effect of generic promotion bestows a pricing advantage upon the retailer.

(2).

In a case where there is positive demand in both channels, if remanufacturers implement the channel promotion strategy, the promotional effort level will increase in the difference coefficient of consumer value perception. This suggests that as consumers exhibit an increasing preference for products available through the online channel, the remanufacturer should enhance the level of promotion effort in the offline channel. Conversely, under the generic promotion strategy, the remanufacturer’s promotional efforts decrease initially and then increase with the difference coefficient of consumer value perception. Specifically, when $\beta <0.4$, the promotional effort level of the remanufacturers in channel promotion surpasses that of generic promotion. Moreover, when $0.4\le \beta \le 0.7$, the level of promotion effort for generic promotion by the remanufacturers surpasses those for channel promotion strategy.

(3).

An examination is conducted on the fluctuations in the remanufacturer’s profit (${\Pi }_d$) and retailer’s profit (${\Pi }_r$) in response to changes in the difference coefficient of consumer value perception ($\beta$). In a case where the demand is positive in both channels, the implementation of a channel promotion strategy by the remanufacturer results in an increase in profits for the remanufacturer, retailer, and the supply chain as the difference coefficient of consumer value perception rises. This implies that under the channel promotion strategy, higher consumer recognition of products sold through the online channel yields benefits for the remanufacturer, retailer, and the total supply chain. In the case of the remanufacturer adopting the generic promotion strategy, both remanufacturer and retailer profits exhibit an initial decrease followed by an increase with an escalation in the difference coefficient of consumer value perception. Moreover, when the remanufacturer implements generic promotion and the difference coefficient of consumer value perception is moderate, the profits of the retailer surpass those under channel promotion.

(4).

When the difference coefficient of consumer value perception is low, it is more profitable for a remanufacturer to implement the channel promotion strategy than the generic promotion. With a moderate perceived value difference coefficient, the generic promotion strategy is better than channel promotion for the remanufacturers. Under this circumstance, the profits of remanufacturers, retailers, and the supply chain are all greater under generic promotion than under channel promotion, and the spillover effects of generic promotion are evident. When the difference coefficient of consumer value perception is high, the channel promotion strategy by the remanufacturer implements generic promotion.

Based on the findings of this analysis, it is evident that the difference coefficient of consumer value perception significantly influences the remanufacturer’s selection of promotion strategies. It is suggested that remanufacturers adopt promotion strategies in conjunction with the characteristics of the remanufactured products. When remanufactured products have strong experiential attributes and weak digitization, such as high-tech products and mechanical equipment parts, remanufacturers should implement a channel promotion strategy. In this case, it is necessary to further increase the service difference between online and offline to improve the consumer’s perception of the difference, which is conducive to the remanufacturer obtaining higher profits. For remanufactured products with moderate experiential attributes and a general degree of digitization, such as fast-moving consumer goods, the remanufacturer should implement generic promotion, which not only allows consumers to recognize the characteristics of remanufactured products but also fosters healthy competition in the supply chain and improves the profits of the supply chain. When remanufactured products have weak experiential attributes and a strong degree of digitization, such as books, audiovisuals, etc., it is recommended that remanufacturers choose channel promotion. In this case, the difference between online and offline services is smaller, and consumers are more inclined to accept remanufactured products sold online. To improve the competitiveness of offline channels, remanufacturers can offer offline free trials, thereby increasing consumer willingness to purchase through offline channels and ultimately achieving higher profits.

6. Conclusions

This study focuses on the market where remanufacturers hold a dominant position and sell remanufactured products directly offline. It investigates the optimal pricing strategies for remanufactured products in different channels under the remanufacturer’s channel promotion and generic promotion, as well as the level of promotion effort of the remanufacturers. Additionally, our research also analyzes the impact of market conditions, particularly the difference coefficient of consumer value perception, on product sales prices, the level of promotion effort, and the profits of supply chain members. Furthermore, it addresses the critical matter of selecting the optimal promotion strategy for remanufacturers. The outcomes of the study reveal the following:

(i).

The impact of the difference coefficient of consumer value perception on prices, the level of promotion effort, and profits under different promotion strategies are analyzed. Within the context of remanufacturer channel promotion, elevated perceived value difference coefficients correspond to increased prices and heightened promotional efforts for both online and offline products. In contrast, under the remanufacturer’s generic promotion strategy, sales prices and promotional efforts for online and offline channels exhibit an initial decrease followed by an increase with the consumer-perceived value difference coefficient.

(ii).

The impacts of remanufacturer promotion on market competition are examined. In instances where the remanufacturer implements generic promotion, the online channel price markedly surpasses that of channel promotion, and a noticeable reduction in the price difference between online and offline channels occurs. Consequently, the spillover effect of generic promotion mitigates price competition between online and offline products. Concurrently, when the difference coefficient of consumer value perception is low, the remanufacturers are advised to allocate more efforts to channel promotion in comparison to generic promotion.

(iii).

Optimal promotion strategy selection for the remanufacturer. In instances where the difference coefficient of consumer value perception is either relatively small or large, the remanufacturer realizes increased benefits by implementing channel promotion. However, when the difference coefficient of consumer value perception assumes a moderate value, the spillover effect generated by the generic promotion strategy creates a mutually beneficial situation for both the remanufacturers and the retailers, establishing generic promotion as the optimal choice for the remanufacturers.

In this research, we only consider the game between remanufacturers and retailers under the assumption of complete information. However, in the real context, remanufactured products involve multi-dimensional information such as remanufacturing costs, patent protection, government subsidies, etc. Supply chain members often conceal certain information to advance their interests, resulting in information asymmetry that ultimately undermines supply chain efficiency. Therefore, the assumption of information asymmetry can be incorporated into the model for further research. In addition, remanufactured products involve multiple stages, such as recycling, production, and sales. The selection of promotion strategies in more complex supply chain models can also be further explored, such as scenarios involving multiple competing retailers, retailer dominance, or remanufacturers lacking sales channels.

In summary, this paper can be further explored from the following two aspects:

(i).

Relaxing the assumption of information symmetry: Investigate the impact of information asymmetry on the pricing decisions and promotional strategy selection for remanufactured products. Future studies can consider different scenarios of information asymmetry, including asymmetries in quality information, cost information, and market demand information, and how these asymmetries influence the game and cooperation between remanufacturers and retailers.

(ii).

Considering the entire process of remanufactured products, in the recycling stage, introduce recyclers to explore how different incentive contracts (such as discounts and reward points) affect consumer recycling behavior. In the production and sales stages, we can explore how reproduction costs or promotion costs impact the sales of remanufactured products.