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Article

Operational Decisions on Remanufacturing under the Product Innovation Race

1
College of Management Science, Chengdu University of Technology, Chengdu 610059, China
2
School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China
3
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(6), 4920; https://doi.org/10.3390/su15064920
Submission received: 13 February 2023 / Revised: 8 March 2023 / Accepted: 8 March 2023 / Published: 9 March 2023 / Corrected: 8 August 2023
(This article belongs to the Section Sustainable Management)

Abstract

:
To obtain a competitive advantage in the marketplace, firms usually need to adopt an innovation program as a key strategic initiative. New product innovation is usually accompanied by discarding the old products and results in negative effects on the environment. Conversely, to maintain environmental sustainability, a greater number of governments have enacted regulations to promote remanufacturing as an integral part of manufacturers’ existing businesses. However, at the firm level, remanufacturing may induce the cannibalization of new product sales. The primary goal of this paper is to provide firms with guidelines for the operational decisions on remanufacturing under the product innovation race. In particular, from a profit-maximization perspective, we suggest that the cost-efficient firm should look for cost-reduction opportunities in remanufacturing operations; otherwise, it should invest more resources into new product development. Our analysis also provides insights for environmental groups and agencies by indicating that improved environmental sustainability should involve not only setting collection targets but the implementation of additional reuse targets as well.

1. Introduction

Product innovation is increasingly seen as a strategic means to obtain a competitive advantage within the marketplace. A survey by PA Consulting Group showed that nearly three-quarters of the global top-performing companies adopted an innovation program as a key strategic initiative. Similarly, Fortune magazine and Harvard Business Review found that innovative companies not only have healthier growth rates but also deliver twice as much profitability as the industry average [1]. For instance, the world’s top 2500 industrial firms, based in 39 countries, have invested EUR 36 million in R&D for a total investment of USD 908.6 billion in 2021 [2]. Top-earning companies, such as Alphabet (USD 27.8 billion), Huawei (USD 19.5 billion), Samsung (USD 16.8 billion), Apple (USD 19.3 billion), and Volkswagen (USD 15.6 billion) reported R&D cost-ranging from 6.5% to 16.9% of revenue for 2021 [3].
However, the rapid introduction of new products increases the product-level discount rate [4]. For example, products that accompany the rapid pace of innovation, including mobile phones, video game consoles, televisions, and personal computers, are typically discarded when a more technologically advanced version enters the market [5]. Such electronic and electrical waste is growing by between 3% and 5% yearly—about three times faster than general waste [6].
Fortunately, the remanufacturing of used products provides an ideal initiative because it recovers used items, keeping them out of landfills. Typically, remanufacturing is profitable because it can reduce 50% of the costs spent on producing the same product [7]. On average, the global automotive parts remanufacturing market is estimated to grow at a value CAGR of 7.1% over 2018–2026, roughly equating to USD 91 billion by the end of 2026. On the other hand, in terms of energy consumption, remanufacturing can reduce energy use to about 85% of that invested in new production [8]. It is estimated that remanufacturing can reduce energy consumption by over 120 trillion BTUs annually, which equals about 16 million barrels of crude oil [9].
Unfortunately, although environmental groups and agencies are calling for an increase in remanufacturing business practices, the current response is not overly optimistic [10,11]. The major barrier stopping manufacturers from engaging in remanufacturing is the belief that remanufactured products can cannibalize the sales for new products [12]. For example, Hewlett-Packard remanufactures very little of returned or discarded products because they firmly believe that for every four remanufactured sales, one new sale is cannibalized. Although there are many mature waste-avoidance strategies, with established rates of sale as high as 80% for certain products, many manufacturers are reluctant to use recycled materials because of concerns over cannibalization [6].
To accomplish the research objectives of this study, we construct models for manufacturers with the flexibility to introduce an improved version in the market for new products under two scenarios: with remanufacturing or without remanufacturing. Using these two theoretical models, indicated in Figure 1, we focus on the following key questions:
Should business leaders choose to engage in remanufacturing when promoting innovation in the market for new products? How does the cost reduction from remanufacturing impact the innovation of new products?
Should environmental groups always expect remanufacturing to provide better results for environmental sustainability? How do the key drivers impact the environment?
Although numerous studies on remanufacturing have focused on the problems of cannibalization and technology selection (see, e.g., [13,14,15,16]), the research assumes that manufacturers are actively involved in remanufacturing and has thus focused on technology selection as part of remanufacturing. Surprisingly, there is relatively scant attention paid to the tradeoff between remanufacturing and innovation. Thus, this paper enables practitioners to better understand how they can meet the urgent need for cost reduction from remanufacturing while still making essential profits from innovation.
In particular, our work has clear implications for both manufacturers and environmental groups. In spite of the fact that both remanufacturing and innovation contribute to profitability, the prospect of remanufacturing always reduces the incentive for new product innovation and, under some circumstances, results in lower profits for manufacturers. Thus, to obtain a competitive advantage in the new product markets, stakeholders need to be cautious in combining innovation in new products and remanufacturing of used products.
On the other hand, we also provide insights for environmental groups and agencies. First, our results confirm the conventional wisdom that remanufacturing a product can create environmental benefits. Second, and surprisingly, we find that rather than increasing remanufacturing, the most common response by manufacturers to more stringent collection targets of take-back legislation is to decrease the availability of new products in the previous period. Hence, our results suggest that if social planners care more about environmental performance, they should not only set collection targets but implement additional reuse targets as well.
This paper is organized as follows: Section 2 explains our research contribution through a review of the related literature, Section 3 develops the two theoretical models, Section 4 presents the main results, and Section 5 offers a discussion and conclusion to our work.

2. Relevant Literature

Remanufacturing is a process that restores end-of-life cores to their original working condition [17,18,19]. The prior studies on remanufacturing usually assumed that manufacturers are actively involved in remanufacturing and thus focused on the technology selection for remanufacturing operations (see, e.g., [1,20,21,22,23,24]). As a body of knowledge, these studies do not address the effect of remanufacturing on new product innovations among firms, which forms a focus of this paper. On the one hand, confronting the current and unforgiving realities of market competition, the key role of R&D Centers for technological development in industrial companies is undeniable and clearly impacts the competitive strategies of the industry [25]. In particular, a number of authors consider new product innovation to be a strategic decision to survive (see, e.g., [1,20,21,22,23,24]). Among this stream of literature, Plambeck and Wang [4] are particularly instrumental to our research, as they highlight the design and introduction of new products in the presence of take-back legislation. However, our work differs in two important aspects: First, we assume that all the collected core products are remanufactured and resold in the market and acknowledge the fact that both cost-cutting from remanufacturing and performance improvement from innovation contribute to manufacturer profitability. Thus, this paper extends the literature with a better understanding of the implications of remanufacturing on new product innovation. Second, the decision to introduce an upgraded version was not covered in Plambeck and Wang’s [3] study, whereas this forms a distinctive feature of our framework.
Another stream of literature related to this paper deals with the potential for the cannibalization of new product sales by remanufactured products. In particular, Atalay et al. [26] studied the effects of introducing remanufactured products in the OEM market of new products and found that remanufacturing indeed hurt the profits from new product sales while creating greater total profits. Zhang and Zhang [27] studied the impact of cannibalization between new and remanufactured products on supply chain network design and operations by considering a joint pricing–location–inventory problem. Huang et al. [28] considered the competition between a third-party remanufacturer and an original equipment manufacturer and investigated the incentives of cost information-sharing. Several authors, including Dai and Zhang [29], Hong et al. [30], Li [31], Li et al. [32], and Sarkar et al. [33], have recently paid attention to the concept of green process innovation. Evidently, our aim and model setting are quite different from the above literature. For example, we allow the manufacturer to decide whether or not to introduce an improved version. In addition, the focus of this paper is to address how business leaders can stay in the race by trading between the cost reduction from remanufacturing and the essential profitability from new product innovation.
Last, our work is indirectly related to the literature on the implications of take-back regulations. For example, Esenduran et al. [34] highlighted the impact of take-back regulation on the proper treatment of waste through recycling or remanufacturing. Subsequently, Zhao et al. [35] developed a decision-making model considering both consumer preference for remanufactured products and the effect of government subsidization, while Huang et al. [36] analyzed the product design implications of extended producer responsibility-based take-back legislation on durable goods. More recently, Pazoki and Samarghandi [37] investigated a manufacturer that produces and distributes a single product, which is regulated by a take-back environmental regulation and showed that if eco-design can sufficiently reduce production costs, no take-back regulation is necessary for a more polluting product. We complement these studies by adding a word of caution on take-back mechanisms that enforce producer responsibilities for the collection of used items. More specifically, our analysis suggests that if social planners care more about environmental performance, they should not only set collection targets but implement additional reuse targets as well. To highlight the research contributions, we provide a comparison with some related studies (see Table 1).

3. Model Formulation and Solution

All the definitions of the variables are shown in Table 2. The assumptions and decision-making framework are as follows:
Assumption 1.
All remanufacturing cores are obtained from new products that sold in Period 1.
Assumption 1 is consistent with the fact that, in the remanufacturing industry, the remanufactured cores are derived from the products at the end of their useful life at the market. For example, the WEEE directive required the original equipment manufacturers to take responsibility for recycling their products when those products are at the end of their useful life. To reflect the above fact, in this paper, we consider a dual period model in which the manufacturer only provides the new product in Period 1 and both new and remanufactured products (if remanufacturing) in Period 2. For convenience, and in keeping with Yenipazarli and Vakharia [40] and Zhou et al. [41], we assume that only used core products can be remanufactured. That is, any given item in Period 1 can have two lives: it is new when sold in Period 1 and then classified as “remanufactured” once it is remanufactured in Period 2.
Assumption 2.
The factor δ 1 = 1 + a represents the level of content differentiation between the improved and existing versions.
One of the distinguishing features of this paper is that we allow the manufacturer to decide whether to introduce an improved version of the new product. Given the fact that producers of sequential versions of products have a trade-off to make, in Period 2, the manufacturer has the option to offer the improved versions of the existing new products sold in Period 1 (“improved” and “existing” versions to be used hereafter following this distinction). Like Yin et al. [24], to model the difference between the improved and existing versions, we model a factor, δ 1 = 1 + a , where a > 0 represents the level of content differentiation between the improved and existing versions.
Assumption 3.
The investment cost of product innovation is c i = K δ 1 2 1 / 2 , that associated with the levels of innovation of δ 1 .
In practice, the rate of innovation shapes a firm’s effort in investments in R&D. That is, in our models, if the firm continues with the existing version, then it would invest nothing in its R&D behavior; however, if it decides to release a new version, then the investment cost would be positive. Furthermore, higher levels of innovation of δ 1 are associated with the greater investment cost of K δ 1 2 1 / 2 [24,42].
Assumption 4.
Consumer willingness to pay for the remanufactured version is a fraction γ ( 0 , 1 ) of that for the existing version.
In practice, the consumer usually prefers new products to remanufactured products. That is, the consumer willingness to pay for the remanufactured version is lower than that for the existing version. For instance, the eBay Business for a commercial product shows that the willingness to pay for the remanufactured product is 9.7% lower than that for the new one [12]. Then, to reflect the cannibalization problem with the remanufactured versions, all consumers are considered capable of distinguishing the remanufactured from new products [16,27,41]. That is, we assume that in Period 2, consumer willingness-to-pay for the existing version is uniformly distributed in the interval [ 0 , 1 ] ; however, their willingness to pay for the remanufactured version is a fraction γ ( 0 , 1 ) of that for the existing version.
Based on the vertical heterogeneity of their willingness to pay, we can derive the inverse demand functions in Period 2 as follows:
p n = 1 + a 1 q n γ q r p r = γ 1 q n q r
where p n is the market-clearing price of the new product ( a > 0 represents the improved version, while a = 0 represents the existing version), and p r is the market-clearing price of the remanufactured product (if remanufacturing). Recall that the manufacturer only provides the existing versions in Period 1; thus, the inverse demand function in Period 1 is as follows:
p 1 = 1 q 1
Assumption 5.
b ( 0 , 1 ) denotes the collection target as a fraction of new goods sold, then the units of used cores are b q 1 .
In practice, many forms of take-back regulation, including the European Commission’s Waste Electrical and Electronic Equipment (WEEE) and Japan’s Specified Household Appliances Recycling Law (SHARL), impose a lower bound on product cores to be collected. We thusly assume that b ( 0 , 1 ) denotes the collection target as a fraction of new goods sold [34]. Since all remanufactured products are derived from used cores, then q r b q 1 . As with Esenduran et al. [34], we denote the unit collection cost by c , the unit cost of producing a new product by c n , and the unit cost of remanufacturing by c r .
In both models, the manufacturer first decides whether to introduce an improved version of the product in Period 2, and subsequently sets the optimal quantities for both periods. Variable π i j refers to the profits of Period i under Scenario j ; subscript i { 1 , 2 } denotes Periods 1 and 2, respectively, while superscript j { N , R } denotes the scenarios of “no remanufacturing” and “remanufacturing”, respectively.

3.1. Benchmark: No Remanufacturing

Although this model may not have a high practical value in practice, to establish a benchmark for the remanufacturing scenario, like [16,24], we analyze no remanufacturing scenario, in which all consumers have access only to the new products; however, the manufacturer has the flexibility to provide improved versions in Period 2. The inverse demand functions are as follows:
p n = 1 + a 1 q n
Note that the absence of remanufactured products means that the two periods in our model are independent, and the manufacturer’s problem is to maximize profits over both periods by choosing optimal quantities, q 1 * and q n * . That is, it maximizes
π T N = π 1 N + π 2 N = p 1 c n q 1 + ρ p n c n q n K δ 1 2 1 / 2
where 0 ρ 1 is the discount factor of the money. The equilibrium decisions and profits for the manufacturer in the no remanufacturing scenario are given in Table 1 (The more detailed technical analysis accompanying this paper is provided in the Appendix A). Note that the threshold value of K means below the point at which the manufacturer would choose δ 1 = 1 + a and release its improved version; otherwise, the manufacturer would prefer δ 1 = 1 and make the existing version available.

3.2. Remanufacturing Scenario

In this scenario, the manufacturer provides existing versions of the new product in Period 1 while offering both new (the existing or improved versions) and remanufactured products in Period 2. Since all consumers are forward-looking, we recognize the manufacturer’s problem in Period 2 is to maximize
π 2 R = p n c n q n + p r c r q r c b q 1
Note that b ( 0 , 1 ) denotes the collection rates. Given the optimal q n * and q r * , the manufacturer optimizes its two-period profits by choosing q 1 * . That is, it maximizes
π T R = π 1 R + ρ π 2 R = p 1 c n q 1 + ρ p n c n q n + ρ p r c r q r ρ c b q 1 K δ 1 2 1 / 2
We again use backward induction to solve this scenario, and the equilibrium decisions and profits are again summarized in Table 3.

4. Discussion

This paper attempts to enable practitioners to better understand how they should meet their urgent need for cost reduction from remanufacturing and still make essential profits from new product innovation. In this section, we intend to answer the above question from the viewpoint of the manufacturers and the environmental groups and agencies, respectively.

4.1. Implications for Business Leaders and Practitioners

In this subsection, we first intend to answer the initial question of whether manufacturers should choose to engage in remanufacturing when promoting innovation in the new products market. To accomplish this, we compare the difference in the incentives for new products innovation in both models, beginning with
Proposition 1.
Remanufacturing is always detrimental to the incentives for new product innovation (i.e., K R < K N ).
To illustrate the impact of remanufacturing on the incentives for new product innovation, we provide a representative plot in Figure 2 (unless otherwise stated, all graphical illustrations are provided with the parameters of a = 0.2 , c n = 0.8 , γ = 0.6 , b = 0.7 , c = 0.05 , ρ = 1 ). Based on Figure 2, we can conclude that for any remanufacturing cost, i.e., c r , the incentives for new product innovation under the remanufacturing scenario are always lower than that under the no remanufacturing scenario. This can be explained as follows: in both our models, the main “prizes” from product innovation are equal to the price premium for the improved version times its sales volume. That is, the incentives of new product innovation depend on whether the main “prizes” arise from the process. Based on the outcomes in Table 3, we find that the sales price for the improved version remains the same, irrespective of whether any remanufactured product is available. Under the remanufacturing scenario, however, the optimal sales volume of the improved product decreases with the consumer value discount for the remanufactured product, that is, q n R / γ = c n c r 2 ( 1 + a γ ) 2 < 0 . Put differently, selling remanufactured products in the market would cannibalize the sales volume of the manufacturer’s new products. Such cannibalization naturally decreases the main “prizes” from product innovation and results in lower incentives for new product innovation than that under the no remanufacturing scenario (i.e., K R < K N ).
Proposition 1 suggests that manufacturers must be cautious of the negative effects of remanufacturing on new product innovation. In practice, Fuji-Xerox looked five years ahead to estimate the possible effects of remanufacturing on the new product innovation in its copier systems. In doing so, the company identified which components should be designed as replaceable by the newly improved version versus those that should be designed for remanufacturing [43,44].
It should be noted that the pioneering literature on remanufacturing looked at the potential for the cannibalization of new product sales by remanufactured products (see, e.g., Atalay et al. [45], Debo et al. [13], Guide and Li [12]), these studies all ignored the question of whether manufacturers should choose to engage in remanufacturing when promoting innovation in the new products market. Thus, as mentioned earlier, we complement these studies by allowing the manufacturer to have the option to decide whether to introduce an upgraded version or not.
We now go a step further to highlight how the cost reduction from remanufacturing impacts the incentives for new product innovation:
Proposition 2.
Under the remanufacturing scenario, the incentives for new product innovation increase with the remanufacturing cost, that is, K R / c r > 0 .
We explain the intuition behind this result as follows. Based on the outcomes in Table 3, we can conclude that, under the remanufacturing scenario, the optimal sales volume of the improved product increases with the remanufacturing cost, that is, q n R / c r = 1 2 ( 1 + a γ ) > 0 . This is consistent with the intuition that, as the remanufactured cost increases, lesser quantities of remanufactured products become availed to the market (i.e., q r R / c r = 1 + a 2 γ ( 1 + a γ ) < 0 ), which enlarges the potential market for the new, improved products. Recall that the sales price for the improved version remains the same, irrespective of whether any remanufactured product is available. Thus, as the remanufacturing cost increases, the increased sales volume of the improved products prompts the “prizes” of product innovation to increase. Then, as illustrated in Figure 2, as the remanufacturing cost increases, the incentives for new product innovation under the remanufacturing scenario also increase, resulting in the difference between the incentives for new product innovation among both models decreasing.
So far, Proposition 1 suggests that the additional remanufacturing operations deter the manufacturer’s new product innovation. Such negative effects would seem to be particularly pronounced when the remanufacturing cost c r is small (see, Proposition 2). Hence, one might expect that when the remanufacturing cost is not pronounced, the remanufacturing operations would naturally harm the manufacturer’s new product innovation and lead to lower profitability. However, this is not always the case, and we offer the following proposition as a case in point.
Proposition 3.
The profits under the remanufacturing scenario are higher than that of no remanufacturing (i.e., π T R > π T N ) if, and only if, the cost of c r is not pronounced (i.e., c r < c r Δ ); otherwise, the opposite is true.
As Figure 3 shows, Proposition 3 clearly indicates that the remanufacturing operations can severely harm the manufacturer’s new product innovation and lead to lower profitability. This is particularly so if the collection cost of c is sufficiently large (i.e., c > c Δ ), in which case remanufacturing would not be a profitable business due to the fact that product returns have a huge cost disadvantage. That is to say, although remanufacturing can increase the profits through cost-saving measures when the collection cost for the remanufacturing operations is pronounced, as c enlarges, the profits of remanufacturing from cost reduction are limited. Such limited profits from remanufacturing cannot “compensate” for the profit “loss” in new product innovation. Furthermore, even when the collection cost of c is not pronounced (i.e., c < c Δ ), the manufacturer should take care of the remanufacturing cost of c r . In particular, when the remanufacturing cost c r > c r Δ , the profits from remanufacturing are so limited that they cannot “compensate” for the profit “loss” in new product innovation incurred through the huge disadvantage in remanufacturing operations. This stands even if the collection cost for the remanufacturing operations is not binding (i.e., c < c Δ ). It should be noted that Proposition 3 suggests the contrasting effect whereby for the costs of c < c Δ and c r < c r Δ , the remanufacturing operations would be so profitable that they would “compensate” for the profit “loss” in the new product innovation.
In summary, from a managerial perspective, Propositions 1–3 provide a thorough understanding of how manufacturers remain competitive by a tandem approach to remanufacturing and new product innovation. For instance, as Proposition 1 has shown, although the remanufacturing operation may be a low-cost alternative for production, it can undermine the incentive for new product innovation. This negative effect is particularly notable when the remanufacturing cost of c r is not pronounced (see, Proposition 2). Therefore, as indicated in Proposition 3, the cost-efficient firm should look for cost-reduction opportunities in remanufacturing operations because the benefits from cost-cutting in remanufacturing can “compensate” for the “loss” in the new product innovation. If, however, a company is confronted with certain barriers in setting up a low-cost remanufacturing operation, it should focus its resources on new product development.

4.2. Implications for Environmental Groups and Agencies

In this subsection, we first analyze whether environmental groups and agencies should expect remanufacturing to perform better in areas of environmental sustainability. Consistent with the fact that environmental groups and agencies usually lobby for landfill bans or regulations imposing disposal fees, we define the total environmental impact as weighted units of landfilling. Let i d and E j represent the unit and total environmental impact, respectively. Then, following Agrawal et al. [42] and Zhang et al. [46], E j = i d ( q 1 j + q n j ) . As Figure 4 illustrates, we address the question of whether environmental agencies should expect remanufacturing to perform better in areas of environmental sustainability with the following:
Proposition 4.
The presence of remanufacturing is always beneficial to the environment, that is, E N > E R .
Compared to the quantities of new products in both scenarios, we find that q 1 N * > q 1 R * and q n N * > q n R * . It is easy to derive that the presence of remanufacturing can reduce landfilling and benefit the environment. This is consistent with the conventional wisdom that remanufacturing always increases environmental sustainability, though it cannibalizes new product sales. In practice, to reduce waste landfilling and conserve the environment, a greater number of governments have enacted regulations to promote remanufacturing as an integral part of manufacturers’ existing businesses. For example, in 2007, China’s government initiated a pilot project in automotive parts, engineering machinery, and machine tools. In this pilot program, the government supported many typical manufacturers in the abovementioned industries to undertake remanufacturing, and it established a national remanufacturing management system [41].
How do the key drivers impact areas of environmental sustainability? To understand, we first turn our attention to how cost reduction from remanufacturing impacts environmental performance, which is summarized as follows:
Proposition 5.
Under the partial remanufacturing scenario, the total environmental impact increases with the remanufacturing cost, that is, E R / c r > 0 ; however, under the full remanufacturing scenario, the opposite is true, that is, E R / c r < 0 .
Based on the outcomes in Table 3, we find that E R / c r = 1 2 ( 1 + a γ ) > 0 . This means that the environmental impact under remanufacturing scenario increases with the remanufacturing costs. As a result, the difference between the environmental impact under the no remanufacturing scenario and remanufacturing scenario decreases with the remanufacturing costs (see Figure 4). Put differently, if social planners care more about environmental improvement, they need to select the more cost-efficient manufacturers. This result has an intuitive appeal but may be consistent with the fact that, in its pilot program, the Chinese government seems to prefer manufacturers concerned more with their own remanufacturing operations to undertake the remanufacturing operations.
Most social planners acknowledge the link between this type of regulation and the collection efforts of manufacturers; however, the effect on remanufacturing activity remains unclear [32]. Unfortunately, we find that as collection targets increase, the manufacturer decreases the availability of new products in the previous period but does not undertake greater efforts in remanufacturing. That is,
Proposition 6.
The threshold values of  c r Δ increase with the collection target of  b , i.e.,  c r Δ / b > 0 ; moreover, the equilibrium quantities  q 1 / b < 0 .
Proposition 6 characterizes how the manufacturer’s response to more stringent collection targets as a way of protecting the profitability from new product innovation develops: as the collection targets, b , increase, both the threshold of c Δ and c r Δ decrease. This means that as the collection targets increase, the manufacturer would confront pricier conditions for remanufacturing. However, in response to more stringent reuse targets, rather than undertaking greater efforts to remanufacture ( q r / b = 0 ), the manufacturer would decrease the new products in Period 1, i.e., q 1 / b = c 2 < 0 . Intuitively, the more stringent collection targets would cost more for the manufacturer because each returned unit is associated with the necessary buyback payment and transportation cost, etc. Consequently, on the one hand, when confronted with the increased costs in waste collections, only those cost-efficient OEMs would be able to look for cost-reduction opportunities in remanufacturing (i.e., c Δ / b < 0 , c r Δ / b < 0 ). On the other hand, to limit the total costs of collection, the manufacturer is more likely to reduce the source of the waste, i.e., b q 1 . Moreover, the pricier conditions for remanufacturing can enlarge the potential market for the newly improved versions and limit the cannibalization problem as well.
The past two decades have seen rapid growth in take-back regulation. Major regulations include the waste electrical and electronic equipment and end-of-life vehicle (ELV) directives in Europe, SHARL Law and the PC Recycling System in Japan, and the Regulations on the Administration of the Recovery and Disposal of Waste Electrical and Electronic Products in China. These laws and directives enforce producers to take responsibility for the collection of their products once they reach the end of their useful lives. The diffusion of take-back regulations raises the question of what is their ultimate goal. From the social planner’s perspective, the ultimate goal should be extending producer responsibility to collect the end-of-use products and reduce waste in landfills [47]; however, from the manufacturer’s perspective, they usually comply with these laws at the minimum cost. In the U.S., industry resistance has been a primary barrier to the enforcement of such take-back regulations [4]. Thus, take-back regulations are usually confronted with certain conflicts associated with environmental benefits versus economic impact (i.e., increased costs) [7,48]. Unfortunately, the long-term implications of take-back regulation on the remanufacturing industry are unclear [5,49,50].
Proposition 6 suggests that if social planners care more about environmental performance, they should not only set collection targets but implement additional reuse targets as well. This may be consistent with the fact that, in addition to the collection targets, some social planners have recently advocated the inclusion of reuse targets for take-back laws and directives. For example, Computer Aid firmly believes that reusing is better than recycling when it comes to social and environmental responsibility. Thus, Computer Aid [5] intends to submit all collected IT equipment to remanufacturing for distribution to different programs across the world. European policymakers also intend to impose proper treatment levels in the WEEE Directive, which imposes targets on collection [34].

5. Conclusions

In spite of the fact that government mandates are calling for environmentally friendly business practices, remanufacturing operations face a less than optimistic outlook due to manufacturers believing that remanufactured products cannibalize new product sales. Unfortunately, this is only one piece of a disturbing picture. When discussing the current and unforgiving competitive realities, almost all business executives acknowledge the link between new product innovation and the ability to create future profitability. In practice, although the remanufactured units can cannibalize new product sales; however, manufacturers can control this through strategic behavior, including careful technology selection for new product innovations. Hence, in this context, the key question facing manufacturers is clear: how can they stay in the race by riding two horses, one for remanufacturing, the other for new product innovation?
Although the body of research on remanufacturing has focused on cannibalization and technology selection problems, it assumes that manufacturers are actively involved in remanufacturing and have thus focused on the technology selection for remanufacturing. Thus, researchers have paid little attention to the tradeoff between the cost-cutting involved in remanufacturing and the potential benefits from new product innovation. To fill this gap, the current paper has sought to provide a more thorough understanding of how to meet the urgent need for cost reduction with remanufacturing while still achieving essential profitability from new product innovation.
Specifically, we achieved this by applying two theoretical models in which the manufacturer invests in new product innovation under the two scenarios: with and/or without remanufacturing operations. Using these two theoretical models, we focused on the key questions of whether business leaders should choose to engage in remanufacturing when promoting innovation in the new product market and whether environmental groups should expect remanufacturing to perform better in areas of sustainability.
Our work provides implications for industry. In particular, our analysis reveals that although cost-cutting from remanufacturing and improved performance from innovation contribute to profitability, the former always reduces the incentive for new product innovation and, under some circumstances, results in lower profits for manufacturers. Thus, stakeholders must be cautious when conducting a balanced program combining innovation in new products and the remanufacturing of waste.
In practice, many brand-name manufacturers, including Hewlett-Packard, Bosch Tool, Black & Decker, and Electrolux USA, have claimed that new product sales can be heavily cannibalized when they undertake remanufacturing operations. The manager from a global computer manufacturer even stated confidently that for every four remanufactured products sold, one new product sale is cannibalized. Our analysis goes one step further in exploring this cautionary observation by providing a thorough understanding of how manufacturers can remain competitive by adopting a tandem approach to remanufacturing and new product innovation. For instance, our results suggest that a cost-efficient firm should look for cost-reduction opportunities in remanufacturing operations. Conversely, if a company confronts certain barriers in setting up low-cost remanufacturing operations, it should focus its resources on new product development.
We also provide insights for environmental groups and agencies. First, our results confirmed the conventional wisdom that remanufacturing a product could create environmental benefits. Second, and to our surprise, we found that rather than increasing remanufacturing, the most common response by manufacturers to more stringent collection targets initiated by enforced take-back legislation is to decrease the availability of new products in Period 1. The past two decades have seen rapid growth in take-back regulations that impose a lower bound on cores to be collected. However, our results suggest that if social planners care more about environmental performance, they should not only set collection targets but implement additional reuse targets as well. These results are quite robust and hold true irrespective of whether the market scenario is monopolistic or competitive.
This work can be extended in several directions. First, although we provide a comprehensive understanding of how manufacturers can approach remanufacturing and new product innovation, the paper does not pay attention to the possibility of interchangeability, where the new product innovation allows the waste to be more thoroughly disassembled for remanufacturing. For instance, Wu [51] showed that product interchangeability is effective for the OEM in competing with the remanufacturer. As such, it is a meaningful direction for future research to address how product innovation with interchangeability impacts remanufacturing. Second, in prompting social planners to implement additional reuse targets along with setting new collection targets, it would be potentially useful to devise a detailed policy that encourages companies to carry out remanufacturing activities. In particular, Wang et al. [9] and Zhang et al. [44] have recently started to address the optimal mechanisms imposed on manufacturers in areas of environmental performance and social welfare. Then, it is helpful to address the possible changes in remanufacturing decisions under the product innovation race while implementing additional reuse targets rather than only highlighting the collection targets. Third, another desirable extension of this research would be an examination of green consumers whose purchase decisions are based on environmental concerns. For example, it is an interesting issue for future literature to address whether the preference of green consumers would impact the manufacturer’s operational decisions on remanufacturing under product innovation.

Author Contributions

Writing—original draft preparation, Q.Y.; writing—review and editing, D.Y.; supervision, L.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Humanities and Social Sciences Foundation for Young Scholars of China’s Ministry of Education (15YJC630154) and the Fundamental Research Funds for the Central Universities (ZYGX2016J238) for supporting this research.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Technical Proofs

(1)
Analysis of the Scenario with No Remanufacturing.
Using backward induction, we first maximize π 2 N = p n c n q n K δ 1 2 1 / 2 with q n and obtain that q n * = 1 + a c n 2 ( 1 + a ) . Then, substituting it into π T N = π 1 N + π 2 N = p 1 c n q 1 + ρ p n c n q n K δ 1 2 1 / 2 , and maximizing it with q n . Solving the FOCs of it, we then obtain q 1 N = 1 c n 2 . This leads to the manufacturer’s total profit being
Π T N = p 1 c n q 1 + ρ p n c n q n K 1 + a 2 1 / 2 = 1 + ρ 2 ρ c n + 2 ρ a + ρ c n 2 2 ρ a c n + ρ a 2 + a 2 c n 2 a c n + c n 2 + a c n 2 4 a + 4 K 1 + a 2 1 / 2
Based on the above equation, we can obtain that, if a = 0 , then the above profit can be rewritten as Π T N a = 0 = ( 1 + ρ ) ( 1 c n ) 2   4 .
Clearly, the manufacturer prefers δ 1 = 1 + a over δ 1 = 1 if K < K N , otherwise, it would choose δ 1 = 1 over δ 1 = 1 + a if K > K N , where K N satisfies Π T N δ 1 = 1 = Π T N δ 1 = 1 + a ; i.e., K N = ρ ( 1 + a c n 2 ) 2 ( a + 1 ) ( a + 2 ) . All equilibrium decisions and profits are presented in Table 3.
(2)
Analysis of the Scenario with Remanufacturing.
Applying backward, starting from Period 2 again. In Stage 1 of Period 2, the manufacturer sets ( q n , q r ) to maximize the profit in Period 2. That is,
Π 2 R = p n c n q n + p r c r q r c b q 1
subject to q r b q 1 , and q n , q r > 0 .
To maximize the problems with constraints, like [52] and [41], we write the above problem as following the Lagrangean:
L = p n c n q n + p r c r q r c b q 1 + λ ( b q 1 q r )
Using the KKT optimality conditions:
L q n = 1 + a 2 q n 2 q n a 2 γ q r c n L q r = γ 2 γ q n 2 γ q r c r + λ λ ( b q 1 q r ) = 0
The above equations have two solutions. They depend on whether λ are greater than or equal to zero.
(i) λ = 0 . Solving the gradient conditions with λ = 0 , we have
q n = 1 + a c n γ + c r 2 ( 1 + a γ ) , q r = γ c n a c r c r 2 γ ( 1 + a γ )
(ii) λ > 0 . Solving the system, we obtain
q n = 1 + a 2 γ b q 1 c n 2 1 + a , q r = b q 1 , λ = 2 γ b q 1 2 r 2 b q 1 + 2 γ b q 1 a γ c n + c r + a c r ( 1 + a )

Appendix B. Proof of Proposition 1

(i) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
Solving K R i K N = ρ ( a c r 2 2 c r c n a + c n 2 γ a 2 c r c n c n 2 γ 2 + 2 c n 2 γ + c r 2 ) 2 ( a 2 + 3 a + 2 ) ( γ 1 ) ( 1 + a γ ) , we find that whether K R i K N > 0 depends on the numerator of the above equation. Then, let t = a c r 2 2 c r c n a + c n 2 γ a 2 c r c n c n 2 γ 2 + 2 c n 2 γ + c r 2 , we can obtain:
c r 1 = c n + a c n + c n a + 1 γ 1 a γ + 1 a + 1 ,   c r 2 = c n + a c n c n a + 1 γ 1 a γ + 1 a + 1 . Comparing c r 1 , c r 2   c r ¯ and c ¯ r , we find that c r ¯ < c ¯ r < c r 1 < c r 2 , which means K N > K R i .
(ii) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a , solving  K R i i K N = ρ 2 c n 2 γ 2 b 3 + 2 γ c n b 2 c r + 2 γ c n b 2 c + 3 c n 2 γ b + 2 γ c n b 2 2 γ b 2 c a 2 γ b c n a + c n 2 γ 2 b 3 a + 2 c n 2 γ b a 2 c n 2 γ b 2 a 2 c n γ b 3 c 2 c r b 2 γ a + 2 c n γ b 2 a + c r 2 b 3 γ a + c 2 b 3 γ a + 2 c r b 3 c γ 2 c n γ b 3 c r + 2 γ c n b 2 c r a + 2 γ c n b 2 c a 2 c r b 2 γ c n 2 γ 3 b 3 + c r 2 b 3 γ + c 2 b 3 γ 2 c n b c r a 2 c n 2 γ b 2 2 c n b c a 2 c n γ b 3 c a + 2 c r b 3 c γ a 2 c n γ b 3 c r a + 2 c n + 2 c n a 2 c n 2 a 2 c n b c 2 b γ c n 2 γ b 2 c 2 c n b c r + b γ 2 c n 2 + γ b a 2 a + 2 1 γ 2 b 2 + γ b 2 1 + a γ 2 b 2 + γ b 2 + γ b 2 a we find that whether K R i i K N > 0 depends on the numerator of the above equation. Then, similar to scenario (i), we can yield the roots of:
c r 1 = 2 b γ 2 b γ c n 2 γ b 2 c 2 γ b 2 c a + 2 γ c n b 2 2 γ b c n a + 2 c n γ b 2 a + 2 c n a + 2 c n + 2 γ b a + 2 ( c n 2 ( 1 γ 2 b 2 + γ b 2 ) ( 1 + a ) ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) ) 1 / 2 2 ( b γ + γ b a ) b
c r 2 = 2 b γ 2 b γ c n 2 γ b 2 c 2 γ b 2 c a + 2 γ c n b 2 2 γ b c n a + 2 c n γ b 2 a + 2 c n a + 2 c n + 2 γ b a 2 ( c n 2 ( 1 γ 2 b 2 + γ b 2 ) ( 1 + a ) ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) ) 1 / 2 2 ( b γ + γ b a ) b
Comparing c r 1 , c r 2   c r ¯ and c ¯ r , we find that c r ¯ < c ¯ r < c r 1 < c r 2 , which means K N > K R i i .
In sum, we can conclude that remanufacturing is always detrimental to the incentives for new product innovation (i.e., K R < K N ).

Appendix C. Proof of Proposition 2

Based on Table 1, K R i c r = ρ ( c n c r ) a + 2 1 γ a γ + 1 > 0 and K R i i c r = ρ γ b b γ + c n c r b 2 γ b γ c n γ b 2 c + γ c n b 2 2 a + 2 1 γ 2 b 2 + γ b 2 1 + a γ 2 b 2 + γ b 2 + γ b 2 a > 0 .
In sum, we can conclude that under the remanufacturing scenario, the incentives for new product innovation increase with the remanufacturing cost, that is, K R / c r > 0 .

Appendix D. Proof of Proposition 3

Based on the outcomes in Table 1, we can find that π T R i π T N = ( c r r c n + a c r ) 2 4 r ( 1 + a r ) ( 1 + a ) > 0 ,
This means that π T R i π T N > 0 is always true.
(ii) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
After the observation of
π T R i i π T N = γ b a 2 2 c n c r 4 c n c r a + 2 γ c n b c r a 2 c n b 2 c γ 2 a c 2 b 3 γ 2 γ 2 b + 2 γ c n b 2 c + c n 2 γ b + 2 c n 2 γ 4 γ b 2 c a 4 γ b c n a + 2 γ 2 b c + 2 c b γ c n a + 2 c n 2 γ b a + 2 c 2 b 3 γ a + 4 γ c n b 2 c a 2 γ c n a + 2 a 2 c r + c 2 b 3 γ 2 c n b 2 c γ 2 2 c r b c a 2 2 c n γ b a 2 2 c n c r a 2 + 2 γ 2 b c n a + 2 γ c n b c r 4 c r b c a c r 2 b + 2 c r 2 b γ c n 2 γ b 2 c 2 γ c n + 4 a c r + 2 c b γ c n + b γ + 2 γ b a 2 c r b c 2 c r 2 b a n + 2 c n 2 γ a γ 2 b a + 2 c b 2 γ 2 2 c n 2 γ 2 b c r 2 b a 2 + 2 c n γ b 2 c a 2 + c n 2 γ b a 2 + c 2 b 3 γ a 2 2 b 2 c γ a 2 + 2 c b 2 γ 2 a c n 2 γ 2 b a c 2 b 3 γ 2 a 4 ( γ 2 b 2 1 a γ b 2 γ b 2 a ) ( 1 + a ) we find that whether π T R i i π T N > 0 depends on the numerator of the above equation. Then, solving the above equation, we can yield the roots as follows:
c r 1 = 2 a 2 c n a 2 c b a 2 c b 2 c n + 2 + 2 b γ c n + 2 ( 1 c n c b ) ( 1 + a ) ( 1 + a r 2 b 2 + r b 2 + r b 2 a ) 2 b ( 1 + a )   c r 2 = 2 a 2 c n a 2 c b a 2 c b 2 c n + 2 + 2 b γ c n 2 ( 1 c n c b ) ( 1 + a ) ( 1 + a r 2 b 2 + r b 2 + r b 2 a ) 2 b ( 1 + a ) comparing c r 1 , c r 2   c r ¯ and c ¯ r , we find that, for any c > 0 , then c r ¯ < c r 2 < c ¯ r < c r 1 . That is, if, and only if, the cost of c r < c r 2 , then π T R i i > π T N , otherwise, π T R i i < π T N .
In sum, we can conclude that the profits under the remanufacturing scenario are higher than that of no remanufacturing (i.e., π T R > π T N ) if, and only if, the cost of c r is not pronounced (i.e., c r < c r Δ = c r 2 ); otherwise, the opposite is true.

Appendix E. Proof of Proposition 4

Since E R = i d q 1 R + q n R , then we can obtain
(i) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
E R i E N = i d a c r + c r γ c n 2 a + 1 ( 1 + a γ ) < 0 is always true.
(ii) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
solving E R i i E N = i d b 2 c n γ a + γ b c r a + γ b c a + γ 2 b + c n γ b a 2 c b 2 γ 2 a + c b 2 r a 2 c n γ 2 b a + γ b c + γ b c r a 2 c r γ b a 2 γ a + γ 2 b a c b 2 γ 2 2 a c r 2 c n γ 2 b 2 b γ a γ + c n γ b + 2 c n γ + 2 γ b 2 c a + 2 c n γ b a c r b γ + γ b 2 c 2 ( a + 1 γ 2 b 2 + γ b 2 + γ b 2 a ) ( a + 1 ) , we find that whether E R i i E N < 0 depends on the numerator of the above equation. Then, solving the above equation, we can yield the root of: c r 1 = r b c a 1 + c n b a 2 r b 2 c a + c b 2 a 2 c n γ b a + 2 c b 2 a + 2 c n b a + c n b + c b 2 + b γ a + 2 c n a b a 2 γ b 2 c 2 c n γ b 2 b a + 2 c n b + b γ a + b c 1 b γ a b γ + a 2 + 2 a . When c r > c r 1   E R i i E N < 0 is true.
Comparing c r 1 , c r ¯ and c ¯ r , we find that c r 1 < c r ¯ < c ¯ r .
Then, we can conclude that, for any c r ¯ < c r < c ¯ r , E R i i E N < 0 is always true.
In sum, we can conclude that the presence of remanufacturing is always beneficial to the environment, that is, E N > E R .

Appendix F. Proof of Proposition 5

(i) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a
E R i / c r = 1 2 ( a γ + 1 ) > 0 is always true.
(ii) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
E R i i / c r = b ( 1 + a b γ ) 2 ( a + 1 γ 2 b 2 + γ b 2 + γ b 2 a ) < 0 is always true.
Under the partial remanufacturing scenario, the total environmental impact increases with the remanufacturing cost, that is, E R / c r > 0 ; however, under the full remanufacturing scenario, the opposite is true, that is, E R / c r < 0 .

Appendix G. Proof of Proposition 6

Based on the analysis of Proposition 3, we find that, for γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a , there is a threshold of c r Δ = c r 2 = 2 a 2 c n a 2 c b a 2 c b 2 c n + 2 + 2 b γ c n 2 ( 1 c n c b ) ( 1 + a ) ( 1 + a r 2 b 2 + r b 2 + r b 2 a ) 2 b ( 1 + a )  then for c r Δ b = a c n a + γ b 3 c a + 1 + γ b 3 c c n γ 2 b 3 c + ( c n 1 ) ( 1 + a ) ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) b 2 ( 1 + a ) ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) we find that for any c > 0 , c r Δ b > 0 is always true.
We are now in a position to prove q 1 / b < 0 as follows.
(i) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a
q 1 R i / b = c 2 < 0
(ii) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a = c r ¯ < c r < c ¯ r = γ c n 1 + a ,
q 1 R i i / b = q 1 R i i = 2 γ 2 b a c n γ 2 b 2 a a 2 c r 2 γ b a 2 + γ c b 2 c γ 2 b 2 + c r γ b 2 + 2 b γ c n c r γ 2 b 2 + c n γ a c n γ 2 b 2 + c n γ 3 b 2 + 4 b γ c n a + c a 2 γ b 2 a c r γ 2 b 2 + 2 c r γ b 2 a + 2 c γ b 2 a c a 2 c + a 2 c r γ b 2 c a γ 2 b 2 2 γ 2 b c n a c r + c n γ + 2 γ b c n a 2 + 2 γ 2 b 2 γ b 2 b γ 2 c n 2 a c r 2 c a 4 γ b a 2 ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) 2
Then, solving the above equation, we can yield the root of:  c r 1 = 4 b γ c n a c c n γ 2 b 2 a + c a 2 γ b 2 + 2 γ c b 2 a c a γ 2 b 2 2 γ 2 b c n a + 2 γ b c n a 2 4 γ b a + c n γ 3 b 2 c γ 2 b 2 c n γ 2 b 2 + c γ b 2 + 2 b γ c n + 2 γ 2 b a 2 γ 2 b c n 2 γ b a 2 + c n γ a 2 b γ + 2 γ 2 b + c n γ c a 2 2 c a 1 a 2 γ b 2 2 γ b 2 a + a γ 2 b 2 + γ 2 b 2 γ b 2 + a 2 + 2 a . When c r > c r 1   q 1 R i i / b < 0 is true.
Comparing c r 1 , c r ¯ and c ¯ r , we find that c r 1 < c r ¯ < c ¯ r .
Then, we can conclude that, for any c r ¯ < c r < c ¯ r , q 1 R i i / b < 0 is always true.
In sum, we can conclude the equilibrium quantities as q 1 / b < 0 .

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Figure 1. Research plan of this paper.
Figure 1. Research plan of this paper.
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Figure 2. Impact on the incentives for innovation.
Figure 2. Impact on the incentives for innovation.
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Figure 3. Impact on the profitability.
Figure 3. Impact on the profitability.
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Figure 4. Impact on environmental sustainability.
Figure 4. Impact on environmental sustainability.
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Table 1. Comparison with some related studies.
Table 1. Comparison with some related studies.
Research IssuesInnovation DecisionsRemanufacturing DecisionsTake-Back Regulations
Researh Papers
This paper
Galbreth et al. [14], Qian et al. [16], Galbreth and Blackburn [38], Liu et al. [39], Dai and Zhang [29]××
Manso [20], Ederer and Manso [21], Hall et al. [22], Rosokha and Younge [23], Yin et al. [24]××
Esenduran et al. [34], Zhao et al. [35], Huang et al. [36], Pazoki and Samarghandi [37]××
√ means “yes”, × means “N/A”.
Table 2. Main notations in this paper.
Table 2. Main notations in this paper.
NotationDefinition
a The innovation level of the improved version
γ The value discount of remanufactured products
p n j / q n j The price/quantity of the new product in Model j, j ( N , R )
p r j / q r j The price/quantity of the remanufactured products Model j
p 1 / q 1 The price/quantity of the new product in Period 1.
c n / c r The unit production/remanufacturing cost
ρ The discount factor of the money
c The unit collection cost for a used core
i d / E j The unit/total environmental impact of landfilling
b The collection rates of the used cores
π i j The profits of Period i in Model j
Table 3. Equilibrium decisions and profits in both models.
Table 3. Equilibrium decisions and profits in both models.
No Remanufacturing Scenario
 Equilibrium decisions: q 1 N = 1 c n 2 , q n N * = 1 + a c n 2 ( 1 + a ) , K N = ρ ( 1 + a c n 2 ) 2 ( a + 1 ) ( a + 2 )
 Equilibrium profits: π T N = ρ 2 ρ c n + 2 ρ a + ρ c n 2 2 ρ a c n + 1 + ρ a 2 + a 2 c n 2 a c n + c n 2 + a c n 2 4 ( 1 + a ) K δ 1 2 1 / 2 .
Remanufacturing Scenario
 (i) For γ ( b γ + b 2 c + b 2 c a b b a b 2 γ c b γ c n + c n + b c n a + c n ) 1 + a < c r < γ c n 1 + a ,
 Equilibrium decisions: q 1 R i = 1 c n b c 2 , q n R i = 1 + a c n + c r γ 2 1 + a γ ,
q r R i = γ c n c r a c r 2 γ ( 1 + a γ ) , K R i = ρ ( 1 + a 2 γ + 2 c n c r a γ c n 2 c r 2 + γ 2 ) 2 a + 2 1 γ 1 + a γ .
 Equilibrium profits:
π T R = 2 ρ c b γ c n 2 ρ γ c n 2 ρ c b γ 2 c n + 2 ρ c 2 b 2 γ 2 γ c n + ρ c r 2 + a γ c n 2 2 a γ c n 2 ρ c b γ b 2 c 2 γ b 2 c 2 a γ + b 2 c 2 γ 2 + γ + ρ γ a 2 ρ γ 2 a + 2 ρ γ 2 c n γ 2 c n 2 + 2 ρ γ a 2 ρ γ a c n + a γ + ρ γ c n 2 + ρ c γ 2 a + 2 ρ c b γ 2 + 2 ρ c b γ a c n + ρ γ + 2 ρ c 2 b 2 γ a + γ c n 2 2 ρ c 2 b 2 γ 2 ρ γ 2 2 ρ c b γ a + 2 γ 2 c n γ 2 2 ρ γ c n c r 4 γ a γ + 1 K δ 1 2 1 / 2 .
 (ii) For γ c n 1 + a < c r < 1 + a c n c n a + b γ c n c b c b a b ( 1 + a ) ,
 Equilibrium decisions: q 1 R i i = 1 + a c n c n a + c n γ b c r b b a c r c b c b a 2 ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) , q n R i i = 1 + a + γ b 2 a + c n γ b γ b + γ b 2 + γ b 2 c r + γ b 2 c c n γ c n b 2 γ 2 b 2 2 ( 1 + a γ 2 b 2 + γ b 2 + γ b 2 a ) ,
q r R i i = b q 1 R i i , K R i i = ρ 1 + a + 2 γ 2 b 2 c n + γ 4 b 4 2 γ 3 b 4 + γ 2 b 4 + 2 c b 3 γ 2 γ 3 b 4 a + γ 2 b 4 a 2 c n γ 2 b 3 c n 2 γ 2 b 2 c r 2 b 4 γ 2 c 2 b 4 γ 2 + 2 c n 2 γ 2 b 3 c n 2 γ 2 b 4 + 2 c r b 3 γ 2 γ 2 b 2 a + 2 γ b 2 a 2 c n γ b c n 2 3 γ 2 b 2 + 2 γ b 2 + 2 c n 2 γ b + 2 c n γ b 2 c r + 2 c n γ b 2 c 2 c n 2 γ b 2 2 c r b 4 c r 2 + 2 c n γ 2 b 4 c r + 2 c n γ 2 b 4 c 2 c n c r b 3 γ 2 2 c n c b 3 γ 2 2 a + 2 1 γ 2 b 2 + γ b 2 1 + a γ 2 b 2 + γ b 2 + γ b 2 a .
 Equilibrium profits:
π T R i i = π 1 R i i + π 2 R i i = p 1 c n q 1 + p n c n q n + p r c r q r c b q 1 K 1 + a 2 1 / 2 .
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Yang, D.; Yang, Q.; Zhang, L. Operational Decisions on Remanufacturing under the Product Innovation Race. Sustainability 2023, 15, 4920. https://doi.org/10.3390/su15064920

AMA Style

Yang D, Yang Q, Zhang L. Operational Decisions on Remanufacturing under the Product Innovation Race. Sustainability. 2023; 15(6):4920. https://doi.org/10.3390/su15064920

Chicago/Turabian Style

Yang, Dexiang, Qin Yang, and Lei Zhang. 2023. "Operational Decisions on Remanufacturing under the Product Innovation Race" Sustainability 15, no. 6: 4920. https://doi.org/10.3390/su15064920

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