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Competitive strategies for original equipment manufacturers considering carbon cap and trade
Transportation Research Part D 78 (2020) 102193
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Competitive strategies for original equipment manufacturers considering carbon cap and trade
T
Qiangfei Chaia, Zhongdong Xiaoa, , Guanghui Zhoub,c ⁎
a b c
School of Management, Xi’an Jiaotong University, Xi’an 710049, China School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China
ARTICLE INFO
ABSTRACT
Keywords: Remanufacturing Competition Carbon cap and trade Fixed-fee licensing Royalty licensing
This paper considers an original equipment manufacturer (OEM) faces competition from an independent remanufacturer (IR) and they both are regulated by carbon cap and trade policy (CTP). We develop models to explore the OEM’s optimal competitive strategy in the face of IR’s competition and environmental regulation. We first investigate the impact of CTP on the OEM and IR. Then, we analyze three competitive strategies that the OEM may choose: remanufacturing, fixed-fee licensing, and royalty licensing. We investigate their optimal decisions under each strategy and identify the conditions under which these strategies can coordinate the OEM and IR. Finally, we explore conditions under which one strategy is superior to another. The results show that the OEM is worse off when competing with the IR under CTP if the carbon cap allocated to the OEM is small. Fixed-fee licensing and royalty licensing can coordinate the OEM and IR not only from an economic perspective but also from an environmental perspective. The OEM’s optimal competitive strategy is determined by thresholds of three critical parameters: the fixed cost of setting up a remanufacturing system, the fixed-fee, and the per-unit royalty. We provide specific guidance on strategy selection for the OEM.
1. Introduction As we all know, the environment around us is getting worse because of human activities. One of the effective ways to reduce human impact on the environment is remanufacturing, since it can not only save production costs but also save energy consumption and reduce waste emissions (Guide and Van Wassenhove, 2001, Atasu et al., 2008, Ovchinnikov et al., 2014). Although remanufacturing is environmentally friendly and cheaper than producing new products, many original equipment manufacturers (OEMs) do not engage in it. The OEMs’ major concerns about remanufacturing include cost and cannibalization (Ferguson and Toktay, 2006). Too high costs of setting up a remanufacturing system are usually unacceptable for them. For cannibalization, OEMs worry that their new products’ market share will be eroded by remanufactured products if remanufactured products price lower, and such cannibalization is undesirable if the margin profit of new products is higher than that of remanufactured products. If remanufacturing is profitable and OEMs do not perform it, independent remanufacturers (IRs) may enter the market. Thus, OEMs will inevitably face external competition under this situation. How to cope with external competition has been bothering OEMs. Due to the importance of this problem for OEMs, many studies have explored it, such as Majumder and Groenevelt (2001), Ferguson and Toktay (2006), Webster and Mitra (2007), Wu and Wu (2016), Wu and Zhou (2016).
⁎
Corresponding author. E-mail addresses: [email protected] (Q. Chai), [email protected] (Z. Xiao), [email protected] (G. Zhou).
https://doi.org/10.1016/j.trd.2019.11.022
1361-9209/ © 2019 Elsevier Ltd. All rights reserved.
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In addition, it should be noted that many countries have implemented or plan to implement some environmental policies to protect the environment, and firms must adjust their operation decisions under this situation. However, research on how to help OEMs cope with external competition under environmental regulation is absent. One of the popular environmental policies is carbon cap and trade policy (CTP). The European Union Emission Trading Scheme (EU ETS) is an exemplary example of CTP. It has operated in Europe for many years and remains to be the biggest emissions trading scheme in the world so far. Moreover, China has been working on reducing carbon emissions and launched seven pilot emissions trading markets in 2011. After then, China established a national emissions trading market in 2017 (Chai et al., 2018). There are also other emissions trading markets in the world, such as the Chicago Climate Exchange and the Australia Climate Exchange (Zhang and Xu, 2013). Under CTP, firms are first allocated some emission allowances, then they can purchase insufficient allowances or sell surplus allowances according to their situation. Therefore, a firm that emits less pollution may obtain extra profits by selling surplus allowances. This flexible mechanism provides an opportunity for IRs to obtain more profits when the carbon cap allocated to them is large. Hence, the IRs’ free riding behavior becomes more obvious under CTP because IRs enjoy not only low cost advantage but also low emission advantage of remanufactured products while they do not produce new products. To prevent IRs’ free riding, several strategies are available to OEMs. In this paper, we examine two strategies, namely remanufacturing strategy and licensing strategy. Remanufacturing strategy means that OEMs engage in remanufacturing. For example, Caterpillar collects and remanufactures its own construction and mining equipment. Licensing strategy means OEMs charge IRs a patent licensing fee if IRs want to enter the remanufacturing market. Recently, several patent lawsuits about remanufactured products attract researchers’ attention. To give an example, Canon v. Recycle Assist is an important intellectual property event in the world. The cause of this lawsuit is that Recycle Assist imported and sold Canon’s remanufactured cartridges with no authorization. Canon filed a lawsuit against Recycle Assist in Japan and finally won (Hong et al., 2017). This case implies that OEMs have begun to pay attention to patent protection of their renewable products and also means that IRs have to pay a patent licensing fee to engage in remanufacturing if OEMs charge them. Therefore, licensing strategy can be a powerful strategy for preventing IRs’ free riding behavior. The licensing strategy can be further divided into two strategies, namely fixed-fee licensing and royalty licensing. These two licensing strategies are widely used in academic research and practice (Wang et al., 2018, Yang et al., 2019). Fixed-fee licensing means that OEMs charge IRs a fixed licensing fee, which is independent of IRs’ production quantities of remanufactured products. Royalty licensing means that OEMs charge IRs a per-unit royalty for per unit remanufactured products. Although research on entry-deterring strategy for OEMs is flourishing, studies about competitive strategy for OEMs under CTP are quite scant, especially for studies simultaneously considering licensing strategy and CTP. We aim to fill this gap. In this paper, we provide insights into the following questions: (1) How does CTP, and to what extent, influence the OEM and IR? (2) What are the conditions that the three strategies (remanufacturing, fixed-fee licensing, and royalty licensing) are able to coordinate the OEM and IR under CTP? Will they attain a better environmental performance under the three strategies? (3) For the three strategies, which one should the OEM choose? Which parameters significantly influence the choice? This paper aims to provide decision support for OEMs that face competition from IRs, and that may be simultaneously regulated by CTP. In this study, we examine a competitive situation where an IR collects and remanufactures used products that were originally produced by an OEM, and thus leading to external competition. Furthermore, we consider both the OEM and IR would be regulated by CTP. We develop models of competition without CTP and under CTP to characterize the influence of CTP. In addition, we explore three alternative strategies that the OEM can choose, namely remanufacturing strategy, fixed-fee licensing strategy, and royalty licensing strategy. We identify the conditions under which these strategies are able to coordinate the OEM and IR and meanwhile coordinate economic performance and environmental performance. Finally, we investigate the OEM’s optimal strategy when competing with the IR under CTP. The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces the research problem and gives some essential assumptions and notations. Section 4 investigates the influence of CTP on both the OEM and IR. The OEM’s optimal competitive strategy under CTP is explored in Section 5. Section 6 presents our conclusions and limitations. All proofs are shown in the Appendix A. 2. Related research Our research is related to three streams of literature: competition between OEMs and IRs, operations management under CTP, and technology licensing. In this section, we review some prominent studies and position our research in the literature. To the best of our knowledge, Majumder and Groenevelt (2001) are the first who explore the area of competition between OEMs and IRs by using mathematical models. They develop a two-period model and investigate the effect of competition under four reverse logistics configurations. They mainly focus on understanding the incentives for OEMs and IRs and find that OEMs would like to increase IRs’ cost while IRs have incentives to reduce OEMs’ cost. But they do not vertically distinguish between new products and remanufactured products. Ferguson and Toktay (2006) differentiate new products from remanufactured products and examine OEMs’ entry-deterrent strategies, which includes collection strategy and remanufacturing strategy. Webster and Mitra (2007) examine the influence of take-back laws under a competitive situation where OEMs compete with IRs. They investigate the impact of collective WEEE take-back and individual WEEE take-back on OEMs and society. Then, Mitra and Webster (2008) consider a similar competitive situation and investigate the impact of government subsidies on profits and remanufacturing activity. They mainly consider the 2
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influence of different subsidy schemes. Webster and Mitra (2007) and Mitra and Webster (2008) explore the influence of take-back laws or subsidies when OEMs face competition from IRs; however, alternative strategies that OEMs can choose are not addressed. In contrast, our focus is on investigating alternative strategies that OEMs can choose in the face of competition. Recently, some researchers are interested in studying if IRs are always detrimental to OEMs. Wu and Zhou (2016) examine whether IRs always hurt OEMs and find that OEMs may benefit from the entry of IRs. Jin et al. (2017) also find IRs may be beneficial to OEMs by taking suppliers into consideration. These studies reinforce the notion that OEMs and IRs can coexist. Therefore, it is necessary to study what strategies or contracts can coordinate OEMs and IRs and our study focus on this problem. Operations management under CTP is a hot topic in recent years. Consequently, a number of studies appear in this research area. These studies can be classified as emission reduction technology investment considering CTP (Dong et al., 2016, Drake et al., 2016, Xia et al., 2018), production and inventory decisions under CTP (Benjaafar et al., 2013, Chen et al., 2016, Du et al., 2016, Xu et al., 2017, Tang et al., 2018), supply chain coordination under CTP (Jaber et al., 2013, Xu et al., 2016, Xu et al., 2018), as well as supply chain network design and transport mode selection aimed at minimizing carbon emissions (Hoen et al., 2014, Gao et al., 2018, Zhang et al., 2018). Benjaafar et al. (2013) study how to integrate several regulatory policies into operational decision-making, using simple and widely used models. Their focus is on studying whether operational adjustments and collaboration with other members within the same supply chain are able to reduce carbon emissions. Dong et al. (2016) examine a manufacturer’s sustainability investment and a retailer’s order quantity considering CTP for decentralized and centralized supply chains. Moreover, they investigate supply chain coordination. Xia et al. (2018) focus on emission reduction of a supply chain under CTP. They think traditional self-interest hypothesis is imperfect and attempt to incorporate reciprocal preferences and consumers’ low-carbon awareness into their supply chain model. For research on production and pricing decisions under CTP, considering consumers’ low-carbon premium, Du et al. (2016) study whether low-carbon production under CTP is profitable and explore the optimal production quantity of the low-carbon product. Xu et al. (2017) study the production and pricing problem in a make-to-order supply chain consisting of a manufacturer that is regulated by CTP and a retailer. Furthermore, studies on closed-loop supply chain management considering CTP begin to emerge recently. Chang et al. (2015) study a monopolist manufacturer’s production decisions when it engages in both manufacturing and remanufacturing under CTP. Liu et al. (2015) investigate an IR’s optimal remanufacturing quantity under three common carbon emission policies: CTP, carbon tax, and mandatory carbon emissions capacity. Wang et al. (2017) consider a monopolistic manufacturer is constrained by capital and study the optimal manufacturing/remanufacturing decisions under CTP. Chai et al. (2018) explore whether CTP is favorable for a monopolistic manufacturer that engages in both manufacturing and remanufacturing. However, these studies do not capture the competition between OEMs and IRs considering CTP. Different from these studies, by taking remanufacturing and IRs into consideration, we investigate the potential impact of CTP on both OEMs and IRs and explore appropriate strategies that are effective to coordinate them. The last stream of literature related to our study is technology licensing. Researchers often study technology licensing under competitive situations (Chen et al., 2017, Hong et al., 2017, Huang and Wang, 2019, Jeon, 2019, Yang et al., 2019). For example, Chen et al. (2017) investigate a component supplier’s intellectual property licensing strategy selection problem under a duopoly competition situation. They assume that the supplier can charge a licensing fee to two downstream manufactures either according to the downstream manufacturers’ sales (product-based strategy) or according to the supplier’s wholesales (component-based strategy). Yang et al. (2019) study optimal licensing strategy under a situation where two suppliers compete with each other considering supply disruption. They examine the effect of the supply risk on one supplier’s willingness to license technology and investigate fixed-fee licensing and royalty licensing strategy. Their focus is on studying the influence of supply disruption on the optimal licensing strategy selection. These studies introduce licensing strategies into the forward supply chain, however, not the closed-loop supply chain. The one who introduces licensing strategies into the closed-loop supply chain is Hong et al. (2017). They consider a manufacturer (the licensor) and a remanufacturer (the licensee) compete in collecting and remanufacturing used products. They investigate two licensing strategies, fixed-fee licensing strategy and royalty licensing strategy, and find that there exists a threshold of the fixed fee below which royalty licensing is better for the manufacturer. Similar to their study, we also investigate licensing strategies in the context of remanufacturing. However, we further extend their study and aim to explore licensing strategies in the context of environmental regulation, which previous studies do not address. We integrate CTP and licensing strategies into traditional manufacturing and remanufacturing production models and obtain insights about how does CTP affect an OEM’s and an IR’s decisions, and whether licensing strategies are effective to coordinate them. Thus, our results complement the above three streams of literature. We contribute knowledge to the literature in four respects. First, we investigate the influence of CTP on both the OEM and IR when they compete with each other. Second, we explore the licensing strategy as a coordination contract under the situation where the OEM competes with the IR under CTP. Third, we identify the conditions under which the OEM and IR can be coordinated under CTP. Finally, we explore the OEM’s preference for the three strategies under different remanufacturing scenarios. 3. Problem description and assumptions We consider a competitive situation in which there are an OEM and an IR. The OEM produces new products and the IR produces remanufactured products by acquiring used products that were originally produced by the OEM. We assume the planning horizon is two periods. Because a two-period model is capable of capturing major dynamics of the problem and is widely used in extant studies about remanufacturing (Ferguson and Toktay, 2006, Bulmus et al., 2014, Mutha et al., 2016). The OEM produces new products in both periods, while the IR collects end-of-use products from consumers and remanufactures these products in the second period. Thus, the quantities of remanufactured products are limited by the quantities of new products produced by the OEM in the first period. As the remanufactured product has the same functions as the new product but is cheaper than the latter, it inevitably leads to 3
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market cannibalization and affects the new product sales. Guide Jr and Li, 2010 empirically prove that remanufactured products have the potential to cannibalize new product sales. It means that the OEM would face competition from the IR if the IR enters the market in the second period. We assume that consumers value remanufactured products lower than new products and make purchasing decisions based on their utility obtained from buying the two types of products. This assumption is true in practice and has been validated by empirical evidence. For example, Guide Jr and Li, 2010 found that consumers’ willingness to pay (WTP) for remanufactured products is about 15% lower than that for new products. Other empirical evidence can be found in Ovchinnikov (2011) and Abbey and Blackburn (2015). In addition, Amazon usually prices remanufactured products (or called refurbished products) lower than new products, such as products like cell phones, computers, and office products, demonstrating the fact of different consumers’ WTP for the two types of products. Based on the above assumption, the demand functions can be obtained from consumers’ utility. The consumers’ WTP for the new product is heterogeneous, denoted as . We assume is distributed uniformly between 0 and 1. denotes consumers’ tolerance for the remanufactured product, higher means that consumers are more easily accept the remanufactured product. We assume 0 < < 1. pn , and a consumer’s utility from buying a remanufactured Therefore, a consumer’s utility from buying a new product is Un = pr , where pn and pr represent the selling price of the new and remanufactured product, respectively. A consumer product is Ur = would buy a new product if Un > Ur and Un > 0 and buy a remanufactured product if Ur > Un and Ur > 0 . We normalize the market size to 1. Therefore, we can obtain the demand functions, see Chai et al. (2018). We use inverse demand functions in this paper, which can be derived from the demand functions by simple algebra, shown as follows:
p1 = 1
(1)
q1
p2n = 1
q2n
p2r = (1
q2n
(2)
q2r
(3)
q2r )
where q1, q2n , and q2r represent the demand of new products in the first period, in the second period, and the demand of remanufactured products in the second period, respectively. As there are no used products available to collect in the first period, there are only new products on the market. The above inverse demand functions reflect the substitution and competition between new and remanufactured products because as the production quantity of remanufactured (new) products increase, the new (remanufactured) product’s price would decrease. We consider the government implements CTP for emission reduction. Let C1O and C2O denote the carbon cap allocated to the OEM in the first and second period, C2I denotes the carbon cap allocated to the IR in the second period. Both the OEM and IR can purchase or sell emission allowances in price P in an emission trading market but they have to offset the emissions beyond the cap by purchasing emission allowances at the end of each period. We assume that the carbon emissions and production cost from production per new product are e and c . The carbon emission savings and cost savings per remanufactured product are vk and sk (k = O (OEM), I (IR) ). Therefore, the carbon emissions and production cost from production per remanufactured product are e vk and c sk . For tractability, we assume that when the OEM engages in remanufacturing, the IR would be ruled out of the market. It means that remanufacturing is available for the IR if the OEM has no intention of remanufacturing. This assumption is already validated in prior studies, such as Ferguson and Toktay (2006), Subramanian and Subramanyam (2012), and Subramanian et al. (2013). Furthermore, this is true in many situations. For example, some business equipment manufacturers have a strong relationship with their customers because they not only sell products to their customers but also provide maintenance service. Therefore, the OEMs are able to easily obtain the end-of-life equipment, leaving little room for IRs to collect and remanufacture the equipment. In addition, some OEMs may Table 1 Notation. Parameters
Definition
pijk ,
The sale price and production quantity of product j in period i for firm k. i = 1, 2 ; j = n (newproducts), r (remanufacturedproducts) ; k = O (OEM), I (IR) . Since only OEM produces new products, we omit k when j = n. The production cost per new product and cost savings per remanufactured product, 0 < sk < c . The carbon emissions from production per new product and carbon emission savings per remanufactured product, 0 < vk < e . The carbon cap allocated to firm k in period i.
c, e,
Cik Tik P
Ek Fr F r kh g
qijk sk vk
The carbon trading quantity of firm k in period i. The carbon trading price. Consumers’ tolerance for remanufactured products, 0 < < 1. Core collection ratio, defined as the fraction of new products sold in the first period that can be collected in the second period, 0 < The total carbon emissions of firm k. The The The The
fixed cost of setting up a new remanufacturing system. fixed-fee that the OEM charges the IR for remanufacturing licensing. per-unit royalty that the OEM charges the IR for per unit remanufactured products. firm k’s profit in optimal solution scenario h in model g. k = O (OEM), I (IR) ; h = a , b, c ; g = B, C , R , LF , LR .
4
< 1.
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provide a trade-in business model to attract their old customers, leading to an inevitable collection of the majority of the used products. Thus, it would be expensive for IRs to entry the market. For convenience of reference, we summarize the model’s notation in Table 1. 4. The impact of CTP In this section, we investigate the impact of CTP on the OEM and IR. We answer the questions: “If the introduction of CTP would affect the OEM’s profit and, if so, whether the IR’s profit would increase, and what is the OEM’s optimal production decisions under this situation?” We use subscript g {B , C } to denote the model of competition without CTP and under CTP, respectively. 4.1. The model of competition without CTP-Model B We first analyze the traditional competition between the OEM and IR when there is no CTP implemented by the government. The OEM’s and IR’s profit functions can be written as O B
= (pB1
c ) qB1 + (pB2n
I B
= (pBI 2r
c + sI ) qBI 2r , s. t. ,qBI 2r
(4)
c ) qB2n
(5)
qB1
The OEM’s and IR’s optimal decisions are characterized by Proposition 1. Superscript h optimal solution scenarios.
{a, b , c } represents three different
Proposition 1.. The OEM’s and IR’s optimal production quantities when competition without CTP are: (i) qBa1 = (1 (ii) qBb1 = (1 (iii) qBc1 = (1
c )/2 , qBa2n = (1 c )/2 , and qBIa2r = 0 , when sI t1; 2c + 2sI )/ ( c )/2 , qBb2n = (c + + sI 2)/( 4) , and qBIb2r = (c + )/4 , and qBIc2r = (1 c )/2, when sI > t2 ; c )/2 , qBc 2n = (1 c )(2
where t1 =
(c + 1) /2 + c , t2 =
(4
)(1
c )/4
4), when t1 < sI
t2 ;
(c + 1)/2 + c .
When deciding to engage in remanufacturing, the IR has to consider the cost savings per remanufactured product. If sI is low (sI t1), which means that the production cost of a remanufactured product is almost like that of a new product, the IR tends to quit the market. We call the first optimal solution scenario no remanufacturing situation. However, if sI is moderate (t1 < sI t2 ), the IR will enter the market and produce remanufactured products. It should be noted that the IR will only remanufacture a portion of available used products in this situation, and we call this partial remanufacturing situation. Further, if sI is large (sI > t2 ), the IR will remanufacture all available used products because remanufacturing is lucrative enough now, and we call the third optimal solution scenario full remanufacturing situation. 4.2. The model of competition under CTP-Model C When the government decides to implement CTP, both the OEM and IR have to make decisions under CTP. In this case, the OEM’s profit function is: O C
= (pC1
s. t. ,
c ) qC1 + (pC 2n
c ) qC 2n
PT1O
PT2O
eqC1 = C1O + T1O eqC 2n = C2O + T2O
(6)
The IR’s profit function is: I C
= (pCI 2r
s. t. ,
(e qCI 2r
c + sI ) qCI 2r
PT2I
vI ) qCI 2r = C2I + T2I qC1
(7)
The following proposition characterizes the OEM’s and IR’s optimal decisions. Proposition 2.. The OEM’s and IR’s optimal production quantities when competition under CTP are: (i) qCa1 = (1 (ii) qCb1 = (1 when t3 < (iii) qCc1 = (1
c c PvI c
Pe )/2 , qCa2n = (1 c Pe )/2 , and qCIa2r = 0 , when PvI + sI t3 ; Pe )/2 , qCb2n = (Pe + PvI + c + sI + 2)/( 4) , and qCIb2r = (2(Pe PvI + c sI ) + sI t4 ; Pe )/2 , qCc 2n = (2 )(1 c Pe )/4 , and qCIc2r = (1 c Pe )/2 , when PvI + sI > t4 ;
5
(1 + c + Pe ))/ (
4) ,
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where t3 = Pe + c
(1 + c + Pe )/2 , t4 = Pe + c
(1 + c + Pe )/2
(
4)(1
c
Pe )/4 .
Different from Model B, the IR has to put the carbon emission savings into consideration when making remanufacturing decisions in Model C. To be specific, when the total cost savings PvI + sI , which includes the carbon emission cost savings and the production cost savings, are small (PvI + sI t3 ), the IR will not engage in remanufacturing. Once PvI + sI is beyond the threshold t3 , remanufacturing is profitable for the IR and the IR will enter the market and competes with the OEM. The IR will only remanufacture a portion of available used products in this situation. When PvI + sI is large, the IR will remanufacture all available cores. The three optimal solution scenarios in Model C also correspondent to three remanufacturing situations: no remanufacturing, partial remanufacturing, and full remanufacturing. 4.3. Comparison and analysis 4.3.1. Profit analysis Since we would like to know the impact of implementing CTP on the OEM and IR, we compare the optimal decisions and profits of Model B and Model C. By substituting the optimal decisions shown in Proposition 1 and Proposition 2 back into the OEM’s and IR’s profit functions, we can obtain the optimal profits of the OEM and IR. Comparing the OEM’s optimal profits in Model B and Model C under the three remanufacturing situations, we have the following proposition. Proposition 3.. The OEM’s optimal profits in Model B and Model C are related as follows: (i) When C1O + C2O < el/2 , BOa > COa ; 4)2 , (ii) When C1O + C2O < el/4 + m /( (iii) When C1O + C2O < eln/16 , BOc > COc ; where l = 2
2c
Pe , m =
Ob B
>
Ob C ;
2)) , and n =
(e + vI )(P (e + vI ) + 2(c + sI +
2 2
4
+ 8.
Proposition 3 reveals that the impact of implementing CTP on the OEM’s profits is negative when the carbon cap allocated to the OEM is small for all of the three optimal solution scenarios. It means that when the carbon cap is tight, which would happen after CTP has been implemented a period of time, the OEM will worse off if competing with the IR under CTP. However, it is surprising that CTP has no influence on the OEM or even is better for the OEM when the carbon cap is large, which usually happens at the beginning of the implementation of CTP. For example, EU ETS aims for carbon emission reduction by 20% relative to 1990′s emission level before 2020 through three phases. The participating firms received adequate allowances that are sufficient to cover their emissions in the first phase; however, the cap is tightened in the second phase and further reduced each year by 1.74% in the last phase (Chan et al., 2013). Therefore, the OEM is able to benefit from CTP at its early stage. Nevertheless, at CTP’s late stage, competing with the IR under CTP will lead to a decrease in the OEM’s profit. Fig. 1 visually shows the results of Proposition 3. The parameters we selected are c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vI = 0.2 ; sI = {0.03, 0.1, 0.3} for the optimal solution scenarios {a, b, c} . Comparing the IR’s optimal profits in Model B and Model C under the three remanufacturing situations, we have the following proposition.
Fig. 1. Comparison of the OEM’s profits in Model B and Model C.
6
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Fig. 2. Comparison of the IR’s profits in Model B and Model C.
Proposition 4.. The IR’s optimal profits in Model B and Model C are related as follows: (i) BIa = CIa = 0 ; (ii) When C2I > u/ ( (iii) When C2I > (e ( where u =
((
4)2 , 2) l
Ib Ib B < C ; 2 + w )/8
2) e + 2vI )(Pe (
,
Ic B
<
Ic C ;
2) + 2 (c + 1) + 2PvI
4c + 4sI ) , w =
2e ((
2)(Pe + 2c ) + 2sI + 2)
4vI (Pe + c
1) .
The IR’s profit is zero in the first optimal solution scenario because the IR doesn’t engage in remanufacturing under this situation. However, the IR will benefit from competing with the OEM under CTP when the carbon cap is large in the second optimal solution scenario. The rationale behind this is that the total cost savings from remanufacturing are moderate in this scenario, and thus a small cap would restrict the IR’s production and a large cap would not only promote the IR’s production but also make it possible to sell surplus emission allowances. Similarly, given a large carbon cap, the IR always obtain more profit when competing with the OEM under CTP than without CTP in the third optimal solution scenario. It is worth to note that the cap threshold 2) l 2 + w )/8) in the third optimal solution scenario above which the IR obtains more profit may be lower than the cap ( (e ( 4) 2 ), due to more cost savings in the third optimal solution scenario. We threshold in the second optimal solution scenario (u/ ( plot Fig. 2 to show it as well as the results of Proposition 4. We set c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vI = 0.2 ; sI = {0.1, 0.3} for the optimal solution scenarios {b , c} . From Fig. 2, we can easily understand Proposition 4. As the IR’s profit is zero in the first optimal solution scenario a , we do not plot it. The two critical cap thresholds of the scenario b and c are represented by X1 and X2 in Fig. 2. Thus, when C2I > X1 in the scenario b or C2I > X2 in the scenario c , the IR obtains more profit when competing with the OEM under CTP than without CTP. These two cap thresholds X1 and X2 are relatively small in Fig. 2, which means that the IR can always benefit from competition under CTP as long as the carbon cap is not very small. It should be noted that X2 < X1. This implies that with the increase of the total cost savings from remanufacturing, the critical cap threshold will decrease. In other words, benefiting from competition under CTP will become easier for the IR with the increase of the total cost savings from remanufacturing. 4.3.2. Carbon emissions analysis By multiplying the total production quantity of the OEM (the IR) by its per unit carbon emissions, we can obtain the total carbon emissions of the OEM (the IR). Comparing the carbon emissions in Model B and Model C, we have the following proposition: Proposition 5.. (i) The carbon emissions of the OEM in Model B and Model C are related as: (a) EBOa > ECOa ; (b) EBOb > ECOb ; (c) EBOc > ECOc . (ii) The carbon emissions of the IR in Model B and Model C are related as: (a) EBIa = ECIa = 0 ; /2) , EBIb > ECIb ; (b) When vI < e (1 (c) EBIc > ECIc . 7
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Fig. 3. Comparison of the OEM’s carbon emissions in Model B and Model C.
Proposition 5 implies that CTP is effective to reduce carbon emissions under the situation where the OEM competes with the IR. The OEM’s carbon emissions when competition without CTP are higher than that when competition under CTP for all the three optimal solution scenarios. However, this is not true for the IR. In the first scenario a , the IR’s carbon emissions are zero because the IR does not perform remanufacturing. In the second scenario b, the IR’s carbon emissions when competition under CTP are even higher than that when competition without CTP if the carbon emission savings are high. This is because the IR can obtain more profits by producing more remanufactured products when the carbon emission savings are high under CTP, and thus the IR’s carbon emissions in Model C will be higher than that in Model B. In the third scenario c , CTP is effective to reduce the IR’s carbon emissions. Figs. 3 and 4 show the results of Proposition 5. The parameters we selected are c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5; vI = 0.2 in Fig. 4(a) and vI = 0.4 in Fig. 4(b). As we can see, CTP is always effective to reduce the OEM’s carbon emissions and the IR’s carbon emissions when vI is small. When vI is large, CTP is ineffective in the second scenario b. However, CTP is always effective to reduce the IR’s carbon emissions in the third scenario c no matter vI is small or large. Therefore, from the perspective of carbon emission reduction, the IR is supposed to use the third optimal solution scenario in which the total cost savings from remanufacturing are large. It suggests that encouraging the IR to improve remanufacturing technology to increase the cost savings from remanufacturing will lead to the reduction of the IR’s carbon emissions under CTP.
Fig. 4. Comparison of the IR’s carbon emissions in Model B and Model C.
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5. OEM’s competitive strategies under CTP Based on the former analysis, it is clear that the OEM is worse off when competing with the IR under CTP. Therefore, in this section, we examine two alternative strategies that the OEM may choose to reduce the negative impact of competition and CTP, namely remanufacturing strategy and licensing strategy. We further divide licensing strategy into two strategies, namely fixed-fee licensing strategy and royalty licensing strategy. We use subscript g {R, LF , LR} to denote the remanufacturing strategy, fixed-fee licensing strategy, and royalty licensing strategy, respectively. 5.1. Remanufacturing strategy-Model R We consider the OEM engages in remanufacturing in the second period and thus deters the IR from entering the market. According to the assumptions in Section 3, the IR would be ruled out of the market when the OEM engages in remanufacturing. Because the OEM usually has a strong relationship with its customers and enjoys a brand advantage over the IR, making the collection of used products easier and cheaper than the IR. However, engaging in remanufacturing would incur a fixed cost, denoted as Fr , since the remanufacturing process is different from the manufacturing process; and thus the OEM has to set up a new remanufacturing system. Therefore, although the OEM has the priority in remanufacturing over the IR, the OEM must balance the trade-off between the input (the fixed cost) and the output (the incremental profit brought by remanufacturing). The OEM’s objective is: O R
= (pR1
c ) qR1 + (pR2n
c ) qR2n + (pR2r
c + sO ) qR2r
Fr
PT1O
PT2O
eqR1 = C1O + T1O s. t. , eqR2n + (e qR2r qR1
vO ) qR2r = C2O + T2O (8)
The OEM’s optimal decisions are characterized by the following proposition: Proposition 6.. The OEM’s optimal production quantities when performing remanufacturing under CTP are: (i) qRa1 = (1 c Pe )/2 , qRa2n = (1 c Pe )/2 , and qRa2r = 0 , when PvO + sO t5 ; qRb2n = (1 sO PvO )/2(1 ), qRb2r = (PvO + sO (1 (ii) qRb1 = (1 c Pe )/2 , and t5 < PvO + sO t6 ; qRc 2n = ( 2 (1 sO PvO ) + (1 )(Pe + c )) + 1 c Pe )/2x , (iii) qRc1 = ( (PvO + sO (1 qRc 2r = qRc1, when t6 < PvO + sO t7 ; (iv) qRd1 = ( (PvO + sO (Pe + c ) + ) + 1 c Pe )/2(1 + 2) and qRd2r = qRd1, when PvO + sO > t7 ; where t5 = (1
)(Pe + c ) , t6 = (1
)(
(1
c
Pe ) + Pe + c ) , t7 = (1
)(1
c
Pe )/
2
),
when
Pe ))/2x ,
and
)(Pe + c ))/2 (1
+1
)(1
c
,x=1+
2
2 2.
Proposition 6 implies that there are four optimal solution scenarios when the OEM engages in remanufacturing under CTP. Depending on the total cost savings from remanufacturing, the OEM would choose not to produce any remanufactured products or new products in the second period. Specifically, when PvO + sO is small enough, remanufacturing is not lucrative, and it is rational that the OEM does not engage in remanufacturing. Interestingly, when PvO + sO is large enough, remanufacturing is a better option than producing new products, and thus the OEM would stop producing new products and would perform remanufacturing only. In addition, there exists a threshold t6 below which the OEM would only remanufacture part of the available used products and above which the OEM would remanufacture all available used products. By substituting the optimal decisions shown in Proposition 6 back into the OEM’s profit function, i.e., Eq. (8), we can obtain the OEM’s optimal profits in Model R. Comparing the OEM’s optimal profits between Model R and Model C, we have the following proposition. Proposition 7.. The OEM’s optimal profits in Model R and Model C are related as follows: (i) ROa = COa ; (ii) When Fr < Fr' , (iii) When Fr < Fr'' ,
Ob R Oc R
> >
Ob C ; Oc C ;
where Fr' and Fr'' are shown in the Appendix A. Proposition 7 demonstrates that the fixed cost Fr is the critical factor that makes the remanufacturing strategy be capable of increasing the OEM’s profit compared with Model C. To be specific, the OEM’s profit in Model R is equal to that in Model C when there are no remanufactured products in the market. This is due to the fact that remanufacturing is not cheaper than producing new products in this situation. Consequently, the OEM would not play the remanufacturing strategy. When remanufacturing is profitable for the OEM, the fixed cost incurred from remanufacturing becomes an obstacle for the OEM to choose the remanufacturing strategy. When Fr is small, the OEM would be better off by playing this strategy. However, with the increase of Fr , the impact of this strategy on the OEM’s profit may reverse. More specifically, there exists a threshold below which using the remanufacturing has a positive impact 9
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Fig. 5. The OEM’s profits in Model R and Model C.
on the OEM. Once the fixed cost beyond the threshold, using the remanufacturing strategy is no longer a good choice. Therefore, we strongly advise the OEM to estimate the fixed cost before deciding to engage in remanufacturing. Using the parameters c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, C1O = C2O = 0.05, vO = 0.2 ; sO = {0.2, 0.3} for the optimal solution scenarios {b , c} , we plot Fig. 5 to show the results of Proposition 7. It is clear that Fr is a decisive parameter. When Fr is small, the OEM is able to obtain more profit by using the remanufacturing strategy. Fig. 5 clearly shows that the OEM’s profits in Model R are higher than that in Model C when Fr is zero. Thus, it is always suggested that the OEM whose fixed cost for remanufacturing is neglectable should engage in remanufacturing when facing competition from the IR under CTP. It also means that the remanufacturing strategy is an effective competitive strategy for the OEM when Fr is small. Next, we compare the carbon emissions of Model R and Model C and make the following observation. Observation 1. The total carbon emissions of Model R are no more than the total carbon emissions of Model C. Example 1.. Let c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5; {vO = 0.4, sO = 0.2, vI = 0.2, sI = 0.1} for the optimal solution scenario b and {vO = 0.4, sO = 0.3, vI = 0.4, sI = 0.3} for the optimal solution scenario c . In the first optimal solution scenario a , the OEM does not remanufacture in both Model R and Model C, and the optimal production quantities of new products are the same in these two models (see Proposition 2(i) and Proposition 6(i)). Thus, the total carbon emissions of Model R is equal to that of Model C, i.e.EROa = ECOa . If the OEM chooses the scenario b, the total carbon emissions in Model R are EROb = e (qRb1 + qRb2n) + (e vO ) qRb2r = 0.217 and in Model C are ECOb = e (qCb1 + qCb2n) + (e vO ) qCIb2r = 0.23. Therefore, we have EROb < ECOb . Similarly, if the OEM chooses the scenario c , the total carbon emissions in Model R and Model C are EROc = 0.209 and ECOc = 0.219, respectively. Naturally, we have EROc < ECOc . Since we obtain the same conclusion in many other cases, we conclude that the total carbon emissions of Model R are no more than the total carbon emissions of Model C.
5.2. Licensing strategy To reduce the negative impact of competition with the IR under CTP on the OEM, we consider that the OEM decides to use licensing strategy. There are two commonly used licensing strategies in existing research, namely fixed-fee licensing strategy and royalty licensing strategy (Hong et al., 2017, Yang et al., 2019). In this section, we assume that the IR’s cost savings and carbon emission savings will reduce to the same level as the OEM after the IR obtains the remanufacturing license from the OEM, i.e., sI =sO , vI = vO . Because the OEM usually has more knowledge about their products than the IR and the OEM will share it with the IR if they can make an agreement, such as a fixed-fee licensing contract or a royalty licensing contract. 5.2.1. Fixed-fee licensing-Model LF Under a fixed-fee licensing contract, the IR will pay a fixed-fee to the OEM to obtain the qualification for remanufacturing used products. Under this strategy, the OEM sets a fixed-fee F first. Then, the IR decides whether to accept it. Finally, the OEM and IR decide their optimal production quantities simultaneously. Therefore, the OEM’s profit function is: O LF
= (pLF1
c ) qLF 1 + (pLF 2n
c ) qLF 2n + F
PT1O
PT2O 10
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s. t. ,
eqLF 1 = C1O + T1O eqLF 2n = C2O + T2O
(9)
The IR’s profit function is: I LF
= (pLF 2r
s. t. ,
(e I qLF 2r
I c + sO ) qLF 2r
F
PT2I
I I I vO ) qLF 2r = C2 + T2
qLF1
(10)
Note that the OEM’s and IR’s profit functions above are similar to the profit functions in Model C. However, the fixed-fee charged to the IR by the OEM cannot be neglected, as it can increase the OEM’s profit and thus reduce the negative impact of competition with the IR under CTP. The OEM’s and IR’s optimal decisions are similar to the optimal decisions shown in Proposition 2, except that the IR’s cost savings sI and the carbon emission savings vI from remanufacturing should be substituted by sO and vO , respectively. By substituting the OEM’s and IR’s optimal decisions back into their respective profit functions shown by Eqs. (9) and (10), we can obtain I O their optimal profits, denoted as LF and LF , respectively. '' O O Proposition 8.. There exist a lower bound of the fixed-fee F ' which is determined by LF B = 0 and an upper bound of the fixed-fee F ' '' I which is determined by LF > 0 , such that when F < F < F , the OEM and IR can make an agreement on the remanufacturing license.
Proposition 8 states that there exists a fixed-fee licensing contract by which the OEM and IR can achieve a win-win situation. To engage in remanufacturing, the IR will pay a fixed fee (the lower bound F ' ) that is large enough to compensate for the OEM’s profit loss resulted from competition under CTP to the OEM. However, it should be noted that the IR’s profit should be positive after paying the fixed fee to ensure the participation of the IR, which means that the fixed fee should not be too high (the upper bound F '' ). Observation 2. The OEM and IR will make a fixed-fee licensing contract when the OEM’s total cost savings from remanufacturing are large. There are three optimal decision scenarios in Model LF that are corresponding to three situations: the total cost savings are small, moderate, and large (see Proposition 2). When the total cost savings are small, called optimal solution scenario a , the IR will not engage in remanufacturing, and therefore the contract will not be made. When the total cost savings are moderate, called optimal solution scenario b , the IR can make a profit by remanufacturing if there is no fixed-fee. However, due to the fixed-fee charged by the OEM, the IR’s profit will be eroded. Meanwhile, the advanced knowledge about remanufacturing that is capable of reducing the remanufacturing cost and carbon emissions is not lucrative. Thus, the contract will not be accepted. In a word, the total cost savings cannot compensate for the fixed-fee paid to the OEM in this situation. But it is profitable for the IR to accept the fixed-fee licensing contract when the OEM’s total cost savings are large, called optimal solution scenario c . This is because the IR’s remanufacturing costs will decrease after taking this contract and the total cost savings are enough to offset the fixed-fee now. The following example illustrates Proposition 8 and Observation 2. Example 2.. Let c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vO = 0.4, sO = 0.3, vI = 0.2, sI = 0.2, C1O = C2O = C2I = 0.05. Since the total cost savings from remanufacturing are large for both the OEM and IR in this setting, they both choose the scenario c . The OEM’s profit O O O = 0.097 + F . Therefore, by solving the equation LF in Model B is BO = 0.108 and in Model LF is LF B = 0 , we can easily get the ' I F = 0.011 = 0.028 F lower bound . The IR’s profit in Model LF is LF . By simple algebra, we can get the upper bound of the fixed fee, F '' = 0.028. Hence, when the fixed-fee charged to the IR is higher than 0.011 and lower than 0.028, the OEM is able to obtain more profit when competing with the IR under CTP than without CTP. Meanwhile, the IR is willing to accept the fixed-fee licensing contract. The rationale behind this is that the OEM’s profit will decrease and the IR’s profit will increase when CTP is implemented. Therefore, only if the OEM’s profit loss is compensated by the IR will the OEM allow the IR to enter the market. That’s why there is a lower bound of the fixed-fee. However, if the fixed-fee is too high, the IR cannot obtain profit and thus will not accept the contract. Therefore, when the fixed-fee is moderate, both the OEM and IR are better off under CTP. Next, we analyze Observation 2. Set vO = 0.4, sO = 0.2, vI = 0.2, sI = 0.1 for the scenario b. In this case, the lower bound of the fixed-fee F ' = 0.025. However, the upper bound of the fixed-fee F '' = 0.019. It is not profitable for the IR to accept the fixed-fee licensing contract in this case. By comparing the total carbon emissions of Model LF and Model C, we have the following proposition. Proposition 9.. When the fixed-fee licensing contract is accepted, the total carbon emissions of Model LF is less than the total carbon emissions of Model C. According to our analysis, the OEM and IR will be better off if they make an agreement on the fixed-fee licensing. Surprisingly, environmental performance will also be better simultaneously. The rationale behind this is that the total cost savings from remanufacturing must be large if the IR accepts the contract, and the IR could get these savings, leading to a decrease in the total carbon emissions. These facts imply that the fixed-fee licensing contract is able to coordinate the OEM and IR and reduce the total carbon emissions meanwhile. Thus, the fixed-fee licensing contract can not only achieve a win-win situation between the OEM and IR but also achieve a win-win situation between the environment and profit. 5.2.2. Royalty licensing-Model LR Under a royalty licensing contract, the IR is required to pay a per-unit royalty r for per unit remanufactured products. The 11
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decision timeline of this model is similar to the decision timeline of Model LF, shown as follows: first, the OEM sets the per-unit royalty r that must be paid by the IR if the IR wants to engage in remanufacturing, then the IR decides whether to accept it, finally both the OEM and IR decide their optimal production quantities. The OEM’s and IR’s problems are: O LR
= (pLR1
s. t. , I LR
=
s. t. ,
c ) qLR1 + (pLR2n
I c ) qLR2n + rqLR 2r
PT1O
PT2O
eqLR1 = C1O + T1O eqLR2n = C2O + T2O I (pLR 2r
(e I qLR 2r
c + sO
(11)
I r ) qLR 2r
PT2I
I I I vO ) qLR 2r = C2 + T2
qLR1
(12)
The following proposition characterizes the OEM’s and IR’s optimal decisions. Proposition 10.. In Model LR, the OEM’s and IR’s optimal production quantities are given by a (i) qLR 1 b (ii) qLR 1 ( c (iii) qLR 1
a = (1 c Pe)/2 , qLR 2n = b = (1 c Pe)/2 , qLR 2n = 4) , when t8 < PvO + sO c = (1 c Pe)/2 , qLR 2n =
Ia t8 ; (1 c Pe )/2 , and qLR 2r = 0 , when PvO + sO Ib PvO + c sO + r ) (Pe + PvO + c + sO + 2 r )/( 4) , and qLR 2r = (2(Pe t9 ; Ic (2 )(1 c Pe )/4 , and qLR c Pe)/2, when PvO + sO > t9 ; 2r = (1
(1 + c + Pe))/
where t8 = t3 + r , t9 = t4 + r . Proposition 10 implies that there are three optimal solution scenarios in Model LR that are similar to Model C. The three optimal solution scenarios are divided by the OEM’s total cost savings from remanufacturing (PvO + sO ), which is different from Model C. When PvO + sO is small, remanufacturing is not profitable, and the IR will not engage in it. When PvO + sO is moderate, the IR will only remanufacture part of available used products. Compared with Model C, the IR’s optimal production quantity decreases as the IR has to pay a per-unit loyalty to the OEM for each remanufactured product. When PvO + sO is large, remanufacturing is profitable, and the IR will produce remanufactured products as much as possible; note that the IR’s optimal production quantity will not be influenced by the per-unit loyalty in this case. By substituting the OEM’s and IR’s optimal decisions back into their respective profit Ib Ob functions shown by Eqs. (11) and (12), we can obtain their optimal profits, denoted as LR and LR for the optimal solution scenario b Ic Oc and LR and LR for the optimal solution scenario c , respectively. Ob Ob Ob is a concave function of r . When r ' r r '' where r ' and r '' are determined by LR Proposition 11.. LR B = 0 , the OEM and IR will Ic Oc make an agreement on the royalty licensing. LR ( LR ) is a monotonic increasing (decreasing) function of r . When r ''' r r '''' where r ''' is '''' Ic Oc Oc determined by LR B = 0 and r is determined by LR = 0 , the OEM and IR will make an agreement on the royalty licensing.
Proposition 11 implies that the royalty licensing contract is able to coordinate the OEM and IR if the per-unit royalty r is moderate. The IR can engage in remanufacturing by paying the per-unit royalty to the OEM. Consequently, the IR is able to reduce its
Fig. 6. The OEM’s profits in Model LR and Model B. 12
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Fig. 7. The IR’s profits in Model LR.
remanufacturing costs and thus obtain profit. Meanwhile, the OEM’s profit loss due to competition under CTP can be compensated. Hence, the royalty licensing contract achieves a win-win situation. To better explain the results of Proposition 11, we plot Figs. 6 and 7, using the same parameter values as Example 2 except forC1O = C2O = C2I = 0.1. Ob Ob Figs. 6 and 7 clearly show the four critical thresholds in Proposition 11, that are r ' , r '' , r ''' , and r '''' . Solving LR B = 0 , we can obtain r ' = 0.082 , r '' = 0.207 . According to Proposition 11, we obtain the conclusion that the OEM and IR will make an agreement on Ib the royalty licensing when 0.082 r 0.207 . Note that LR is always positive, and the IR is able to bear any per-unit royalty that the OEM sets. This is due to that the IR would only remanufacture part of all available used products when the total cost savings are moderate and thus can adjust its production quantity and selling price to guarantee a positive profit. However, too large per-unit royalty is not favorable for the OEM, since this would improve the selling price of both the new and remanufactured product and thus Ic Oc Oc reduce consumers’ demand for both the new and remanufactured product. Solving LR LR = 0 , we can obtain B = 0 and ''' '''' r = 0.004 and r = 0.085. Therefore, the OEM and IR will make an agreement on the royalty licensing when 0.004 r 0.085. Note that these two thresholds (r ''' and r '''' ) are lower than the former two thresholds (r ' and r '' ). This is because the IR would remanufacture all available used products when the total cost savings are large and thus cannot afford a large per-unit royalty in this situation. In conclusion, the per-unit royalty should be moderate and it is supposed to be lower when the IR remanufactures all available used products compared with the situation where the IR only remanufactures part of available used products. Next, we evaluate the environmental performance of the royalty licensing contract by comparing its total carbon emissions with Model C. We obtain the following proposition. Proposition 12.. The total carbon emissions of Model LR and Model C are related as: (i) when > c < ECc . (ii) ELR
'
b < ECb ; (detailed in the Appendix A), ELR
Proposition 12 states that the royalty licensing contract is able to reduce the total carbon emissions in most cases. To be specific, when the total cost savings from remanufacturing are large, the total carbon emissions when using the royalty licensing strategy are definitely lower than those when not using the strategy. Because the IR’s carbon emission savings will increase after obtaining the OEM’s advanced knowledge about the product through the royalty licensing contract, and the IR will remanufacture all available used products in this case. However, when the total cost savings from remanufacturing are moderate, the IR will only remanufacture part of the available used products and its production quantity will be influenced by the consumers’ attitude toward remanufactured products. Therefore, when consumers’ tolerance for remanufactured products is large, the IR will produce more remanufactured products, leading to lower total carbon emissions. 5.3. Which strategy should the OEM choose? In the previous section, we have analyzed three possible strategies that the OEM may choose to mitigate the negative impact resulted from the competition with the IR under CTP. In this section, we answer the question: which strategy should the OEM choose? We explore the conditions under which one strategy is superior to another. There are three optimal solution scenarios in these strategies, corresponding to three situations: full remanufacturing, partial remanufacturing, and no remanufacturing. It is meaningless to compare the three strategies when there is no remanufacturing, therefore, we explore the conditions under the remaining two situations. 13
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5.3.1. Full remanufacturing When the total cost savings are large, all available used products will be remanufactured, and this situation appears. By comparing the OEM’s profits in the three strategies (Model R, Model LF, and Model LR), we obtain the following proposition. Proposition 13.. There exist a threshold of the fixed-fee F¯ and a threshold of the per-unit royalty r¯ (detailed in the Appendix A), such that (i) when F < r (1 c Pe )/2 , fixed-fee licensing is dominated by royalty licensing. Further, (a) when Fr < r¯ , the priority ranking of the three strategies is R > LR > LF; (b) when r¯ < Fr < F¯ , the priority ranking of the three strategies is LR > R > LF; (c) when Fr > F¯ , the priority ranking of the three strategies is LR > LF > R; (ii) when F > r (1 c Pe )/2 , fixed-fee licensing is superior to royalty licensing. Further, (a) when Fr < F¯ , the priority ranking of the three strategies is R > LF > LR; (b) when F¯ < Fr < r¯ , the priority ranking of the three strategies is LF > R > LR; (c) when Fr > r¯ , the priority ranking of the three strategies is LF > LR > R; (iii) when F = r (1 c Pe )/2 , fixed-fee licensing is equal to royalty licensing. Further, (a) when Fr < F¯ = r¯ , the priority ranking of the three strategies is R > LR = LF; (b) when Fr > F¯ = r¯ , the priority ranking of the three strategies is LR = LF > R. Proposition 13 provides a strategy selection guidance for the OEM when he/she faces competition from the IR under CTP. It implies that the fixed cost of setting up a remanufacturing system Fr , the fixed-fee F , and the per-unit royalty r have a significant influence on the strategy selection. It shows that any one of the three strategies can be optimal for the OEM, depending on the relative value of the three critical factors. It should be noted that (1 c Pe )/2 is the maximal production quantity of remanufactured products, thus the threshold r (1 c Pe )/2 means the OEM’s maximal royalty income derived from the IR. Hence, when the fixedfee is lower than the maximal royalty income, the OEM should choose the royalty licensing strategy; otherwise, the OEM should choose the fixed-fee licensing strategy. Deciding between the remanufacturing strategy and the licensing strategy is a little complicated. Based on the relationship between fixed-fee licensing and royalty licensing, we can obtain the priority of the three strategies by comparing Fr with the other two thresholds F¯ and r¯ . Fig. 8 clearly shows the OEM’s strategy selection. The OEM is able to easily find which strategy he/she should choose according to the value of the three critical factors by using Fig. 8. 5.3.2. Partial remanufacturing When the total cost savings are moderate, only part of available used products are remanufactured, and this situation appears. Since the fixed-fee licensing contract will only be made when the total cost savings are large, we do not consider the LF strategy in this section. By comparing the R strategy and the LR strategy, we have the following proposition. Proposition 14.. There exists a threshold of the per-unit royalty that the OEM charges the IR under royalty licensing, r , which is determined Ob by ROb LR = 0 , such that: (i) when Fr < r , remanufacturing strategy is superior to royalty licensing strategy; (ii) when Fr > r , remanufacturing strategy is dominated by royalty licensing strategy; (iii) when Fr = r , remanufacturing strategy is equal to royalty licensing strategy.
Fig. 8. The OEM’s strategy selection. Note: when F > r (1 c Pe )/2 , F¯ < r¯ ; when F < r (1
c
Pe )/2 , F¯ > r¯ . 14
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Proposition 14 gives the OEM’s strategy selection under partial remanufacturing. It shows that there exists a critical per-unit royalty r such that when the fixed cost of setting up a remanufacturing system Fr is lower than r , choosing the remanufacturing strategy is better. However, royalty licensing is a wise choice when Fr is higher than r . Note that there is no difference between these two strategies when Fr is equal to r . Therefore, when facing competition from the IR under CTP and under the situation of partial remanufacturing, the OEM can choose an optimal strategy by Proposition 14. 6. Conclusions In this paper, we provide decision support for OEMs that face competition from IRs and that may be regulated by CTP. Since IRs do not produce new products, they usually collect used products originally produced by OEMs and remanufacture them. Moreover, it is well known that remanufacturing emits lower carbon emissions than producing new products. Therefore, it inevitably leads to free riding by IRs, especially when CTP is implemented by governments. However, the impact of this free riding on OEMs’ profits and carbon emissions under CTP remains unclear yet. We develop models to examine these impacts. Our models capture the main characteristics of remanufacturing and CTP. To be specific, we focus on the market where consumers value remanufactured products lower than new products. The available used products are constrained by the previous sales of new products. In addition, remanufacturing has lower production costs and emits lower carbon emissions than producing new products. Furthermore, emission allowances can be sold or purchased in a carbon trading market. We explore three alternative strategies that OEMs may choose to handle IRs’ free riding, namely remanufacturing strategy, fixedfee licensing strategy, and royalty licensing strategy. We investigate OEMs’ optimal decisions under each strategy and evaluate each strategy’s economic performance and environmental performance. Further, by comparing each strategy’s profits under two possible remanufacturing situations, namely full remanufacturing and partial remanufacturing, we answer the question: “which strategy should the OEM choose?” Our findings provide guidance for when one of the three strategies is optimal over another for an OEM. The main findings are summarized below. First, we find that the OEM is worse off when competing with the IR under CTP if the carbon cap allocated to the OEM is small. However, the OEM has better environmental performance under this situation. This finding implies the truth that the IR’s free riding erodes the OEM’s profit, and the profit loss will expand when CTP is implemented. Therefore, it is suggested that the OEM should take actions to prevent profit loss. Second, both fixed-fee licensing and royalty licensing can be achieved under certain conditions. More importantly, these two strategies are able to coordinate the OEM and IR not only from an economic perspective but also from an environmental perspective. This finding suggests the existence of strategies that are able to prevent an OEM’s profit loss while also attain a better environmental performance under CTP. To achieve this goal, governments should enact a patent law to protect OEMs’ patented products. In return, the total carbon emissions will even become lower than that when implementing CTP. Lastly, we find that any one of the three strategies can be optimal for the OEM depending on three critical factors, namely the fixed cost of setting up a remanufacturing system, the fixed-fee, and the per-unit royalty. According to the value of the three critical factors, the OEM can easily decide which strategy he/she should choose under different situations. We provide detailed guidance in Section 5.3. This paper takes a step towards investigating OEMs’ competitive strategies against IRs under CTP. However, our study is based on a situation where OEMs’ products are protected by patent law. Although many countries have patent law now, there are also some countries that don’t have it or some cases in which the law doesn’t work. Therefore, studying OEMs’ competitive strategies under CTP in situations where it is impossible to charge a patent fee to IRs is our future research. In addition, for tractability, we assume that the IR would be ruled out of the market when the OEM engages in remanufacturing, studying the situation where both the OEM and IR engage in remanufacturing under CTP could also be an interesting future research direction. Acknowledgements The authors thank the editor and anonymous referees for their valuable comments and suggestions throughout the review process. This work was supported by the National Natural Science Foundation of China [grant number 71671136] and the MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 16YJA630058]. Appendix A Proof of Proposition 1. O B
= (pB1
c ) qB1 + (pB2n
I B
= (pBI 2r
c + sI ) qBI 2r , s. t. ,qBI 2r
Here, pB1 = 1
c ) qB2n
qB1, pB2n = 1
The first order conditions of The second derivatives are:
qB2n O B 2 O B qB12
are:
=
qB1 qBI 2r , and pBI 2r = (1
O B
qB1
=
2 < 0,
2qB1 + 1 2 O B qB2n2
=
qB2n
c = 0 and
qBI 2r ) .
O B
qB2n
=
2qB2n
qBI 2r + 1
c = 0.
2 < 0.
Therefore, is concave and achieves a maximum at the point of the solution of first order condition. The OEM’s optimal production quantity in the first period is: O B
15
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qB1 =
1
c 2
The Lagrangean and the Karush-Kuhn-Tucker optimality conditions of
L (qBI 2r ,
I)
L = qBI 2r I
= ( (1
qB 2n )
c+sI ) qBI 2r
c + sI
I
+
I(
are:
qBI 2r )
qB1
=0
qBI 2r ) = 0
Scenario 1:
= 0 and qBI 2r
I
O B
= 0 and
qB2n
period, shown as follows:
c+
qB2n =
qB 2n
2 qBI 2r + (1
( qB1
Solving
qBI 2r )
I B
We need
+ sI 4
c +
L qBI 2r
2
= 0 simultaneously, we obtain the OEM’s and the IR’s optimal production quantities in the second c +
, qBI 2r =
1 (c + 1) + c = t < sI 2 1
2c + 2sI 4)
(
qB1 and qBI 2r
2c + 2sI 4)
(
qB1.
t2 =
0 to hold for this scenario to be valid, leading to the necessary condition in this scenario:
1 4
(4
)(1
c)
1 (c + 1) + c 2
When sI t1, qBI 2r < 0 . It means that the IR will not enter the market and thus the OEM’s optimal production quantity in the second period is the same as that in the first period. Thus, we have:
qB1 =
1
c 2
Scenario 2:
, qB2n =
I
1
c 2
> 0 and qBI 2r = qB1.
The IR remanufactures all available used products. Therefore, solving quantities in the second period, shown as follows:
(1
qB2n =
c )(2 4 1 4
We need I = in this scenario:
sI > t2 =
1 4
) (1
(4
, qBI 2r =
c )(4
)(1
)+
(1
O B
qB2n
= 0 , we obtain the OEM’s and IR’s optimal production
c) 2
1 2
c + sI > 0 to hold for this scenario to be valid, leading to the necessary condition
(1 + c )
1 (c + 1) + c 2
c)
Proof of Proposition 2. The OEM’s problem is: O C
= (pC1
s. t. ,
c ) qC1 + (pC 2n
PT1O
c ) qC 2n
PT2O
eqC1 = C1O + T1O eqC 2n = C2O + T2O
The IR’s problem is: I C
= (pCI 2r
s. t. ,
c + sI ) qCI 2r
PT2I ,
vI ) qCI 2r = C2I + T2I
(e qCI 2r
qC1
Here, pC1 = 1
qC1, pC 2n = 1
The first order conditions of The second derivatives are:
qC 2n O C
2 O C qC12
are:
=
O C
qC1
qCI 2r , and pCI 2r = (1 =
2 < 0,
2qC1 + 1 2 O C qC 2n 2
=
c
qC 2n
qCI 2r ) .
Pe = 0 and
O C
qC 2n
=
2qC 2n
qCI 2r + 1
c
Pe = 0 .
2 < 0.
Therefore, CO is concave and achieves a maximum at the point of the solution of first order condition. The OEM’s optimal production quantity in the first period is:
qC1 =
1
c 2
Pe
The Lagrangean and the Karush-Kuhn-Tucker optimality conditions of
L (qCI 2r ,
I)
= ( (1
qC 2n
qCI 2r )
c+sI ) qCI 2r
P ((e
vI ) qCI 2r 16
C2I )
+
I C
are:
I(
qC1
qCI 2r )
Transportation Research Part D 78 (2020) 102193
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L = qCI 2r I
2 qCI 2r + (1
c + sI
I
=0
qCI 2r ) = 0
( qC1
Scenario 1:
= 0 and qCI 2r
I
O C
Solving
qC 2n) + P ( e + vI )
= 0 and
qC 2n
L qCI 2r
shown as follows:
Pe + PvI c +
qC 2n =
qC1.
= 0 simultaneously, we obtain the OEM’s and IR’s optimal production quantities in the second period,
+ sI
2
4 2(Pe
PvI + c
We need this scenario:
sI ) (
2(Pe
, qCI 2r =
(1 + c + Pe )
qC1 and qCI 2r
4)
sI ) (
1 (1 + c + Pe ) = t < PvI + sI 2 3
Pe + c
PvI + c
(1 + c + Pe ) 4)
0 to hold for this scenario to be valid, leading to the necessary condition in
t4 =
1 4
(4
)(1
c
1 (1 + c + Pe) + Pe + c 2
Pe)
When PvI + sI t3, qCI 2r < 0 . It means that the IR will not enter the market, and thus the OEM’s optimal production quantity in the second period is the same as that in the first period. We have:
1
qC1 =
c 2
Pe
, qC 2n =
1
c 2
Pe
Scenario 2: I > 0 and qCI 2r = qC1. The IR remanufactures all available used products. Therefore, the OEM’s and IR’s optimal production quantities in the second period are:
qC 2n =
(2
)(1 4
c
Pe)
, qCI 2r =
)+ We need I = 4 (1 c Pe )(4 the necessary condition in this scenario: 1
PvI + sI > t4 =
1 4
(4
)(1
c
(1 1 2
c 2
Pe )
(1 + c + Pe)
Pe + PvI + sI > 0 to hold for this scenario to be valid, leading to
c
1 (1 + c + Pe ) + Pe + c 2
Pe )
Proof of Proposition 3. Since we have obtained the OEM’s optimal decisions of Model B and Model C shown in Proposition 1 and Proposition 2, we can easily obtain the OEM’s optimal profits in Model B and Model C by substituting these optimal decisions back into the OEM’s profit functions. Recall that there are three optimal solution scenarios in Proposition 1 and Proposition 2. Correspondently, we have three optimal profits in Model B and Model C, respectively, shown as follows: Profits in Model B: Oa B
=
Ob B
=
Oc B
=
1 (c 2 (c 2 1 ( 16
1) 2; 2c + 5)
2 2
4
2
+ ( 8c 2 + 24c + 8sI
24) + 20c 2 + (8sI 4( 4)2
48) c + 4sI 2
16sI + 32
1)2 .
+ 8)(c
Profits in Model C:
Ob B
Oa C
=
1 (Pe + c 2
Ob C
=
Pe (Pe + 2c 4
2) + P (C1O + C2O ) +
Oc C
=
1 ( 16
+ 8)(Pe + c
2 2
1) 2 + P (C1O + C2O );
4
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2
2))
+
Ob B
1)2 + P (C1O + C2O ).
Comparing the OEM’s optimal profits between Model B and Model C under the three optimal solution scenarios (i.e. vs. COb , and BOc vs. COc ), we have:
(i)
Oa B
Oa C
=
(ii)
Ob B
Ob C
=
(iii)
Oc B
Oc C
=
P (e (Pe + 2c 2 Pe (Pe + 2c 4 Pe 2 2 ( 4 16
2) + 2(C1O + C2O )) ; 2)
P (C1O + C2O )
+ 8)(Pe + 2c
2)
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2 P (C1O + C2O ) .
17
2))
;
Oa B
vs.
Oa C ,
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By simple algebra, we can obtain Proposition 3. Proof of Proposition 4. The proof of Proposition 4 is similar to the proof of Proposition 3 and we omit it. Proof of Proposition 5. By multiplying the total production quantity of the OEM (the IR) by its per unit carbon emissions, we can obtain the total carbon emissions of the OEM (the IR), shown as follows: The total carbon emissions of the OEM in Model B:
EBOa = (1
e ((c
c ) e ; EBOb =
3)
6c 2sI + 8) e ; EBOc = (4 8 4
2
)(1
c)
The total carbon emissions of the OEM in Model C:
ECOa = (1
e ((Pe + c
Pe ) e; ECOb =
c
3) + ( 6e 2
2vI ) P 8
6c
2sI + 8)
; ECOc =
e (4 4
)(1
c
Pe )
It is obvious that EBOa > ECOa , EBOb > ECOb and EBOc > ECOc . The total carbon emissions of the IR in Model B:
(c +
EBIa = 0; EBIb =
2c + 2sI )(e ( 4)
vI )
(1
; EBIc =
c )(e 2
vI )
.
The total carbon emissions of the IR in Model C:
(2(Pe
ECIa = 0; ECIb =
EBIb
PvI + c
sI ) (
(1 + c + Pe ))(e 4)
vI )
; ECIc =
(1
c
Pe)(e 2
vI )
.
It is obvious that EBIa = ECIa = 0 and EBIc > ECIc . Furthermore, by simple algebra, we obtain the result: when vI < e (1 > ECIb .
/2) ,
Proof of Proposition 6. When the OEM engages in remanufacturing under CTP, the OEM faces the problem: O R
= (pR1
c ) qR1 + (pR2n
c ) qR2n + (pR2r
c + sO ) qR2r
PT1O
Fr
PT2O
eqR1 = C1O + T1O s. t. , eqR2n + (e qR2r qR1
vO ) qR2r = C2O + T2O
qR2r , and pR2r = (1 qR2n qR2r ) . Here, pR1 = 1 qR1, pR2n = 1 qR2n The Lagrangean and the Karush-Kuhn-Tucker optimality conditions are: L (qR1, qR2n , qR2r ,
O)
= (1
qR1
c ) qR1 + (1 C1O )
P (eqR1 L = qR1
2qR1
L = qR2n
Pe
2qR2n
L = ( 2qR2n qR2r O(
qR1
c+1+
2 qR2r
qR2r
P (eqR2n + (e
c ) qR2n + ( (1 C2O )
vO ) qR2r
+
O(
qR2n qR1
qR2r )
c+sO ) qR2r
Fr
qR2r )
=0
O
Pe
qR2n
c+1=0
2qR2r + 1) + P ( e + vO )
c + sO
O
=0
qR2r ) = 0
qR1. Scenario 1: O = 0 and qR2r Solving these equations given by the KKT conditions, we obtain the OEM’s optimal production quantities: qR1 =
1
To ensure
(1
c 2
Pe
, qR2n =
PvO + sO (1 )(Pe + c ) 2 ( 1)
1
sO 2(
PvO 1)
qR1 and qR2r
)(Pe + c ) = t5 < PvO + sO
t6 = (1
, qR2r =
PvO + sO
(1 2 (
)(Pe + c ) 1)
0 , the total cost savings from remanufacturing should satisfy the condition: )(
(1
c
Pe ) + Pe + c )
Note that when PvO + sO < t5, qR2r < 0 . It means that the OEM wouldn’t engage in remanufacturing. Thus, the OEM’s optimal production quantities are: 1 c Pe 1 c Pe qR1 = , qR2n = , qR2r = 0 . 2 2 Scenario 2: O > 0 and qR2r = qR1. The OEM remanufactures all available used products. Solving these equations given by the KKT conditions, we obtain the OEM’s optimal production quantities of the new product: 18
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(PvO + sO
qR1 =
(1 )(Pe + c )) + 1 2 2) 2(1 + 2
c
Pe
2 (1
qR2n =
sO PvO ) + (1 2(1 + 2
)(1
c
Pe )
2 2)
Since qR2r = qR1, the OEM’s optimal production quantity of the remanufactured product is:
(
qR2r =
2 (1
sO PvO ) + (1 )(1 2 2) 2(1 + 2
c
Pe))
In addition, we obtain the multiplier: O
(
=
1)(
(Pe + c 1) 1+ 2
Pe
c)
sO
PvO
2 2
Note that the OEM would stop producing the new products if the total cost savings from remanufacturing is large enough. To ensure O > 0 and qR2n > 0 , PvO + sO should satisfy the condition:
t6 < PvO + sO
t7 = (1
)(1
c
Pe )/
2
+1
When PvO + sO > t7 , the OEM only produces remanufactured products in the second period and its optimal production quantities are: ( (PvO + sO (Pe + c ) + ) + 1 c Pe ) (PvO + sO (Pe + c ) + ) + 1 c Pe qR1 = , qR2n = 0 , qR2r = 2(1 + 2) 2(1 + 2) Proof of Proposition 7. To obtain the OEM’s optimal profits in Model R, we substitute the optimal decisions shown in Proposition 6 back into the OEM’s profit function. Therefore, we obtain: The OEM’s profits in Model R: Oa R
=
Ob R
=
1 (Pe + c 2
((Pe + c )(Pe + c
( 2Pe Oc R
1) 2 + P (C1O + C2O );
2 2
2c + 1)
((Pe + c
=
4) + 2)
2
2((PvO + sO 4 (
+ (Pe + c )((Pe + c
2PvO
sO ) + Pe + c 1)2 4+4 (
PvO
2)(Pe + c ) + 1) 1)
(Pe + c
2sO + 2) + 2Pe + 2c
(Pe + c 1) 2
sO )2
PvO
+ P (C1O + C2O )
Fr ;
2)
1) 2
+ P (C1O + C2O )
Fr .
Comparing the OEM’s optimal profits between Model R and Model C (shown in Proof of Proposition 3), we have: (i)
(ii)
Oa R Ob R
Oa C Ob C
= 0; =
((Pe + c )(Pe + c
4) + 2) 2
2((PvO + sO 4 (
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2
(iii)
Oc R
Oc C
=
( 2Pe
Fr
4
(c 2
2))
2 2c + 1) 2 + (Pe + c )((Pe + c
1 ( 2 2 16
2)(Pe + c ) + 1) 1)
2PvO
(Pe + c
sO )2
PvO
2c + 5) 2 + ( 8c 2 + 24c + 8sI
2sO + 2) + 2Pe + 2c 2) 4+4 ( 1) 2
Fr
Pe (Pe 4
24) + 20c 2 + (8sI 4( 4)2
((Pe + c
PvO
+ 2c
sO ) + Pe + c
;
2)
48) c + 4sI 2 1)2
16sI + 32 (Pe + c
1)2
.
1) 2
+ 8)(Pe + c
By algebra, we can obtain Proposition 7. Fr' and Fr'' are determined by
Ob R
Ob C
= 0 and
Oc R
Oc C
= 0 , respectively.
Proof of Proposition 9. According to Observation 2, the OEM and IR will make a fixed-fee licensing contract when the OEM’s total cost savings from remanufacturing are large. It means that the OEM’s and IR’s optimal decisions would be the scenario c shown in Proposition 2, except that the IR’s cost savings sI and the carbon emission savings vI from remanufacturing should be substituted by sO and vO , respectively. Thus, the total carbon emissions in Model LF are:
ELF =
1 (Pe + c 4
1)(( 4 + (
2) ) e + 2 vO )
The total carbon emissions in Model C are:
EC = ECOc + ECIc =
1 (Pe + c 4
Therefore, we have ELF
EC =
1)(( 4 + ( 1 4
(vO
2) ) e + 2 vI )
vI )(Pe + c
1) < 0 .
Proof of Proposition 11. The OEM’s profits in Model LR: Ob LR
=
1 4 ( 3
4) 2
((12
32) r 2 + ( 4(Pe + c + 3)
2
+ ( 8(Pe + c )2 + 24(Pe + c ) + 8(PvO + sO ) 16(PvO + sO ) + 32) ) +
P (C1O
+
+ 16(Pe + c 24)
2
C2O ); 19
PvO
sO )(
2) + 32 ) r + ((Pe + c )(Pe + c
+ (16(Pe + c )2 + 4(Pe + c
PvO
sO ) 2
48(Pe + c )
2) + 5)
Transportation Research Part D 78 (2020) 102193
Q. Chai, et al. Oc LR
=
1 ( 16
2 2
4
1 r (Pe + c 2
1)2
+ 8)(Pe + c
1) + P (C1O + C2O ).
The IR’s profits in Model LR: Ic LR
=
1 ((Pe + c ) 2 ((
1 ( 8
1) r +
2)
2 (Pe
1 8
2)(Pe + c ) + 2(PvO + sO ))
Therefore, the second derivative of The first derivatives of
Oc LR
and
Ic LR
is:
Ob LR
are:
Oc LR
1 1 2 (Pe + c ) + (Pe + c 4 2 2 (Pe + c ) + 1 2 + PC I . 2 8
+ c)2 2
2 Ob LR r2
r
=
24 4 (
1 2
=
64 4)2
1)
2(Pe + c
sO ) +
PvO
1 4
< 0. Ic LR
1) > 0 ,
(Pe + c
1
1) < 0 .
= 2 ((Pe + c )
r
Proof of Proposition 12. The total carbon emissions in Model LR are: b Ob Ib ELR = ELR + ELR e ((Pe + c =
3)
1 ( 4
c Oc Ic ELR = ELR + ELR =
6(Pe + c ) 2(PvO + sO ) + 2r + 8) 2 8
4)(Pe + c
1 (Pe + c 2
1) e
(e
vO )((Pe + c + 1) (
1)(e
2(Pe + c 4)
PvO
sO )
2r )
PvO
sO ))
;
vO ).
The total carbon emissions in Model C are:
e ((Pe + c
ECb = ECOb + ECIb =
ECc = ECOc + ECIc =
1 (Pe + c 4
3)
6(Pe + c ) 2 8
1)(( 4 + (
2(PvI + sI ) + 8)
(e
vI )((Pe + c + 1) (
2(Pe + c 4)
;
2) ) e + 2 vI ).
b c Therefore, by comparing ELR with ECb and ELR with ECc , we obtain: b (i) ELR
ECb =
(vO
4Pe + c + ) + 2P (vO2
vI )(2 Pe
vI2) + 2vO ( c + r + s ) (
By simple algebra, we obtain the result: when c (ii) ELR
ECc =
1 2
(Pe + c
1)(vO
2vI ( c + sI )
(
2)(r
sO + sI ) e
4)
>
'
b < ECb , where , ELR
'
.
=2+
vI ) < 0.
Proof of Proposition 13. Under the full remanufacturing situation, we compare Oc LR
Oc LF
=
1 r (Pe + c 2
2( (vO vI ) P (vO2 vI2) sO vO + sI vI + rvO ) . (2Pe + c + 1)(vO vI ) + e (sO sI + r )
1)
Oc LF
and
Oc LR ,
shown as follows:
F
Oc Oc Oc Oc Oc Oc > LF < LF = LF Therefore, when F < r (1 c Pe )/2 , LR ; when F > r (1 c Pe )/2 , LR ; F = r (1 c Pe )/2 , LR . After knowing the relationship between fixed-fee licensing and royalty licensing, we study the relationship between the remanufacturing strategy and these two licensing strategies. We can obtain the threshold of the fixed-fee F¯ and the threshold of the perOc Oc Oc unit royalty r¯ by solving ROc LF = 0 and R LR = 0 , respectively.
F¯ =
r¯ =
F+
1 16 + 16 2 (
+ 4(A
1)((A + 1)
1 (A 2 4(A
1) r + B)2
2
1)
2 3(
2(A
B ))
1 16 + 16 2 (
1)
+ 4(A
1)((A + 1)
1)( 2 (3
2 3(
2(A
4)(A
1) 2 +
2
7 2A A
6 + 12 A A 7
2 B 3
2 3
4(A
B)2
2
4) ;
1)(
4)(A
1)2 +
B ))
2 (3
4) .
where A = Pe + c and B = PvO + sO . Note that when F = r (1 c Pe )/2 , F¯ = r¯ ; when F < r (1 Oc In addition, (i) when Fr < F¯ , ROc > LF ; when Fr = F¯ , ROc = Oc Oc Oc Oc R = LR ; otherwise R < LR . Based on the above analysis, we can obtain Proposition 13.
c
Oc LF ;
20
2
7 2A A
6 + 12 A A 7
2 B 3
2 3
Pe )/2 , F¯ > r¯ ; when F > r (1 c Pe )/2 , F¯ < r¯ ; Oc Oc otherwise ROc < LF ; (ii) when Fr < r¯ , ROc > LR ; when Fr = r¯ ,
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Transportation Research Part D journal homepage: www.elsevier.com/locate/trd
Competitive strategies for original equipment manufacturers considering carbon cap and trade
T
Qiangfei Chaia, Zhongdong Xiaoa, , Guanghui Zhoub,c ⁎
a b c
School of Management, Xi’an Jiaotong University, Xi’an 710049, China School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China
ARTICLE INFO
ABSTRACT
Keywords: Remanufacturing Competition Carbon cap and trade Fixed-fee licensing Royalty licensing
This paper considers an original equipment manufacturer (OEM) faces competition from an independent remanufacturer (IR) and they both are regulated by carbon cap and trade policy (CTP). We develop models to explore the OEM’s optimal competitive strategy in the face of IR’s competition and environmental regulation. We first investigate the impact of CTP on the OEM and IR. Then, we analyze three competitive strategies that the OEM may choose: remanufacturing, fixed-fee licensing, and royalty licensing. We investigate their optimal decisions under each strategy and identify the conditions under which these strategies can coordinate the OEM and IR. Finally, we explore conditions under which one strategy is superior to another. The results show that the OEM is worse off when competing with the IR under CTP if the carbon cap allocated to the OEM is small. Fixed-fee licensing and royalty licensing can coordinate the OEM and IR not only from an economic perspective but also from an environmental perspective. The OEM’s optimal competitive strategy is determined by thresholds of three critical parameters: the fixed cost of setting up a remanufacturing system, the fixed-fee, and the per-unit royalty. We provide specific guidance on strategy selection for the OEM.
1. Introduction As we all know, the environment around us is getting worse because of human activities. One of the effective ways to reduce human impact on the environment is remanufacturing, since it can not only save production costs but also save energy consumption and reduce waste emissions (Guide and Van Wassenhove, 2001, Atasu et al., 2008, Ovchinnikov et al., 2014). Although remanufacturing is environmentally friendly and cheaper than producing new products, many original equipment manufacturers (OEMs) do not engage in it. The OEMs’ major concerns about remanufacturing include cost and cannibalization (Ferguson and Toktay, 2006). Too high costs of setting up a remanufacturing system are usually unacceptable for them. For cannibalization, OEMs worry that their new products’ market share will be eroded by remanufactured products if remanufactured products price lower, and such cannibalization is undesirable if the margin profit of new products is higher than that of remanufactured products. If remanufacturing is profitable and OEMs do not perform it, independent remanufacturers (IRs) may enter the market. Thus, OEMs will inevitably face external competition under this situation. How to cope with external competition has been bothering OEMs. Due to the importance of this problem for OEMs, many studies have explored it, such as Majumder and Groenevelt (2001), Ferguson and Toktay (2006), Webster and Mitra (2007), Wu and Wu (2016), Wu and Zhou (2016).
⁎
Corresponding author. E-mail addresses: [email protected] (Q. Chai), [email protected] (Z. Xiao), [email protected] (G. Zhou).
https://doi.org/10.1016/j.trd.2019.11.022
1361-9209/ © 2019 Elsevier Ltd. All rights reserved.
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In addition, it should be noted that many countries have implemented or plan to implement some environmental policies to protect the environment, and firms must adjust their operation decisions under this situation. However, research on how to help OEMs cope with external competition under environmental regulation is absent. One of the popular environmental policies is carbon cap and trade policy (CTP). The European Union Emission Trading Scheme (EU ETS) is an exemplary example of CTP. It has operated in Europe for many years and remains to be the biggest emissions trading scheme in the world so far. Moreover, China has been working on reducing carbon emissions and launched seven pilot emissions trading markets in 2011. After then, China established a national emissions trading market in 2017 (Chai et al., 2018). There are also other emissions trading markets in the world, such as the Chicago Climate Exchange and the Australia Climate Exchange (Zhang and Xu, 2013). Under CTP, firms are first allocated some emission allowances, then they can purchase insufficient allowances or sell surplus allowances according to their situation. Therefore, a firm that emits less pollution may obtain extra profits by selling surplus allowances. This flexible mechanism provides an opportunity for IRs to obtain more profits when the carbon cap allocated to them is large. Hence, the IRs’ free riding behavior becomes more obvious under CTP because IRs enjoy not only low cost advantage but also low emission advantage of remanufactured products while they do not produce new products. To prevent IRs’ free riding, several strategies are available to OEMs. In this paper, we examine two strategies, namely remanufacturing strategy and licensing strategy. Remanufacturing strategy means that OEMs engage in remanufacturing. For example, Caterpillar collects and remanufactures its own construction and mining equipment. Licensing strategy means OEMs charge IRs a patent licensing fee if IRs want to enter the remanufacturing market. Recently, several patent lawsuits about remanufactured products attract researchers’ attention. To give an example, Canon v. Recycle Assist is an important intellectual property event in the world. The cause of this lawsuit is that Recycle Assist imported and sold Canon’s remanufactured cartridges with no authorization. Canon filed a lawsuit against Recycle Assist in Japan and finally won (Hong et al., 2017). This case implies that OEMs have begun to pay attention to patent protection of their renewable products and also means that IRs have to pay a patent licensing fee to engage in remanufacturing if OEMs charge them. Therefore, licensing strategy can be a powerful strategy for preventing IRs’ free riding behavior. The licensing strategy can be further divided into two strategies, namely fixed-fee licensing and royalty licensing. These two licensing strategies are widely used in academic research and practice (Wang et al., 2018, Yang et al., 2019). Fixed-fee licensing means that OEMs charge IRs a fixed licensing fee, which is independent of IRs’ production quantities of remanufactured products. Royalty licensing means that OEMs charge IRs a per-unit royalty for per unit remanufactured products. Although research on entry-deterring strategy for OEMs is flourishing, studies about competitive strategy for OEMs under CTP are quite scant, especially for studies simultaneously considering licensing strategy and CTP. We aim to fill this gap. In this paper, we provide insights into the following questions: (1) How does CTP, and to what extent, influence the OEM and IR? (2) What are the conditions that the three strategies (remanufacturing, fixed-fee licensing, and royalty licensing) are able to coordinate the OEM and IR under CTP? Will they attain a better environmental performance under the three strategies? (3) For the three strategies, which one should the OEM choose? Which parameters significantly influence the choice? This paper aims to provide decision support for OEMs that face competition from IRs, and that may be simultaneously regulated by CTP. In this study, we examine a competitive situation where an IR collects and remanufactures used products that were originally produced by an OEM, and thus leading to external competition. Furthermore, we consider both the OEM and IR would be regulated by CTP. We develop models of competition without CTP and under CTP to characterize the influence of CTP. In addition, we explore three alternative strategies that the OEM can choose, namely remanufacturing strategy, fixed-fee licensing strategy, and royalty licensing strategy. We identify the conditions under which these strategies are able to coordinate the OEM and IR and meanwhile coordinate economic performance and environmental performance. Finally, we investigate the OEM’s optimal strategy when competing with the IR under CTP. The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces the research problem and gives some essential assumptions and notations. Section 4 investigates the influence of CTP on both the OEM and IR. The OEM’s optimal competitive strategy under CTP is explored in Section 5. Section 6 presents our conclusions and limitations. All proofs are shown in the Appendix A. 2. Related research Our research is related to three streams of literature: competition between OEMs and IRs, operations management under CTP, and technology licensing. In this section, we review some prominent studies and position our research in the literature. To the best of our knowledge, Majumder and Groenevelt (2001) are the first who explore the area of competition between OEMs and IRs by using mathematical models. They develop a two-period model and investigate the effect of competition under four reverse logistics configurations. They mainly focus on understanding the incentives for OEMs and IRs and find that OEMs would like to increase IRs’ cost while IRs have incentives to reduce OEMs’ cost. But they do not vertically distinguish between new products and remanufactured products. Ferguson and Toktay (2006) differentiate new products from remanufactured products and examine OEMs’ entry-deterrent strategies, which includes collection strategy and remanufacturing strategy. Webster and Mitra (2007) examine the influence of take-back laws under a competitive situation where OEMs compete with IRs. They investigate the impact of collective WEEE take-back and individual WEEE take-back on OEMs and society. Then, Mitra and Webster (2008) consider a similar competitive situation and investigate the impact of government subsidies on profits and remanufacturing activity. They mainly consider the 2
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influence of different subsidy schemes. Webster and Mitra (2007) and Mitra and Webster (2008) explore the influence of take-back laws or subsidies when OEMs face competition from IRs; however, alternative strategies that OEMs can choose are not addressed. In contrast, our focus is on investigating alternative strategies that OEMs can choose in the face of competition. Recently, some researchers are interested in studying if IRs are always detrimental to OEMs. Wu and Zhou (2016) examine whether IRs always hurt OEMs and find that OEMs may benefit from the entry of IRs. Jin et al. (2017) also find IRs may be beneficial to OEMs by taking suppliers into consideration. These studies reinforce the notion that OEMs and IRs can coexist. Therefore, it is necessary to study what strategies or contracts can coordinate OEMs and IRs and our study focus on this problem. Operations management under CTP is a hot topic in recent years. Consequently, a number of studies appear in this research area. These studies can be classified as emission reduction technology investment considering CTP (Dong et al., 2016, Drake et al., 2016, Xia et al., 2018), production and inventory decisions under CTP (Benjaafar et al., 2013, Chen et al., 2016, Du et al., 2016, Xu et al., 2017, Tang et al., 2018), supply chain coordination under CTP (Jaber et al., 2013, Xu et al., 2016, Xu et al., 2018), as well as supply chain network design and transport mode selection aimed at minimizing carbon emissions (Hoen et al., 2014, Gao et al., 2018, Zhang et al., 2018). Benjaafar et al. (2013) study how to integrate several regulatory policies into operational decision-making, using simple and widely used models. Their focus is on studying whether operational adjustments and collaboration with other members within the same supply chain are able to reduce carbon emissions. Dong et al. (2016) examine a manufacturer’s sustainability investment and a retailer’s order quantity considering CTP for decentralized and centralized supply chains. Moreover, they investigate supply chain coordination. Xia et al. (2018) focus on emission reduction of a supply chain under CTP. They think traditional self-interest hypothesis is imperfect and attempt to incorporate reciprocal preferences and consumers’ low-carbon awareness into their supply chain model. For research on production and pricing decisions under CTP, considering consumers’ low-carbon premium, Du et al. (2016) study whether low-carbon production under CTP is profitable and explore the optimal production quantity of the low-carbon product. Xu et al. (2017) study the production and pricing problem in a make-to-order supply chain consisting of a manufacturer that is regulated by CTP and a retailer. Furthermore, studies on closed-loop supply chain management considering CTP begin to emerge recently. Chang et al. (2015) study a monopolist manufacturer’s production decisions when it engages in both manufacturing and remanufacturing under CTP. Liu et al. (2015) investigate an IR’s optimal remanufacturing quantity under three common carbon emission policies: CTP, carbon tax, and mandatory carbon emissions capacity. Wang et al. (2017) consider a monopolistic manufacturer is constrained by capital and study the optimal manufacturing/remanufacturing decisions under CTP. Chai et al. (2018) explore whether CTP is favorable for a monopolistic manufacturer that engages in both manufacturing and remanufacturing. However, these studies do not capture the competition between OEMs and IRs considering CTP. Different from these studies, by taking remanufacturing and IRs into consideration, we investigate the potential impact of CTP on both OEMs and IRs and explore appropriate strategies that are effective to coordinate them. The last stream of literature related to our study is technology licensing. Researchers often study technology licensing under competitive situations (Chen et al., 2017, Hong et al., 2017, Huang and Wang, 2019, Jeon, 2019, Yang et al., 2019). For example, Chen et al. (2017) investigate a component supplier’s intellectual property licensing strategy selection problem under a duopoly competition situation. They assume that the supplier can charge a licensing fee to two downstream manufactures either according to the downstream manufacturers’ sales (product-based strategy) or according to the supplier’s wholesales (component-based strategy). Yang et al. (2019) study optimal licensing strategy under a situation where two suppliers compete with each other considering supply disruption. They examine the effect of the supply risk on one supplier’s willingness to license technology and investigate fixed-fee licensing and royalty licensing strategy. Their focus is on studying the influence of supply disruption on the optimal licensing strategy selection. These studies introduce licensing strategies into the forward supply chain, however, not the closed-loop supply chain. The one who introduces licensing strategies into the closed-loop supply chain is Hong et al. (2017). They consider a manufacturer (the licensor) and a remanufacturer (the licensee) compete in collecting and remanufacturing used products. They investigate two licensing strategies, fixed-fee licensing strategy and royalty licensing strategy, and find that there exists a threshold of the fixed fee below which royalty licensing is better for the manufacturer. Similar to their study, we also investigate licensing strategies in the context of remanufacturing. However, we further extend their study and aim to explore licensing strategies in the context of environmental regulation, which previous studies do not address. We integrate CTP and licensing strategies into traditional manufacturing and remanufacturing production models and obtain insights about how does CTP affect an OEM’s and an IR’s decisions, and whether licensing strategies are effective to coordinate them. Thus, our results complement the above three streams of literature. We contribute knowledge to the literature in four respects. First, we investigate the influence of CTP on both the OEM and IR when they compete with each other. Second, we explore the licensing strategy as a coordination contract under the situation where the OEM competes with the IR under CTP. Third, we identify the conditions under which the OEM and IR can be coordinated under CTP. Finally, we explore the OEM’s preference for the three strategies under different remanufacturing scenarios. 3. Problem description and assumptions We consider a competitive situation in which there are an OEM and an IR. The OEM produces new products and the IR produces remanufactured products by acquiring used products that were originally produced by the OEM. We assume the planning horizon is two periods. Because a two-period model is capable of capturing major dynamics of the problem and is widely used in extant studies about remanufacturing (Ferguson and Toktay, 2006, Bulmus et al., 2014, Mutha et al., 2016). The OEM produces new products in both periods, while the IR collects end-of-use products from consumers and remanufactures these products in the second period. Thus, the quantities of remanufactured products are limited by the quantities of new products produced by the OEM in the first period. As the remanufactured product has the same functions as the new product but is cheaper than the latter, it inevitably leads to 3
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market cannibalization and affects the new product sales. Guide Jr and Li, 2010 empirically prove that remanufactured products have the potential to cannibalize new product sales. It means that the OEM would face competition from the IR if the IR enters the market in the second period. We assume that consumers value remanufactured products lower than new products and make purchasing decisions based on their utility obtained from buying the two types of products. This assumption is true in practice and has been validated by empirical evidence. For example, Guide Jr and Li, 2010 found that consumers’ willingness to pay (WTP) for remanufactured products is about 15% lower than that for new products. Other empirical evidence can be found in Ovchinnikov (2011) and Abbey and Blackburn (2015). In addition, Amazon usually prices remanufactured products (or called refurbished products) lower than new products, such as products like cell phones, computers, and office products, demonstrating the fact of different consumers’ WTP for the two types of products. Based on the above assumption, the demand functions can be obtained from consumers’ utility. The consumers’ WTP for the new product is heterogeneous, denoted as . We assume is distributed uniformly between 0 and 1. denotes consumers’ tolerance for the remanufactured product, higher means that consumers are more easily accept the remanufactured product. We assume 0 < < 1. pn , and a consumer’s utility from buying a remanufactured Therefore, a consumer’s utility from buying a new product is Un = pr , where pn and pr represent the selling price of the new and remanufactured product, respectively. A consumer product is Ur = would buy a new product if Un > Ur and Un > 0 and buy a remanufactured product if Ur > Un and Ur > 0 . We normalize the market size to 1. Therefore, we can obtain the demand functions, see Chai et al. (2018). We use inverse demand functions in this paper, which can be derived from the demand functions by simple algebra, shown as follows:
p1 = 1
(1)
q1
p2n = 1
q2n
p2r = (1
q2n
(2)
q2r
(3)
q2r )
where q1, q2n , and q2r represent the demand of new products in the first period, in the second period, and the demand of remanufactured products in the second period, respectively. As there are no used products available to collect in the first period, there are only new products on the market. The above inverse demand functions reflect the substitution and competition between new and remanufactured products because as the production quantity of remanufactured (new) products increase, the new (remanufactured) product’s price would decrease. We consider the government implements CTP for emission reduction. Let C1O and C2O denote the carbon cap allocated to the OEM in the first and second period, C2I denotes the carbon cap allocated to the IR in the second period. Both the OEM and IR can purchase or sell emission allowances in price P in an emission trading market but they have to offset the emissions beyond the cap by purchasing emission allowances at the end of each period. We assume that the carbon emissions and production cost from production per new product are e and c . The carbon emission savings and cost savings per remanufactured product are vk and sk (k = O (OEM), I (IR) ). Therefore, the carbon emissions and production cost from production per remanufactured product are e vk and c sk . For tractability, we assume that when the OEM engages in remanufacturing, the IR would be ruled out of the market. It means that remanufacturing is available for the IR if the OEM has no intention of remanufacturing. This assumption is already validated in prior studies, such as Ferguson and Toktay (2006), Subramanian and Subramanyam (2012), and Subramanian et al. (2013). Furthermore, this is true in many situations. For example, some business equipment manufacturers have a strong relationship with their customers because they not only sell products to their customers but also provide maintenance service. Therefore, the OEMs are able to easily obtain the end-of-life equipment, leaving little room for IRs to collect and remanufacture the equipment. In addition, some OEMs may Table 1 Notation. Parameters
Definition
pijk ,
The sale price and production quantity of product j in period i for firm k. i = 1, 2 ; j = n (newproducts), r (remanufacturedproducts) ; k = O (OEM), I (IR) . Since only OEM produces new products, we omit k when j = n. The production cost per new product and cost savings per remanufactured product, 0 < sk < c . The carbon emissions from production per new product and carbon emission savings per remanufactured product, 0 < vk < e . The carbon cap allocated to firm k in period i.
c, e,
Cik Tik P
Ek Fr F r kh g
qijk sk vk
The carbon trading quantity of firm k in period i. The carbon trading price. Consumers’ tolerance for remanufactured products, 0 < < 1. Core collection ratio, defined as the fraction of new products sold in the first period that can be collected in the second period, 0 < The total carbon emissions of firm k. The The The The
fixed cost of setting up a new remanufacturing system. fixed-fee that the OEM charges the IR for remanufacturing licensing. per-unit royalty that the OEM charges the IR for per unit remanufactured products. firm k’s profit in optimal solution scenario h in model g. k = O (OEM), I (IR) ; h = a , b, c ; g = B, C , R , LF , LR .
4
< 1.
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provide a trade-in business model to attract their old customers, leading to an inevitable collection of the majority of the used products. Thus, it would be expensive for IRs to entry the market. For convenience of reference, we summarize the model’s notation in Table 1. 4. The impact of CTP In this section, we investigate the impact of CTP on the OEM and IR. We answer the questions: “If the introduction of CTP would affect the OEM’s profit and, if so, whether the IR’s profit would increase, and what is the OEM’s optimal production decisions under this situation?” We use subscript g {B , C } to denote the model of competition without CTP and under CTP, respectively. 4.1. The model of competition without CTP-Model B We first analyze the traditional competition between the OEM and IR when there is no CTP implemented by the government. The OEM’s and IR’s profit functions can be written as O B
= (pB1
c ) qB1 + (pB2n
I B
= (pBI 2r
c + sI ) qBI 2r , s. t. ,qBI 2r
(4)
c ) qB2n
(5)
qB1
The OEM’s and IR’s optimal decisions are characterized by Proposition 1. Superscript h optimal solution scenarios.
{a, b , c } represents three different
Proposition 1.. The OEM’s and IR’s optimal production quantities when competition without CTP are: (i) qBa1 = (1 (ii) qBb1 = (1 (iii) qBc1 = (1
c )/2 , qBa2n = (1 c )/2 , and qBIa2r = 0 , when sI t1; 2c + 2sI )/ ( c )/2 , qBb2n = (c + + sI 2)/( 4) , and qBIb2r = (c + )/4 , and qBIc2r = (1 c )/2, when sI > t2 ; c )/2 , qBc 2n = (1 c )(2
where t1 =
(c + 1) /2 + c , t2 =
(4
)(1
c )/4
4), when t1 < sI
t2 ;
(c + 1)/2 + c .
When deciding to engage in remanufacturing, the IR has to consider the cost savings per remanufactured product. If sI is low (sI t1), which means that the production cost of a remanufactured product is almost like that of a new product, the IR tends to quit the market. We call the first optimal solution scenario no remanufacturing situation. However, if sI is moderate (t1 < sI t2 ), the IR will enter the market and produce remanufactured products. It should be noted that the IR will only remanufacture a portion of available used products in this situation, and we call this partial remanufacturing situation. Further, if sI is large (sI > t2 ), the IR will remanufacture all available used products because remanufacturing is lucrative enough now, and we call the third optimal solution scenario full remanufacturing situation. 4.2. The model of competition under CTP-Model C When the government decides to implement CTP, both the OEM and IR have to make decisions under CTP. In this case, the OEM’s profit function is: O C
= (pC1
s. t. ,
c ) qC1 + (pC 2n
c ) qC 2n
PT1O
PT2O
eqC1 = C1O + T1O eqC 2n = C2O + T2O
(6)
The IR’s profit function is: I C
= (pCI 2r
s. t. ,
(e qCI 2r
c + sI ) qCI 2r
PT2I
vI ) qCI 2r = C2I + T2I qC1
(7)
The following proposition characterizes the OEM’s and IR’s optimal decisions. Proposition 2.. The OEM’s and IR’s optimal production quantities when competition under CTP are: (i) qCa1 = (1 (ii) qCb1 = (1 when t3 < (iii) qCc1 = (1
c c PvI c
Pe )/2 , qCa2n = (1 c Pe )/2 , and qCIa2r = 0 , when PvI + sI t3 ; Pe )/2 , qCb2n = (Pe + PvI + c + sI + 2)/( 4) , and qCIb2r = (2(Pe PvI + c sI ) + sI t4 ; Pe )/2 , qCc 2n = (2 )(1 c Pe )/4 , and qCIc2r = (1 c Pe )/2 , when PvI + sI > t4 ;
5
(1 + c + Pe ))/ (
4) ,
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where t3 = Pe + c
(1 + c + Pe )/2 , t4 = Pe + c
(1 + c + Pe )/2
(
4)(1
c
Pe )/4 .
Different from Model B, the IR has to put the carbon emission savings into consideration when making remanufacturing decisions in Model C. To be specific, when the total cost savings PvI + sI , which includes the carbon emission cost savings and the production cost savings, are small (PvI + sI t3 ), the IR will not engage in remanufacturing. Once PvI + sI is beyond the threshold t3 , remanufacturing is profitable for the IR and the IR will enter the market and competes with the OEM. The IR will only remanufacture a portion of available used products in this situation. When PvI + sI is large, the IR will remanufacture all available cores. The three optimal solution scenarios in Model C also correspondent to three remanufacturing situations: no remanufacturing, partial remanufacturing, and full remanufacturing. 4.3. Comparison and analysis 4.3.1. Profit analysis Since we would like to know the impact of implementing CTP on the OEM and IR, we compare the optimal decisions and profits of Model B and Model C. By substituting the optimal decisions shown in Proposition 1 and Proposition 2 back into the OEM’s and IR’s profit functions, we can obtain the optimal profits of the OEM and IR. Comparing the OEM’s optimal profits in Model B and Model C under the three remanufacturing situations, we have the following proposition. Proposition 3.. The OEM’s optimal profits in Model B and Model C are related as follows: (i) When C1O + C2O < el/2 , BOa > COa ; 4)2 , (ii) When C1O + C2O < el/4 + m /( (iii) When C1O + C2O < eln/16 , BOc > COc ; where l = 2
2c
Pe , m =
Ob B
>
Ob C ;
2)) , and n =
(e + vI )(P (e + vI ) + 2(c + sI +
2 2
4
+ 8.
Proposition 3 reveals that the impact of implementing CTP on the OEM’s profits is negative when the carbon cap allocated to the OEM is small for all of the three optimal solution scenarios. It means that when the carbon cap is tight, which would happen after CTP has been implemented a period of time, the OEM will worse off if competing with the IR under CTP. However, it is surprising that CTP has no influence on the OEM or even is better for the OEM when the carbon cap is large, which usually happens at the beginning of the implementation of CTP. For example, EU ETS aims for carbon emission reduction by 20% relative to 1990′s emission level before 2020 through three phases. The participating firms received adequate allowances that are sufficient to cover their emissions in the first phase; however, the cap is tightened in the second phase and further reduced each year by 1.74% in the last phase (Chan et al., 2013). Therefore, the OEM is able to benefit from CTP at its early stage. Nevertheless, at CTP’s late stage, competing with the IR under CTP will lead to a decrease in the OEM’s profit. Fig. 1 visually shows the results of Proposition 3. The parameters we selected are c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vI = 0.2 ; sI = {0.03, 0.1, 0.3} for the optimal solution scenarios {a, b, c} . Comparing the IR’s optimal profits in Model B and Model C under the three remanufacturing situations, we have the following proposition.
Fig. 1. Comparison of the OEM’s profits in Model B and Model C.
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Fig. 2. Comparison of the IR’s profits in Model B and Model C.
Proposition 4.. The IR’s optimal profits in Model B and Model C are related as follows: (i) BIa = CIa = 0 ; (ii) When C2I > u/ ( (iii) When C2I > (e ( where u =
((
4)2 , 2) l
Ib Ib B < C ; 2 + w )/8
2) e + 2vI )(Pe (
,
Ic B
<
Ic C ;
2) + 2 (c + 1) + 2PvI
4c + 4sI ) , w =
2e ((
2)(Pe + 2c ) + 2sI + 2)
4vI (Pe + c
1) .
The IR’s profit is zero in the first optimal solution scenario because the IR doesn’t engage in remanufacturing under this situation. However, the IR will benefit from competing with the OEM under CTP when the carbon cap is large in the second optimal solution scenario. The rationale behind this is that the total cost savings from remanufacturing are moderate in this scenario, and thus a small cap would restrict the IR’s production and a large cap would not only promote the IR’s production but also make it possible to sell surplus emission allowances. Similarly, given a large carbon cap, the IR always obtain more profit when competing with the OEM under CTP than without CTP in the third optimal solution scenario. It is worth to note that the cap threshold 2) l 2 + w )/8) in the third optimal solution scenario above which the IR obtains more profit may be lower than the cap ( (e ( 4) 2 ), due to more cost savings in the third optimal solution scenario. We threshold in the second optimal solution scenario (u/ ( plot Fig. 2 to show it as well as the results of Proposition 4. We set c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vI = 0.2 ; sI = {0.1, 0.3} for the optimal solution scenarios {b , c} . From Fig. 2, we can easily understand Proposition 4. As the IR’s profit is zero in the first optimal solution scenario a , we do not plot it. The two critical cap thresholds of the scenario b and c are represented by X1 and X2 in Fig. 2. Thus, when C2I > X1 in the scenario b or C2I > X2 in the scenario c , the IR obtains more profit when competing with the OEM under CTP than without CTP. These two cap thresholds X1 and X2 are relatively small in Fig. 2, which means that the IR can always benefit from competition under CTP as long as the carbon cap is not very small. It should be noted that X2 < X1. This implies that with the increase of the total cost savings from remanufacturing, the critical cap threshold will decrease. In other words, benefiting from competition under CTP will become easier for the IR with the increase of the total cost savings from remanufacturing. 4.3.2. Carbon emissions analysis By multiplying the total production quantity of the OEM (the IR) by its per unit carbon emissions, we can obtain the total carbon emissions of the OEM (the IR). Comparing the carbon emissions in Model B and Model C, we have the following proposition: Proposition 5.. (i) The carbon emissions of the OEM in Model B and Model C are related as: (a) EBOa > ECOa ; (b) EBOb > ECOb ; (c) EBOc > ECOc . (ii) The carbon emissions of the IR in Model B and Model C are related as: (a) EBIa = ECIa = 0 ; /2) , EBIb > ECIb ; (b) When vI < e (1 (c) EBIc > ECIc . 7
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Fig. 3. Comparison of the OEM’s carbon emissions in Model B and Model C.
Proposition 5 implies that CTP is effective to reduce carbon emissions under the situation where the OEM competes with the IR. The OEM’s carbon emissions when competition without CTP are higher than that when competition under CTP for all the three optimal solution scenarios. However, this is not true for the IR. In the first scenario a , the IR’s carbon emissions are zero because the IR does not perform remanufacturing. In the second scenario b, the IR’s carbon emissions when competition under CTP are even higher than that when competition without CTP if the carbon emission savings are high. This is because the IR can obtain more profits by producing more remanufactured products when the carbon emission savings are high under CTP, and thus the IR’s carbon emissions in Model C will be higher than that in Model B. In the third scenario c , CTP is effective to reduce the IR’s carbon emissions. Figs. 3 and 4 show the results of Proposition 5. The parameters we selected are c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5; vI = 0.2 in Fig. 4(a) and vI = 0.4 in Fig. 4(b). As we can see, CTP is always effective to reduce the OEM’s carbon emissions and the IR’s carbon emissions when vI is small. When vI is large, CTP is ineffective in the second scenario b. However, CTP is always effective to reduce the IR’s carbon emissions in the third scenario c no matter vI is small or large. Therefore, from the perspective of carbon emission reduction, the IR is supposed to use the third optimal solution scenario in which the total cost savings from remanufacturing are large. It suggests that encouraging the IR to improve remanufacturing technology to increase the cost savings from remanufacturing will lead to the reduction of the IR’s carbon emissions under CTP.
Fig. 4. Comparison of the IR’s carbon emissions in Model B and Model C.
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5. OEM’s competitive strategies under CTP Based on the former analysis, it is clear that the OEM is worse off when competing with the IR under CTP. Therefore, in this section, we examine two alternative strategies that the OEM may choose to reduce the negative impact of competition and CTP, namely remanufacturing strategy and licensing strategy. We further divide licensing strategy into two strategies, namely fixed-fee licensing strategy and royalty licensing strategy. We use subscript g {R, LF , LR} to denote the remanufacturing strategy, fixed-fee licensing strategy, and royalty licensing strategy, respectively. 5.1. Remanufacturing strategy-Model R We consider the OEM engages in remanufacturing in the second period and thus deters the IR from entering the market. According to the assumptions in Section 3, the IR would be ruled out of the market when the OEM engages in remanufacturing. Because the OEM usually has a strong relationship with its customers and enjoys a brand advantage over the IR, making the collection of used products easier and cheaper than the IR. However, engaging in remanufacturing would incur a fixed cost, denoted as Fr , since the remanufacturing process is different from the manufacturing process; and thus the OEM has to set up a new remanufacturing system. Therefore, although the OEM has the priority in remanufacturing over the IR, the OEM must balance the trade-off between the input (the fixed cost) and the output (the incremental profit brought by remanufacturing). The OEM’s objective is: O R
= (pR1
c ) qR1 + (pR2n
c ) qR2n + (pR2r
c + sO ) qR2r
Fr
PT1O
PT2O
eqR1 = C1O + T1O s. t. , eqR2n + (e qR2r qR1
vO ) qR2r = C2O + T2O (8)
The OEM’s optimal decisions are characterized by the following proposition: Proposition 6.. The OEM’s optimal production quantities when performing remanufacturing under CTP are: (i) qRa1 = (1 c Pe )/2 , qRa2n = (1 c Pe )/2 , and qRa2r = 0 , when PvO + sO t5 ; qRb2n = (1 sO PvO )/2(1 ), qRb2r = (PvO + sO (1 (ii) qRb1 = (1 c Pe )/2 , and t5 < PvO + sO t6 ; qRc 2n = ( 2 (1 sO PvO ) + (1 )(Pe + c )) + 1 c Pe )/2x , (iii) qRc1 = ( (PvO + sO (1 qRc 2r = qRc1, when t6 < PvO + sO t7 ; (iv) qRd1 = ( (PvO + sO (Pe + c ) + ) + 1 c Pe )/2(1 + 2) and qRd2r = qRd1, when PvO + sO > t7 ; where t5 = (1
)(Pe + c ) , t6 = (1
)(
(1
c
Pe ) + Pe + c ) , t7 = (1
)(1
c
Pe )/
2
),
when
Pe ))/2x ,
and
)(Pe + c ))/2 (1
+1
)(1
c
,x=1+
2
2 2.
Proposition 6 implies that there are four optimal solution scenarios when the OEM engages in remanufacturing under CTP. Depending on the total cost savings from remanufacturing, the OEM would choose not to produce any remanufactured products or new products in the second period. Specifically, when PvO + sO is small enough, remanufacturing is not lucrative, and it is rational that the OEM does not engage in remanufacturing. Interestingly, when PvO + sO is large enough, remanufacturing is a better option than producing new products, and thus the OEM would stop producing new products and would perform remanufacturing only. In addition, there exists a threshold t6 below which the OEM would only remanufacture part of the available used products and above which the OEM would remanufacture all available used products. By substituting the optimal decisions shown in Proposition 6 back into the OEM’s profit function, i.e., Eq. (8), we can obtain the OEM’s optimal profits in Model R. Comparing the OEM’s optimal profits between Model R and Model C, we have the following proposition. Proposition 7.. The OEM’s optimal profits in Model R and Model C are related as follows: (i) ROa = COa ; (ii) When Fr < Fr' , (iii) When Fr < Fr'' ,
Ob R Oc R
> >
Ob C ; Oc C ;
where Fr' and Fr'' are shown in the Appendix A. Proposition 7 demonstrates that the fixed cost Fr is the critical factor that makes the remanufacturing strategy be capable of increasing the OEM’s profit compared with Model C. To be specific, the OEM’s profit in Model R is equal to that in Model C when there are no remanufactured products in the market. This is due to the fact that remanufacturing is not cheaper than producing new products in this situation. Consequently, the OEM would not play the remanufacturing strategy. When remanufacturing is profitable for the OEM, the fixed cost incurred from remanufacturing becomes an obstacle for the OEM to choose the remanufacturing strategy. When Fr is small, the OEM would be better off by playing this strategy. However, with the increase of Fr , the impact of this strategy on the OEM’s profit may reverse. More specifically, there exists a threshold below which using the remanufacturing has a positive impact 9
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Fig. 5. The OEM’s profits in Model R and Model C.
on the OEM. Once the fixed cost beyond the threshold, using the remanufacturing strategy is no longer a good choice. Therefore, we strongly advise the OEM to estimate the fixed cost before deciding to engage in remanufacturing. Using the parameters c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, C1O = C2O = 0.05, vO = 0.2 ; sO = {0.2, 0.3} for the optimal solution scenarios {b , c} , we plot Fig. 5 to show the results of Proposition 7. It is clear that Fr is a decisive parameter. When Fr is small, the OEM is able to obtain more profit by using the remanufacturing strategy. Fig. 5 clearly shows that the OEM’s profits in Model R are higher than that in Model C when Fr is zero. Thus, it is always suggested that the OEM whose fixed cost for remanufacturing is neglectable should engage in remanufacturing when facing competition from the IR under CTP. It also means that the remanufacturing strategy is an effective competitive strategy for the OEM when Fr is small. Next, we compare the carbon emissions of Model R and Model C and make the following observation. Observation 1. The total carbon emissions of Model R are no more than the total carbon emissions of Model C. Example 1.. Let c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5; {vO = 0.4, sO = 0.2, vI = 0.2, sI = 0.1} for the optimal solution scenario b and {vO = 0.4, sO = 0.3, vI = 0.4, sI = 0.3} for the optimal solution scenario c . In the first optimal solution scenario a , the OEM does not remanufacture in both Model R and Model C, and the optimal production quantities of new products are the same in these two models (see Proposition 2(i) and Proposition 6(i)). Thus, the total carbon emissions of Model R is equal to that of Model C, i.e.EROa = ECOa . If the OEM chooses the scenario b, the total carbon emissions in Model R are EROb = e (qRb1 + qRb2n) + (e vO ) qRb2r = 0.217 and in Model C are ECOb = e (qCb1 + qCb2n) + (e vO ) qCIb2r = 0.23. Therefore, we have EROb < ECOb . Similarly, if the OEM chooses the scenario c , the total carbon emissions in Model R and Model C are EROc = 0.209 and ECOc = 0.219, respectively. Naturally, we have EROc < ECOc . Since we obtain the same conclusion in many other cases, we conclude that the total carbon emissions of Model R are no more than the total carbon emissions of Model C.
5.2. Licensing strategy To reduce the negative impact of competition with the IR under CTP on the OEM, we consider that the OEM decides to use licensing strategy. There are two commonly used licensing strategies in existing research, namely fixed-fee licensing strategy and royalty licensing strategy (Hong et al., 2017, Yang et al., 2019). In this section, we assume that the IR’s cost savings and carbon emission savings will reduce to the same level as the OEM after the IR obtains the remanufacturing license from the OEM, i.e., sI =sO , vI = vO . Because the OEM usually has more knowledge about their products than the IR and the OEM will share it with the IR if they can make an agreement, such as a fixed-fee licensing contract or a royalty licensing contract. 5.2.1. Fixed-fee licensing-Model LF Under a fixed-fee licensing contract, the IR will pay a fixed-fee to the OEM to obtain the qualification for remanufacturing used products. Under this strategy, the OEM sets a fixed-fee F first. Then, the IR decides whether to accept it. Finally, the OEM and IR decide their optimal production quantities simultaneously. Therefore, the OEM’s profit function is: O LF
= (pLF1
c ) qLF 1 + (pLF 2n
c ) qLF 2n + F
PT1O
PT2O 10
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s. t. ,
eqLF 1 = C1O + T1O eqLF 2n = C2O + T2O
(9)
The IR’s profit function is: I LF
= (pLF 2r
s. t. ,
(e I qLF 2r
I c + sO ) qLF 2r
F
PT2I
I I I vO ) qLF 2r = C2 + T2
qLF1
(10)
Note that the OEM’s and IR’s profit functions above are similar to the profit functions in Model C. However, the fixed-fee charged to the IR by the OEM cannot be neglected, as it can increase the OEM’s profit and thus reduce the negative impact of competition with the IR under CTP. The OEM’s and IR’s optimal decisions are similar to the optimal decisions shown in Proposition 2, except that the IR’s cost savings sI and the carbon emission savings vI from remanufacturing should be substituted by sO and vO , respectively. By substituting the OEM’s and IR’s optimal decisions back into their respective profit functions shown by Eqs. (9) and (10), we can obtain I O their optimal profits, denoted as LF and LF , respectively. '' O O Proposition 8.. There exist a lower bound of the fixed-fee F ' which is determined by LF B = 0 and an upper bound of the fixed-fee F ' '' I which is determined by LF > 0 , such that when F < F < F , the OEM and IR can make an agreement on the remanufacturing license.
Proposition 8 states that there exists a fixed-fee licensing contract by which the OEM and IR can achieve a win-win situation. To engage in remanufacturing, the IR will pay a fixed fee (the lower bound F ' ) that is large enough to compensate for the OEM’s profit loss resulted from competition under CTP to the OEM. However, it should be noted that the IR’s profit should be positive after paying the fixed fee to ensure the participation of the IR, which means that the fixed fee should not be too high (the upper bound F '' ). Observation 2. The OEM and IR will make a fixed-fee licensing contract when the OEM’s total cost savings from remanufacturing are large. There are three optimal decision scenarios in Model LF that are corresponding to three situations: the total cost savings are small, moderate, and large (see Proposition 2). When the total cost savings are small, called optimal solution scenario a , the IR will not engage in remanufacturing, and therefore the contract will not be made. When the total cost savings are moderate, called optimal solution scenario b , the IR can make a profit by remanufacturing if there is no fixed-fee. However, due to the fixed-fee charged by the OEM, the IR’s profit will be eroded. Meanwhile, the advanced knowledge about remanufacturing that is capable of reducing the remanufacturing cost and carbon emissions is not lucrative. Thus, the contract will not be accepted. In a word, the total cost savings cannot compensate for the fixed-fee paid to the OEM in this situation. But it is profitable for the IR to accept the fixed-fee licensing contract when the OEM’s total cost savings are large, called optimal solution scenario c . This is because the IR’s remanufacturing costs will decrease after taking this contract and the total cost savings are enough to offset the fixed-fee now. The following example illustrates Proposition 8 and Observation 2. Example 2.. Let c = 0.5, = 0.6 , = 0.5, P = 0.1, e = 0.5, vO = 0.4, sO = 0.3, vI = 0.2, sI = 0.2, C1O = C2O = C2I = 0.05. Since the total cost savings from remanufacturing are large for both the OEM and IR in this setting, they both choose the scenario c . The OEM’s profit O O O = 0.097 + F . Therefore, by solving the equation LF in Model B is BO = 0.108 and in Model LF is LF B = 0 , we can easily get the ' I F = 0.011 = 0.028 F lower bound . The IR’s profit in Model LF is LF . By simple algebra, we can get the upper bound of the fixed fee, F '' = 0.028. Hence, when the fixed-fee charged to the IR is higher than 0.011 and lower than 0.028, the OEM is able to obtain more profit when competing with the IR under CTP than without CTP. Meanwhile, the IR is willing to accept the fixed-fee licensing contract. The rationale behind this is that the OEM’s profit will decrease and the IR’s profit will increase when CTP is implemented. Therefore, only if the OEM’s profit loss is compensated by the IR will the OEM allow the IR to enter the market. That’s why there is a lower bound of the fixed-fee. However, if the fixed-fee is too high, the IR cannot obtain profit and thus will not accept the contract. Therefore, when the fixed-fee is moderate, both the OEM and IR are better off under CTP. Next, we analyze Observation 2. Set vO = 0.4, sO = 0.2, vI = 0.2, sI = 0.1 for the scenario b. In this case, the lower bound of the fixed-fee F ' = 0.025. However, the upper bound of the fixed-fee F '' = 0.019. It is not profitable for the IR to accept the fixed-fee licensing contract in this case. By comparing the total carbon emissions of Model LF and Model C, we have the following proposition. Proposition 9.. When the fixed-fee licensing contract is accepted, the total carbon emissions of Model LF is less than the total carbon emissions of Model C. According to our analysis, the OEM and IR will be better off if they make an agreement on the fixed-fee licensing. Surprisingly, environmental performance will also be better simultaneously. The rationale behind this is that the total cost savings from remanufacturing must be large if the IR accepts the contract, and the IR could get these savings, leading to a decrease in the total carbon emissions. These facts imply that the fixed-fee licensing contract is able to coordinate the OEM and IR and reduce the total carbon emissions meanwhile. Thus, the fixed-fee licensing contract can not only achieve a win-win situation between the OEM and IR but also achieve a win-win situation between the environment and profit. 5.2.2. Royalty licensing-Model LR Under a royalty licensing contract, the IR is required to pay a per-unit royalty r for per unit remanufactured products. The 11
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decision timeline of this model is similar to the decision timeline of Model LF, shown as follows: first, the OEM sets the per-unit royalty r that must be paid by the IR if the IR wants to engage in remanufacturing, then the IR decides whether to accept it, finally both the OEM and IR decide their optimal production quantities. The OEM’s and IR’s problems are: O LR
= (pLR1
s. t. , I LR
=
s. t. ,
c ) qLR1 + (pLR2n
I c ) qLR2n + rqLR 2r
PT1O
PT2O
eqLR1 = C1O + T1O eqLR2n = C2O + T2O I (pLR 2r
(e I qLR 2r
c + sO
(11)
I r ) qLR 2r
PT2I
I I I vO ) qLR 2r = C2 + T2
qLR1
(12)
The following proposition characterizes the OEM’s and IR’s optimal decisions. Proposition 10.. In Model LR, the OEM’s and IR’s optimal production quantities are given by a (i) qLR 1 b (ii) qLR 1 ( c (iii) qLR 1
a = (1 c Pe)/2 , qLR 2n = b = (1 c Pe)/2 , qLR 2n = 4) , when t8 < PvO + sO c = (1 c Pe)/2 , qLR 2n =
Ia t8 ; (1 c Pe )/2 , and qLR 2r = 0 , when PvO + sO Ib PvO + c sO + r ) (Pe + PvO + c + sO + 2 r )/( 4) , and qLR 2r = (2(Pe t9 ; Ic (2 )(1 c Pe )/4 , and qLR c Pe)/2, when PvO + sO > t9 ; 2r = (1
(1 + c + Pe))/
where t8 = t3 + r , t9 = t4 + r . Proposition 10 implies that there are three optimal solution scenarios in Model LR that are similar to Model C. The three optimal solution scenarios are divided by the OEM’s total cost savings from remanufacturing (PvO + sO ), which is different from Model C. When PvO + sO is small, remanufacturing is not profitable, and the IR will not engage in it. When PvO + sO is moderate, the IR will only remanufacture part of available used products. Compared with Model C, the IR’s optimal production quantity decreases as the IR has to pay a per-unit loyalty to the OEM for each remanufactured product. When PvO + sO is large, remanufacturing is profitable, and the IR will produce remanufactured products as much as possible; note that the IR’s optimal production quantity will not be influenced by the per-unit loyalty in this case. By substituting the OEM’s and IR’s optimal decisions back into their respective profit Ib Ob functions shown by Eqs. (11) and (12), we can obtain their optimal profits, denoted as LR and LR for the optimal solution scenario b Ic Oc and LR and LR for the optimal solution scenario c , respectively. Ob Ob Ob is a concave function of r . When r ' r r '' where r ' and r '' are determined by LR Proposition 11.. LR B = 0 , the OEM and IR will Ic Oc make an agreement on the royalty licensing. LR ( LR ) is a monotonic increasing (decreasing) function of r . When r ''' r r '''' where r ''' is '''' Ic Oc Oc determined by LR B = 0 and r is determined by LR = 0 , the OEM and IR will make an agreement on the royalty licensing.
Proposition 11 implies that the royalty licensing contract is able to coordinate the OEM and IR if the per-unit royalty r is moderate. The IR can engage in remanufacturing by paying the per-unit royalty to the OEM. Consequently, the IR is able to reduce its
Fig. 6. The OEM’s profits in Model LR and Model B. 12
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Fig. 7. The IR’s profits in Model LR.
remanufacturing costs and thus obtain profit. Meanwhile, the OEM’s profit loss due to competition under CTP can be compensated. Hence, the royalty licensing contract achieves a win-win situation. To better explain the results of Proposition 11, we plot Figs. 6 and 7, using the same parameter values as Example 2 except forC1O = C2O = C2I = 0.1. Ob Ob Figs. 6 and 7 clearly show the four critical thresholds in Proposition 11, that are r ' , r '' , r ''' , and r '''' . Solving LR B = 0 , we can obtain r ' = 0.082 , r '' = 0.207 . According to Proposition 11, we obtain the conclusion that the OEM and IR will make an agreement on Ib the royalty licensing when 0.082 r 0.207 . Note that LR is always positive, and the IR is able to bear any per-unit royalty that the OEM sets. This is due to that the IR would only remanufacture part of all available used products when the total cost savings are moderate and thus can adjust its production quantity and selling price to guarantee a positive profit. However, too large per-unit royalty is not favorable for the OEM, since this would improve the selling price of both the new and remanufactured product and thus Ic Oc Oc reduce consumers’ demand for both the new and remanufactured product. Solving LR LR = 0 , we can obtain B = 0 and ''' '''' r = 0.004 and r = 0.085. Therefore, the OEM and IR will make an agreement on the royalty licensing when 0.004 r 0.085. Note that these two thresholds (r ''' and r '''' ) are lower than the former two thresholds (r ' and r '' ). This is because the IR would remanufacture all available used products when the total cost savings are large and thus cannot afford a large per-unit royalty in this situation. In conclusion, the per-unit royalty should be moderate and it is supposed to be lower when the IR remanufactures all available used products compared with the situation where the IR only remanufactures part of available used products. Next, we evaluate the environmental performance of the royalty licensing contract by comparing its total carbon emissions with Model C. We obtain the following proposition. Proposition 12.. The total carbon emissions of Model LR and Model C are related as: (i) when > c < ECc . (ii) ELR
'
b < ECb ; (detailed in the Appendix A), ELR
Proposition 12 states that the royalty licensing contract is able to reduce the total carbon emissions in most cases. To be specific, when the total cost savings from remanufacturing are large, the total carbon emissions when using the royalty licensing strategy are definitely lower than those when not using the strategy. Because the IR’s carbon emission savings will increase after obtaining the OEM’s advanced knowledge about the product through the royalty licensing contract, and the IR will remanufacture all available used products in this case. However, when the total cost savings from remanufacturing are moderate, the IR will only remanufacture part of the available used products and its production quantity will be influenced by the consumers’ attitude toward remanufactured products. Therefore, when consumers’ tolerance for remanufactured products is large, the IR will produce more remanufactured products, leading to lower total carbon emissions. 5.3. Which strategy should the OEM choose? In the previous section, we have analyzed three possible strategies that the OEM may choose to mitigate the negative impact resulted from the competition with the IR under CTP. In this section, we answer the question: which strategy should the OEM choose? We explore the conditions under which one strategy is superior to another. There are three optimal solution scenarios in these strategies, corresponding to three situations: full remanufacturing, partial remanufacturing, and no remanufacturing. It is meaningless to compare the three strategies when there is no remanufacturing, therefore, we explore the conditions under the remaining two situations. 13
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5.3.1. Full remanufacturing When the total cost savings are large, all available used products will be remanufactured, and this situation appears. By comparing the OEM’s profits in the three strategies (Model R, Model LF, and Model LR), we obtain the following proposition. Proposition 13.. There exist a threshold of the fixed-fee F¯ and a threshold of the per-unit royalty r¯ (detailed in the Appendix A), such that (i) when F < r (1 c Pe )/2 , fixed-fee licensing is dominated by royalty licensing. Further, (a) when Fr < r¯ , the priority ranking of the three strategies is R > LR > LF; (b) when r¯ < Fr < F¯ , the priority ranking of the three strategies is LR > R > LF; (c) when Fr > F¯ , the priority ranking of the three strategies is LR > LF > R; (ii) when F > r (1 c Pe )/2 , fixed-fee licensing is superior to royalty licensing. Further, (a) when Fr < F¯ , the priority ranking of the three strategies is R > LF > LR; (b) when F¯ < Fr < r¯ , the priority ranking of the three strategies is LF > R > LR; (c) when Fr > r¯ , the priority ranking of the three strategies is LF > LR > R; (iii) when F = r (1 c Pe )/2 , fixed-fee licensing is equal to royalty licensing. Further, (a) when Fr < F¯ = r¯ , the priority ranking of the three strategies is R > LR = LF; (b) when Fr > F¯ = r¯ , the priority ranking of the three strategies is LR = LF > R. Proposition 13 provides a strategy selection guidance for the OEM when he/she faces competition from the IR under CTP. It implies that the fixed cost of setting up a remanufacturing system Fr , the fixed-fee F , and the per-unit royalty r have a significant influence on the strategy selection. It shows that any one of the three strategies can be optimal for the OEM, depending on the relative value of the three critical factors. It should be noted that (1 c Pe )/2 is the maximal production quantity of remanufactured products, thus the threshold r (1 c Pe )/2 means the OEM’s maximal royalty income derived from the IR. Hence, when the fixedfee is lower than the maximal royalty income, the OEM should choose the royalty licensing strategy; otherwise, the OEM should choose the fixed-fee licensing strategy. Deciding between the remanufacturing strategy and the licensing strategy is a little complicated. Based on the relationship between fixed-fee licensing and royalty licensing, we can obtain the priority of the three strategies by comparing Fr with the other two thresholds F¯ and r¯ . Fig. 8 clearly shows the OEM’s strategy selection. The OEM is able to easily find which strategy he/she should choose according to the value of the three critical factors by using Fig. 8. 5.3.2. Partial remanufacturing When the total cost savings are moderate, only part of available used products are remanufactured, and this situation appears. Since the fixed-fee licensing contract will only be made when the total cost savings are large, we do not consider the LF strategy in this section. By comparing the R strategy and the LR strategy, we have the following proposition. Proposition 14.. There exists a threshold of the per-unit royalty that the OEM charges the IR under royalty licensing, r , which is determined Ob by ROb LR = 0 , such that: (i) when Fr < r , remanufacturing strategy is superior to royalty licensing strategy; (ii) when Fr > r , remanufacturing strategy is dominated by royalty licensing strategy; (iii) when Fr = r , remanufacturing strategy is equal to royalty licensing strategy.
Fig. 8. The OEM’s strategy selection. Note: when F > r (1 c Pe )/2 , F¯ < r¯ ; when F < r (1
c
Pe )/2 , F¯ > r¯ . 14
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Proposition 14 gives the OEM’s strategy selection under partial remanufacturing. It shows that there exists a critical per-unit royalty r such that when the fixed cost of setting up a remanufacturing system Fr is lower than r , choosing the remanufacturing strategy is better. However, royalty licensing is a wise choice when Fr is higher than r . Note that there is no difference between these two strategies when Fr is equal to r . Therefore, when facing competition from the IR under CTP and under the situation of partial remanufacturing, the OEM can choose an optimal strategy by Proposition 14. 6. Conclusions In this paper, we provide decision support for OEMs that face competition from IRs and that may be regulated by CTP. Since IRs do not produce new products, they usually collect used products originally produced by OEMs and remanufacture them. Moreover, it is well known that remanufacturing emits lower carbon emissions than producing new products. Therefore, it inevitably leads to free riding by IRs, especially when CTP is implemented by governments. However, the impact of this free riding on OEMs’ profits and carbon emissions under CTP remains unclear yet. We develop models to examine these impacts. Our models capture the main characteristics of remanufacturing and CTP. To be specific, we focus on the market where consumers value remanufactured products lower than new products. The available used products are constrained by the previous sales of new products. In addition, remanufacturing has lower production costs and emits lower carbon emissions than producing new products. Furthermore, emission allowances can be sold or purchased in a carbon trading market. We explore three alternative strategies that OEMs may choose to handle IRs’ free riding, namely remanufacturing strategy, fixedfee licensing strategy, and royalty licensing strategy. We investigate OEMs’ optimal decisions under each strategy and evaluate each strategy’s economic performance and environmental performance. Further, by comparing each strategy’s profits under two possible remanufacturing situations, namely full remanufacturing and partial remanufacturing, we answer the question: “which strategy should the OEM choose?” Our findings provide guidance for when one of the three strategies is optimal over another for an OEM. The main findings are summarized below. First, we find that the OEM is worse off when competing with the IR under CTP if the carbon cap allocated to the OEM is small. However, the OEM has better environmental performance under this situation. This finding implies the truth that the IR’s free riding erodes the OEM’s profit, and the profit loss will expand when CTP is implemented. Therefore, it is suggested that the OEM should take actions to prevent profit loss. Second, both fixed-fee licensing and royalty licensing can be achieved under certain conditions. More importantly, these two strategies are able to coordinate the OEM and IR not only from an economic perspective but also from an environmental perspective. This finding suggests the existence of strategies that are able to prevent an OEM’s profit loss while also attain a better environmental performance under CTP. To achieve this goal, governments should enact a patent law to protect OEMs’ patented products. In return, the total carbon emissions will even become lower than that when implementing CTP. Lastly, we find that any one of the three strategies can be optimal for the OEM depending on three critical factors, namely the fixed cost of setting up a remanufacturing system, the fixed-fee, and the per-unit royalty. According to the value of the three critical factors, the OEM can easily decide which strategy he/she should choose under different situations. We provide detailed guidance in Section 5.3. This paper takes a step towards investigating OEMs’ competitive strategies against IRs under CTP. However, our study is based on a situation where OEMs’ products are protected by patent law. Although many countries have patent law now, there are also some countries that don’t have it or some cases in which the law doesn’t work. Therefore, studying OEMs’ competitive strategies under CTP in situations where it is impossible to charge a patent fee to IRs is our future research. In addition, for tractability, we assume that the IR would be ruled out of the market when the OEM engages in remanufacturing, studying the situation where both the OEM and IR engage in remanufacturing under CTP could also be an interesting future research direction. Acknowledgements The authors thank the editor and anonymous referees for their valuable comments and suggestions throughout the review process. This work was supported by the National Natural Science Foundation of China [grant number 71671136] and the MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 16YJA630058]. Appendix A Proof of Proposition 1. O B
= (pB1
c ) qB1 + (pB2n
I B
= (pBI 2r
c + sI ) qBI 2r , s. t. ,qBI 2r
Here, pB1 = 1
c ) qB2n
qB1, pB2n = 1
The first order conditions of The second derivatives are:
qB2n O B 2 O B qB12
are:
=
qB1 qBI 2r , and pBI 2r = (1
O B
qB1
=
2 < 0,
2qB1 + 1 2 O B qB2n2
=
qB2n
c = 0 and
qBI 2r ) .
O B
qB2n
=
2qB2n
qBI 2r + 1
c = 0.
2 < 0.
Therefore, is concave and achieves a maximum at the point of the solution of first order condition. The OEM’s optimal production quantity in the first period is: O B
15
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qB1 =
1
c 2
The Lagrangean and the Karush-Kuhn-Tucker optimality conditions of
L (qBI 2r ,
I)
L = qBI 2r I
= ( (1
qB 2n )
c+sI ) qBI 2r
c + sI
I
+
I(
are:
qBI 2r )
qB1
=0
qBI 2r ) = 0
Scenario 1:
= 0 and qBI 2r
I
O B
= 0 and
qB2n
period, shown as follows:
c+
qB2n =
qB 2n
2 qBI 2r + (1
( qB1
Solving
qBI 2r )
I B
We need
+ sI 4
c +
L qBI 2r
2
= 0 simultaneously, we obtain the OEM’s and the IR’s optimal production quantities in the second c +
, qBI 2r =
1 (c + 1) + c = t < sI 2 1
2c + 2sI 4)
(
qB1 and qBI 2r
2c + 2sI 4)
(
qB1.
t2 =
0 to hold for this scenario to be valid, leading to the necessary condition in this scenario:
1 4
(4
)(1
c)
1 (c + 1) + c 2
When sI t1, qBI 2r < 0 . It means that the IR will not enter the market and thus the OEM’s optimal production quantity in the second period is the same as that in the first period. Thus, we have:
qB1 =
1
c 2
Scenario 2:
, qB2n =
I
1
c 2
> 0 and qBI 2r = qB1.
The IR remanufactures all available used products. Therefore, solving quantities in the second period, shown as follows:
(1
qB2n =
c )(2 4 1 4
We need I = in this scenario:
sI > t2 =
1 4
) (1
(4
, qBI 2r =
c )(4
)(1
)+
(1
O B
qB2n
= 0 , we obtain the OEM’s and IR’s optimal production
c) 2
1 2
c + sI > 0 to hold for this scenario to be valid, leading to the necessary condition
(1 + c )
1 (c + 1) + c 2
c)
Proof of Proposition 2. The OEM’s problem is: O C
= (pC1
s. t. ,
c ) qC1 + (pC 2n
PT1O
c ) qC 2n
PT2O
eqC1 = C1O + T1O eqC 2n = C2O + T2O
The IR’s problem is: I C
= (pCI 2r
s. t. ,
c + sI ) qCI 2r
PT2I ,
vI ) qCI 2r = C2I + T2I
(e qCI 2r
qC1
Here, pC1 = 1
qC1, pC 2n = 1
The first order conditions of The second derivatives are:
qC 2n O C
2 O C qC12
are:
=
O C
qC1
qCI 2r , and pCI 2r = (1 =
2 < 0,
2qC1 + 1 2 O C qC 2n 2
=
c
qC 2n
qCI 2r ) .
Pe = 0 and
O C
qC 2n
=
2qC 2n
qCI 2r + 1
c
Pe = 0 .
2 < 0.
Therefore, CO is concave and achieves a maximum at the point of the solution of first order condition. The OEM’s optimal production quantity in the first period is:
qC1 =
1
c 2
Pe
The Lagrangean and the Karush-Kuhn-Tucker optimality conditions of
L (qCI 2r ,
I)
= ( (1
qC 2n
qCI 2r )
c+sI ) qCI 2r
P ((e
vI ) qCI 2r 16
C2I )
+
I C
are:
I(
qC1
qCI 2r )
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L = qCI 2r I
2 qCI 2r + (1
c + sI
I
=0
qCI 2r ) = 0
( qC1
Scenario 1:
= 0 and qCI 2r
I
O C
Solving
qC 2n) + P ( e + vI )
= 0 and
qC 2n
L qCI 2r
shown as follows:
Pe + PvI c +
qC 2n =
qC1.
= 0 simultaneously, we obtain the OEM’s and IR’s optimal production quantities in the second period,
+ sI
2
4 2(Pe
PvI + c
We need this scenario:
sI ) (
2(Pe
, qCI 2r =
(1 + c + Pe )
qC1 and qCI 2r
4)
sI ) (
1 (1 + c + Pe ) = t < PvI + sI 2 3
Pe + c
PvI + c
(1 + c + Pe ) 4)
0 to hold for this scenario to be valid, leading to the necessary condition in
t4 =
1 4
(4
)(1
c
1 (1 + c + Pe) + Pe + c 2
Pe)
When PvI + sI t3, qCI 2r < 0 . It means that the IR will not enter the market, and thus the OEM’s optimal production quantity in the second period is the same as that in the first period. We have:
1
qC1 =
c 2
Pe
, qC 2n =
1
c 2
Pe
Scenario 2: I > 0 and qCI 2r = qC1. The IR remanufactures all available used products. Therefore, the OEM’s and IR’s optimal production quantities in the second period are:
qC 2n =
(2
)(1 4
c
Pe)
, qCI 2r =
)+ We need I = 4 (1 c Pe )(4 the necessary condition in this scenario: 1
PvI + sI > t4 =
1 4
(4
)(1
c
(1 1 2
c 2
Pe )
(1 + c + Pe)
Pe + PvI + sI > 0 to hold for this scenario to be valid, leading to
c
1 (1 + c + Pe ) + Pe + c 2
Pe )
Proof of Proposition 3. Since we have obtained the OEM’s optimal decisions of Model B and Model C shown in Proposition 1 and Proposition 2, we can easily obtain the OEM’s optimal profits in Model B and Model C by substituting these optimal decisions back into the OEM’s profit functions. Recall that there are three optimal solution scenarios in Proposition 1 and Proposition 2. Correspondently, we have three optimal profits in Model B and Model C, respectively, shown as follows: Profits in Model B: Oa B
=
Ob B
=
Oc B
=
1 (c 2 (c 2 1 ( 16
1) 2; 2c + 5)
2 2
4
2
+ ( 8c 2 + 24c + 8sI
24) + 20c 2 + (8sI 4( 4)2
48) c + 4sI 2
16sI + 32
1)2 .
+ 8)(c
Profits in Model C:
Ob B
Oa C
=
1 (Pe + c 2
Ob C
=
Pe (Pe + 2c 4
2) + P (C1O + C2O ) +
Oc C
=
1 ( 16
+ 8)(Pe + c
2 2
1) 2 + P (C1O + C2O );
4
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2
2))
+
Ob B
1)2 + P (C1O + C2O ).
Comparing the OEM’s optimal profits between Model B and Model C under the three optimal solution scenarios (i.e. vs. COb , and BOc vs. COc ), we have:
(i)
Oa B
Oa C
=
(ii)
Ob B
Ob C
=
(iii)
Oc B
Oc C
=
P (e (Pe + 2c 2 Pe (Pe + 2c 4 Pe 2 2 ( 4 16
2) + 2(C1O + C2O )) ; 2)
P (C1O + C2O )
+ 8)(Pe + 2c
2)
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2 P (C1O + C2O ) .
17
2))
;
Oa B
vs.
Oa C ,
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By simple algebra, we can obtain Proposition 3. Proof of Proposition 4. The proof of Proposition 4 is similar to the proof of Proposition 3 and we omit it. Proof of Proposition 5. By multiplying the total production quantity of the OEM (the IR) by its per unit carbon emissions, we can obtain the total carbon emissions of the OEM (the IR), shown as follows: The total carbon emissions of the OEM in Model B:
EBOa = (1
e ((c
c ) e ; EBOb =
3)
6c 2sI + 8) e ; EBOc = (4 8 4
2
)(1
c)
The total carbon emissions of the OEM in Model C:
ECOa = (1
e ((Pe + c
Pe ) e; ECOb =
c
3) + ( 6e 2
2vI ) P 8
6c
2sI + 8)
; ECOc =
e (4 4
)(1
c
Pe )
It is obvious that EBOa > ECOa , EBOb > ECOb and EBOc > ECOc . The total carbon emissions of the IR in Model B:
(c +
EBIa = 0; EBIb =
2c + 2sI )(e ( 4)
vI )
(1
; EBIc =
c )(e 2
vI )
.
The total carbon emissions of the IR in Model C:
(2(Pe
ECIa = 0; ECIb =
EBIb
PvI + c
sI ) (
(1 + c + Pe ))(e 4)
vI )
; ECIc =
(1
c
Pe)(e 2
vI )
.
It is obvious that EBIa = ECIa = 0 and EBIc > ECIc . Furthermore, by simple algebra, we obtain the result: when vI < e (1 > ECIb .
/2) ,
Proof of Proposition 6. When the OEM engages in remanufacturing under CTP, the OEM faces the problem: O R
= (pR1
c ) qR1 + (pR2n
c ) qR2n + (pR2r
c + sO ) qR2r
PT1O
Fr
PT2O
eqR1 = C1O + T1O s. t. , eqR2n + (e qR2r qR1
vO ) qR2r = C2O + T2O
qR2r , and pR2r = (1 qR2n qR2r ) . Here, pR1 = 1 qR1, pR2n = 1 qR2n The Lagrangean and the Karush-Kuhn-Tucker optimality conditions are: L (qR1, qR2n , qR2r ,
O)
= (1
qR1
c ) qR1 + (1 C1O )
P (eqR1 L = qR1
2qR1
L = qR2n
Pe
2qR2n
L = ( 2qR2n qR2r O(
qR1
c+1+
2 qR2r
qR2r
P (eqR2n + (e
c ) qR2n + ( (1 C2O )
vO ) qR2r
+
O(
qR2n qR1
qR2r )
c+sO ) qR2r
Fr
qR2r )
=0
O
Pe
qR2n
c+1=0
2qR2r + 1) + P ( e + vO )
c + sO
O
=0
qR2r ) = 0
qR1. Scenario 1: O = 0 and qR2r Solving these equations given by the KKT conditions, we obtain the OEM’s optimal production quantities: qR1 =
1
To ensure
(1
c 2
Pe
, qR2n =
PvO + sO (1 )(Pe + c ) 2 ( 1)
1
sO 2(
PvO 1)
qR1 and qR2r
)(Pe + c ) = t5 < PvO + sO
t6 = (1
, qR2r =
PvO + sO
(1 2 (
)(Pe + c ) 1)
0 , the total cost savings from remanufacturing should satisfy the condition: )(
(1
c
Pe ) + Pe + c )
Note that when PvO + sO < t5, qR2r < 0 . It means that the OEM wouldn’t engage in remanufacturing. Thus, the OEM’s optimal production quantities are: 1 c Pe 1 c Pe qR1 = , qR2n = , qR2r = 0 . 2 2 Scenario 2: O > 0 and qR2r = qR1. The OEM remanufactures all available used products. Solving these equations given by the KKT conditions, we obtain the OEM’s optimal production quantities of the new product: 18
Transportation Research Part D 78 (2020) 102193
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(PvO + sO
qR1 =
(1 )(Pe + c )) + 1 2 2) 2(1 + 2
c
Pe
2 (1
qR2n =
sO PvO ) + (1 2(1 + 2
)(1
c
Pe )
2 2)
Since qR2r = qR1, the OEM’s optimal production quantity of the remanufactured product is:
(
qR2r =
2 (1
sO PvO ) + (1 )(1 2 2) 2(1 + 2
c
Pe))
In addition, we obtain the multiplier: O
(
=
1)(
(Pe + c 1) 1+ 2
Pe
c)
sO
PvO
2 2
Note that the OEM would stop producing the new products if the total cost savings from remanufacturing is large enough. To ensure O > 0 and qR2n > 0 , PvO + sO should satisfy the condition:
t6 < PvO + sO
t7 = (1
)(1
c
Pe )/
2
+1
When PvO + sO > t7 , the OEM only produces remanufactured products in the second period and its optimal production quantities are: ( (PvO + sO (Pe + c ) + ) + 1 c Pe ) (PvO + sO (Pe + c ) + ) + 1 c Pe qR1 = , qR2n = 0 , qR2r = 2(1 + 2) 2(1 + 2) Proof of Proposition 7. To obtain the OEM’s optimal profits in Model R, we substitute the optimal decisions shown in Proposition 6 back into the OEM’s profit function. Therefore, we obtain: The OEM’s profits in Model R: Oa R
=
Ob R
=
1 (Pe + c 2
((Pe + c )(Pe + c
( 2Pe Oc R
1) 2 + P (C1O + C2O );
2 2
2c + 1)
((Pe + c
=
4) + 2)
2
2((PvO + sO 4 (
+ (Pe + c )((Pe + c
2PvO
sO ) + Pe + c 1)2 4+4 (
PvO
2)(Pe + c ) + 1) 1)
(Pe + c
2sO + 2) + 2Pe + 2c
(Pe + c 1) 2
sO )2
PvO
+ P (C1O + C2O )
Fr ;
2)
1) 2
+ P (C1O + C2O )
Fr .
Comparing the OEM’s optimal profits between Model R and Model C (shown in Proof of Proposition 3), we have: (i)
(ii)
Oa R Ob R
Oa C Ob C
= 0; =
((Pe + c )(Pe + c
4) + 2) 2
2((PvO + sO 4 (
P (e + vI )(P (e + vI ) + 2(c + sI + ( 4)2
(iii)
Oc R
Oc C
=
( 2Pe
Fr
4
(c 2
2))
2 2c + 1) 2 + (Pe + c )((Pe + c
1 ( 2 2 16
2)(Pe + c ) + 1) 1)
2PvO
(Pe + c
sO )2
PvO
2c + 5) 2 + ( 8c 2 + 24c + 8sI
2sO + 2) + 2Pe + 2c 2) 4+4 ( 1) 2
Fr
Pe (Pe 4
24) + 20c 2 + (8sI 4( 4)2
((Pe + c
PvO
+ 2c
sO ) + Pe + c
;
2)
48) c + 4sI 2 1)2
16sI + 32 (Pe + c
1)2
.
1) 2
+ 8)(Pe + c
By algebra, we can obtain Proposition 7. Fr' and Fr'' are determined by
Ob R
Ob C
= 0 and
Oc R
Oc C
= 0 , respectively.
Proof of Proposition 9. According to Observation 2, the OEM and IR will make a fixed-fee licensing contract when the OEM’s total cost savings from remanufacturing are large. It means that the OEM’s and IR’s optimal decisions would be the scenario c shown in Proposition 2, except that the IR’s cost savings sI and the carbon emission savings vI from remanufacturing should be substituted by sO and vO , respectively. Thus, the total carbon emissions in Model LF are:
ELF =
1 (Pe + c 4
1)(( 4 + (
2) ) e + 2 vO )
The total carbon emissions in Model C are:
EC = ECOc + ECIc =
1 (Pe + c 4
Therefore, we have ELF
EC =
1)(( 4 + ( 1 4
(vO
2) ) e + 2 vI )
vI )(Pe + c
1) < 0 .
Proof of Proposition 11. The OEM’s profits in Model LR: Ob LR
=
1 4 ( 3
4) 2
((12
32) r 2 + ( 4(Pe + c + 3)
2
+ ( 8(Pe + c )2 + 24(Pe + c ) + 8(PvO + sO ) 16(PvO + sO ) + 32) ) +
P (C1O
+
+ 16(Pe + c 24)
2
C2O ); 19
PvO
sO )(
2) + 32 ) r + ((Pe + c )(Pe + c
+ (16(Pe + c )2 + 4(Pe + c
PvO
sO ) 2
48(Pe + c )
2) + 5)
Transportation Research Part D 78 (2020) 102193
Q. Chai, et al. Oc LR
=
1 ( 16
2 2
4
1 r (Pe + c 2
1)2
+ 8)(Pe + c
1) + P (C1O + C2O ).
The IR’s profits in Model LR: Ic LR
=
1 ((Pe + c ) 2 ((
1 ( 8
1) r +
2)
2 (Pe
1 8
2)(Pe + c ) + 2(PvO + sO ))
Therefore, the second derivative of The first derivatives of
Oc LR
and
Ic LR
is:
Ob LR
are:
Oc LR
1 1 2 (Pe + c ) + (Pe + c 4 2 2 (Pe + c ) + 1 2 + PC I . 2 8
+ c)2 2
2 Ob LR r2
r
=
24 4 (
1 2
=
64 4)2
1)
2(Pe + c
sO ) +
PvO
1 4
< 0. Ic LR
1) > 0 ,
(Pe + c
1
1) < 0 .
= 2 ((Pe + c )
r
Proof of Proposition 12. The total carbon emissions in Model LR are: b Ob Ib ELR = ELR + ELR e ((Pe + c =
3)
1 ( 4
c Oc Ic ELR = ELR + ELR =
6(Pe + c ) 2(PvO + sO ) + 2r + 8) 2 8
4)(Pe + c
1 (Pe + c 2
1) e
(e
vO )((Pe + c + 1) (
1)(e
2(Pe + c 4)
PvO
sO )
2r )
PvO
sO ))
;
vO ).
The total carbon emissions in Model C are:
e ((Pe + c
ECb = ECOb + ECIb =
ECc = ECOc + ECIc =
1 (Pe + c 4
3)
6(Pe + c ) 2 8
1)(( 4 + (
2(PvI + sI ) + 8)
(e
vI )((Pe + c + 1) (
2(Pe + c 4)
;
2) ) e + 2 vI ).
b c Therefore, by comparing ELR with ECb and ELR with ECc , we obtain: b (i) ELR
ECb =
(vO
4Pe + c + ) + 2P (vO2
vI )(2 Pe
vI2) + 2vO ( c + r + s ) (
By simple algebra, we obtain the result: when c (ii) ELR
ECc =
1 2
(Pe + c
1)(vO
2vI ( c + sI )
(
2)(r
sO + sI ) e
4)
>
'
b < ECb , where , ELR
'
.
=2+
vI ) < 0.
Proof of Proposition 13. Under the full remanufacturing situation, we compare Oc LR
Oc LF
=
1 r (Pe + c 2
2( (vO vI ) P (vO2 vI2) sO vO + sI vI + rvO ) . (2Pe + c + 1)(vO vI ) + e (sO sI + r )
1)
Oc LF
and
Oc LR ,
shown as follows:
F
Oc Oc Oc Oc Oc Oc > LF < LF = LF Therefore, when F < r (1 c Pe )/2 , LR ; when F > r (1 c Pe )/2 , LR ; F = r (1 c Pe )/2 , LR . After knowing the relationship between fixed-fee licensing and royalty licensing, we study the relationship between the remanufacturing strategy and these two licensing strategies. We can obtain the threshold of the fixed-fee F¯ and the threshold of the perOc Oc Oc unit royalty r¯ by solving ROc LF = 0 and R LR = 0 , respectively.
F¯ =
r¯ =
F+
1 16 + 16 2 (
+ 4(A
1)((A + 1)
1 (A 2 4(A
1) r + B)2
2
1)
2 3(
2(A
B ))
1 16 + 16 2 (
1)
+ 4(A
1)((A + 1)
1)( 2 (3
2 3(
2(A
4)(A
1) 2 +
2
7 2A A
6 + 12 A A 7
2 B 3
2 3
4(A
B)2
2
4) ;
1)(
4)(A
1)2 +
B ))
2 (3
4) .
where A = Pe + c and B = PvO + sO . Note that when F = r (1 c Pe )/2 , F¯ = r¯ ; when F < r (1 Oc In addition, (i) when Fr < F¯ , ROc > LF ; when Fr = F¯ , ROc = Oc Oc Oc Oc R = LR ; otherwise R < LR . Based on the above analysis, we can obtain Proposition 13.
c
Oc LF ;
20
2
7 2A A
6 + 12 A A 7
2 B 3
2 3
Pe )/2 , F¯ > r¯ ; when F > r (1 c Pe )/2 , F¯ < r¯ ; Oc Oc otherwise ROc < LF ; (ii) when Fr < r¯ , ROc > LR ; when Fr = r¯ ,
Transportation Research Part D 78 (2020) 102193
Q. Chai, et al.
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