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1 Author's Accepted Manuscript Managing channel profits of different cooperative Models in closed-loop supply chains Zu-JunMa, Nian Zhang, Ying ai, Shu Hu PII: OI: eference: To appear in: S ( OME565 Oega eceived date: 3 January 03 evised date: 5 June 05 Accepted date: 7 June 05 ite this article as: Zu-JunMa, Nian Zhang, Ying ai, Shu Hu, Managing channel profits of different cooperative Models in closed-loop supply chains, Oega, This is a PF file of an unedited anuscript that has been accepted for publication. As a service to our custoers we are providing this early version of the anuscript. The anuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable for. Please note that during the production process errors ay be discovered which could affect the content, and all legal disclaiers that apply to the journal pertain.

2 Managing hannel Profits of ifferent ooperative Models in losed-loop Supply hains Abstract: The iportance of closed-loop supply chains has been widely recognized in literature and in practice. The paper investigates interactions aong the different parties in a three-echelon closed-loop supply chain consisting of a single anufacturer, a single retailer and two recyclers and focuses on how cooperative strategies affect closed-loop supply chain decision-aking. Various cooperative odels are considered by observing recent research and current cases, and the optial decisions and supply chain profits of these odels are discussed. By coparing various coalition structures, we discover that cooperative strategies can lead to win-win outcoes and increase an alliance s profit and can be effective ways of achieving greater efficiency fro the point of view of the overall supply chain. Finally, the paper presents a detailed coparative analysis of these odels and provides insights into the anageent of closed-loop supply chains. Keywords: losed-loop supply chain; ooperative strategies; hannel profits Introduction losed-loop supply chains (LSs focus on taking back products fro custoers and recovering added value by reusing the entire product and/or certain of its odules, coponents, and parts. Over the past 0 years, LSs have gained considerable attention in industry and acadeia [, ]. To achieve high supply chain efficiency, soe channel ebers in LSs ay choose to cooperate with other channel ebers to for an alliance; such cooperation can bring great benefits or copetitive advantages [3]. This paper focuses on developing a detailed coprehension of the iplications that interactions aong the different parties in a LS have for optial decisions and supply chain profits and on how cooperative strategies affect the LS decision. In current practice, we find various coalition structures in LSs. In soe cases, anufacturers establish strategic alliances with recyclers or invest in their own collection channel for collecting used products. For instance, the big three auto anufacturers (i.e., GM, Ford, hrysler have ade large investents in reanufacturing progras and have established a long-ter cooperative partnership with recyclers in the United States [4]. Nike has created a strategic alliance with an eco-non-profit organization, the National ecycling oalition, to collect used tennis shoes [5]. Soe copanies, such as IBM [6] and ell [7], have designed their own reverse supply chain and fored a departent

3 or subsidiary to take part in collecting used products [8], a siilar approach to a coalition consisting of a anufacturer and a recycler foring to produce products and recycle used products. In real life, any anufacturers cooperate with retailers not only in the selling arket but also in the collecting arket. For exaple, Haier and hanghong not only set up their own subsidiaries that priarily engage in collecting and handling used products but also established a coalition with large retailers (e.g., Suning, Goe in hina [9, 0]. Xerox and Eastan Kodak opany also established cooperative relationships with retailers, in which the coalition not only produces and sells products but also participates in collecting and handling used products [, ]. These alliances function as coalitions including anufacturer, retailer and recycler, all taking part in the operations of a LS. In other cases, independent and non-overlapping recyclers are utilized for collecting and handling used products. For instance, there are two large, independent and non-overlapping Industry Alliances (IA that anage their own recovery, reuse and recycling of used products in Japan [3]. Hewlett Packard orporation also built two independent factories to collect and handle its own used coputers in the US [4]. Based on observations of current practice and the literature, it is necessary to conduct a deeper study of how cooperative strategies affect the equilibriu profits and optial decisions of all channel ebers in LSs. In this paper, we consider four cooperative forats in a three-echelon closed-loop supply chain consisting of a single anufacturer (M, a single retailer ( and two recyclers (: ( The anufacturer cooperates with one of the recyclers (M- coalition structure. ( The anufacturer builds a coalition with the retailer (M- coalition structure. (3 The anufacturer builds a coalition with two recyclers (M-- coalition structure. (4 The anufacturer, the recycler and the retailer build alliances with one another (M-- coalition structure. We analyze the results of the cooperative odels by contrasting the with a copletely decentralized structure (all channel ebers enter into an alliance with one another and act as a single entity and a copletely centralized structure (all channel ebers independently ake their own decisions to illustrate potential sources of efficiencies in LSs. More specifically, we address the following research questions: ( Should channel ebers cooperate with one another and, if so, how should they cooperate with one another? ( How do coalition structures affect the equilibriu profits and optial decisions of the ebers in LSs? Soe of the key results of this paper deonstrate that the cooperation between the anufacturer

4 and the retailer would increase each s profits and return rates. By approaching the selling arket together, they can jointly optiize the final price of the product and efficiently reflect unit net savings fro anufacturing and reanufacturing. Additionally, return rates are sensitive to changes in deand. When a anufacturer establishes a coalition with recycler/recyclers, the coalition structure ay iprove the return rates, the alliance s profit and the retailers profit. Fro econoies of scale and by being closer to the final deand, they jointly optiize return rates and net savings by reanufacturing directly and efficiently controlling the wholesale price. The anufacturer has a dual role because it produces products by using either new aterials or reanufactured aterials in LSs. Although the anufacturer creates an alliance with both the retailer and the recycler/recyclers, this coalition structure is the ost-preferred option because of direct proxiity to the selling arket and the recycling arket, and of jointly optiizing the retail price and the return rate. By coparing various coalition structures, we find that cooperative strategies can lead to win-win outcoes and increase the alliance s profit. Additionally, ore ebers entering into an alliance increase return rates. On a broader level, this paper contributes to our understanding about interactions aong the different parties in a LS and the effects of cooperative strategies on the LS decision. The rest of the paper is organized as follows. A coprehensive literature review is exhibited in Section. The notations and assuptions of odels are described in Section 3. Various cooperative odels are considered, and optial decisions and supply chain profits are analyzed in Section 4. A detailed coparative analysis of these odels is ade and soe interesting propositions are presented about the relationships of various coalition structures in Section 5. esearch contributions are suarized, and future research directions are outlined in Section 6. Literature eview A broader collection and coprehensive review of reverse supply chains and LSs can be found in review articles [5, 6]. Fro a survey of the literature, reverse channel anageent of LSs is one of the ost iportant topics. Savaskan et al. introduced and copared three different reverse channels (i.e., the anufacturer collecting channel, the retailer collecting channel and the third-party collecting channel and suarized soe results fro the three channels []. Savaskan and Wassenhove studied a two-stage LS consisting of a single anufacturer and two retailers and priarily discussed the anufacturer collecting odel and the retailer collecting odel [7]. Wei and Zhao considered a LS with one anufacturer and two copetitive retailers and extended the

5 anufacturer collecting odel with fuzzy deand [8]. Hong and Yeh proposed a retailer collecting odel, in which the retailer collected used products and the anufacturer cooperated with a third-party recycler to handle used products [9]. They deonstrated that the anufacturer ight cooperate with a recycler without considering the cooperation of other ebers in LS. Huang et al. considered three decentralized third-party collecting odels and represented a LS consisting of a recycler, a anufacturer and a retailer, in which the retailer, the recycler and the anufacturer act as the channel leader (Stackelberg leader, respectively [0]. The above studies largely focus on different reverse channel structures. However, due to econoies of scale and the fixed investent, the collecting and handling cost paid by the third-party recycler is usually lower than that paid by the anufacturer or the retailer [, ], and the third-party collecting odel is coon in current practical activities. Therefore, in this paper, we focus on the third-party collecting odel, in which the anufacturer produces the product, the retailer sells the product and the recycler collects the used product. Moreover, the literature did not study interactions aong the different parties in a LS. In contrast, we will investigate various cooperative odels in a LS with a third-party collecting channel. Specifically, we exaine the effect of these cooperation odels on optial decisions and supply chain profits. ooperative interactions in a supply chain have been coprehensively researched in the past. achon investigated several types of supply chain contracts to proote cooperation between a anufacturer and a retailer [3]. Li et al. [9], Huang and Li [4], and Zhang et al. [5] discussed cooperative advertising odels in a anufacturer-retailer supply chain and investigated the effect of cooperation on investent effort levels. Gurnani et al. analyzed the effect of supply chain co-opetition on product prices and investent decisions [6, 7]. Leng and Parlar analyzed how the cooperative effect would influence cost savings fro a supply chain with a anufacturer, a distributor and a retailer [8]. The above studies ai at the issues of cooperation in forward supply chains. In contrast, in this paper, we specifically investigate cooperative interactions aong ebers in LSs. Next, we present our odeling assuptions and the four cooperative odels in LSs. 3 Model Assuptions and Notations We consider a three-echelon LS consisting of a single anufacturer, a single retailer and two recyclers. The anufacturer can anufacture a new product directly fro raw aterials, or reanufacture part or all of a returned unit into a new product. We consider product categories in which there is no distinction between a reanufactured product and a anufactured product [7]. The

6 anufacturer sets the wholesale price paid to the retailer per unit of product and the transfer price paid to the recycler for per unit used product. The retailer sets the selling price and sells the product to consuers. The recyclers collect used products and sell the to the anufacturer, who also deterines the return rate affecting the investent in the collection of used products. The priary goal of this paper is to understand the iplications of different cooperative strategies in LSs for optial decisions and supply chain profits. Hence, we extend the odels of Savaskan et al. [] and Jena et al. [9] to a single period odel with a three-echelon LS consisting of a single anufacturer (M, a single retailer ( and two recyclers (. We specifically consider four cooperative odels in LSs, viz., the M- cooperative odel (Model M, see Figure c, the M- cooperative odel (Model M, see Figure d, the M-- cooperative odel (Model M, see Figure e, and the M-- cooperative odel (Model M, see Figure f. In addition, the copletely centralized odel (Model, see Figure a and the copletely decentralized odel (Model, see Figure b are provided as benchark cases. For each odel, we characterize the optial decision variables and the supply chain profits, respectively. We also exaine the sensitivity of the optial return rate, retail price, deand, and total channel profits to various paraeters to reveal the effect of interactions aong the different parties on the LS decision. We use the following notations throughout the paper. c : Unit cost of anufacturing a new product. c r : Unit cost of reanufacturing a used product into a new product, where cr c : Unit saving cost fro reanufacturing, where = c cr [3, 3]. ω : Unit wholesale price of a new product. p : Unit retail price of a new product. : The deand of new products in the arket, where ( p and is the elasticity of deand [33, 34]. b : Unit transfer price of a used product fro the anufacturer to the recyclers. A : Unit cost of recycling a used product, where A < [, 35]. [7, 30]. = α p, α is the arket size, I : The investent in product collection activities, where I = B, where B is the scaling paraeter and denotes the return rate of used products [, 36, 37].

7 (a opletely centralized odel (Model (b opletely decentralized odel (Model (c M- cooperative odel (Model M (d M- cooperative odel (Model M (e M-- cooperative odel (Model M (f M-- cooperative odel (Model M Figure ooperative odels i l : The profit function of participant l in cooperative odel i. The superscript i will take values,, M, M, M and M. The subscript l will take values, M,, and, denoting the cooperative alliance, the anufacturer, recycler, recycler and the retailer, respectively. i j : The return rate of used products for recycler j ( j =, in cooperative odel i, i 0. j i i i i : The total return rates of used products in cooperative odel i, i = +, 0. Without loss of generality, we ake the following odeling assuptions. Assuption. Manufacturing a new product by using a used product is less costly than using raw

8 aterials, i.e., cr c. Additionally, c r is the sae for all reanufactured products, while c is the sae for all new products [, 9]. Assuption. To ensure profitable reanufacturing, the unit cost of collecting and handling a used product is not higher than the unit cost saving fro reanufacturing, i.e., A <, and A is an exogenously specified payent [, 35]. [, 34]. Assuption 3. The arket size α and the elasticity of deand are positive, and α > c Assuption 4. To analyze the different coalition structures of reverse channels, used products are collected by two independent recyclers [3, 38]. This assuption enables us to focus on the gae between the anufacturer and the recycler, which deonstrates several characteristics of the recovery arket in Japan. Given the restriction on techniques for collecting and handling used products, and the existing large quantity of used products, the copetition between recyclers is not intense in the recovery arket [39]. Assuption 5. In LSs, the anufacturer has absolute channel power over the retailer and the recyclers, acting as a Stackelberg leader [, 40]. In LSs, used products have a positive econoic value, and the anufacturer hopes to take back as any used products as possible. However, the return rate is affected by the recyclers' willingness, and that willingness depends on onetary rewards relating to the transfer price. Siultaneously, the wholesale price and the retail price are affected by the transfer price. In the following parts of this paper, we deepen our study of the optial decisions and supply chain profits of the cooperative odels. Based on the notations and the assuptions, we derive the profit functions of the anufacturer, the retailer and the recyclers. ( ( p ω M = ω c + b = b = ( B + A b = ( B + A 4 ooperative Models in LSs This section priarily analyzes various coalition structures in a three-echelon LS, viz., Model M, Model M, Model M, and Model M, and their effect on optial decisions and supply chain profits. As benchark cases, Models and are analyzed to highlight benefits resulting fro

9 cooperative strategies. We solve these odels to obtain optial decisions and copare the optial decision variables such as the wholesale price, retail price, product return rate, and total chain profits. All the profit functions are shown to be concave in the decision variables (see Appendix A, so we use the first-order conditions throughout to characterize the optiality of the decision variables (see Appendix B. 4.. opletely centralized odel (Model In Model (as shown in Figure a, all ebers enter into an alliance with one another and act as a single entity. Therefore, there is only a single decision aker, and the wholesale price and the transfer price are irrelevant to the profit function. Hence, the central planner optiizes ( ( ( ( Max M, p c A B p, = = ( Proposition. In Model, the optial values of the retail price and return rates are given by ( α ( A α B c p = ( B and ( ( α B ( A A c = = (. Proposition states that there exist the optial solutions ( p,,, which axiize the su of the supply chain ebers profits. Model provides a benchark scenario to copare with other odels. We find that the optial retail price is sallest aong all odels (see Table and Table. With a lower retail price, which also iproves the deand for products, ore profits are gained fro the deand of new custoers. Substituting the values of p,, and back in, the total profit can be obtained. 4.. opletely decentralized odel (Model In Model (as shown in Figure b, the anufacturer decides wholesale price and unit transfer price. ecycler deterines return rate. The retailer sets retail price by considering wholesale price. Thus, the proble of Model can be stated as ω, b M ( Max = ω c + b Max = b j B j A j j j s. t. Max = ( p ω p ( Proposition. In Model, the optial values of the retail price, the wholesale price, the unit transfer price, and return rates are as follows:

10 ( α B c α p = b ( 8B ( A, ( α 4B c α ω = ( 8B ( A ( ( α A + A c =, and = = 8 ( B ( A Proposition shows that the optial solutions ( p, ω, b,, of Model can be obtained. In this odel, the optial return rate is the outcoe of the trade-off between the investent in collection effort and the cost saving fro reanufacturing. The optial wholesale price is deterined by considering two effects: the direct effect of the wholesale price on deand and the indirect effect on the return rate. In particular, higher deand (i.e., a lower wholesale price fro the consuer arket is associated with a higher nuber of return products for reanufacturing, resulting in obtaining higher arginal benefit fro investing in the collection effort M- cooperative odel (Model M In Model M (as shown in Figure c, the anufacturer can ally with either of recyclers. Here we just take the alliance between the anufacturer and recycler for exaple. Thus, the central planner pays transfer price to recycler, pays wholesale price to the retailer, and deterines recycler s return rate. The retailer decides retail price, and recycler sets recycler s return rate. Therefore, the proble of Model M is forulated as., ω, b, M ( Max = ω c + b B A M Max = b B A s. t. M Max = ( p ω p (3 Proposition 3. In Model M, the optial values of the retail price, the wholesale price, the unit transfer price, and return rates are given by ( α ( A M α 4B c p = ( 6B 3, ( α ( A M α 8B c ω = ( 6B 3, b M A + =, and ( ( α B ( A M M A c = = 6 3. M M M M Proposition 3 indicates that we can obtain the optial solutions ( p, ω, b,, M of Model M. Surprisingly, we find that return rate is twice return rate M (i.e., M =. M M

11 Additionally, the optial solutions can then be used to copute the supply chain ebers profits (see Table 3. We find that the central planner s profit is greater than the total profit of the anufacturer and recycler in Model (i.e., +. ecycler s profit in Model M is greater than that M M in Model (i.e.,. etailer s profit in Model M is also greater than that in Model M (i.e.,. Therefore, the total profit in Model M is greater than that in Model (i.e., M M. (see Appendix. It shows that cooperation strategy between the anufacturer and one recycler not only increases the alliance s profit, but also increases the profits of other supply chain ebers. Therefore, the anufacturer and the recycler would like to cooperate with each other M- cooperative odel (Model M In this odel (as shown in Figure d, the anufacturer and the retailer build a coalition with one another and are viewed as a central planner. Wholesale price is irrelevant in this odel. The central planner decides retail price and transfer price. ecyclers set their respective return rates. Hence, the proble of Model M is given by b, p M ( ( Max = p c + b M Max = b B A s. t. M Max = b B A (4 Proposition 4. In Model M, the optial vales of the retail price, the unit transfer price, and return rates are as follows: ( α ( A M α B c p =, ( 4B b M A + =, and = = 4 ( ( α B ( A M M A c (. M M M Proposition 4 iplies that there exist the optial solutions ( p, b,, M, which axiize the profit functions in Model M. oparing equilibriu channel profits in Table 3, we find that the central planner s profit in Model M is greater than the total profit of the anufacturer and the retailer in Model (i.e., +. ecycler s profit in Model M is greater than that in M Model (i.e.,. Additionally, recycler s profit in Model M is also greater than that in M Model (i.e., M (see Appendix. It indicates that cooperation strategy between the anufacturer and the retailer also not only increases the alliance s profit, but also increases the profits

12 of other supply chain ebers. Therefore, the anufacturer and the retailer are willing to cooperate with each other M-- cooperative odel (Model M In this odel (as shown in Figure e, the anufacturer and recyclers establish the coalition structure and are viewed as a central planner. Transfer price is irrelevant in this odel. The central planner decides wholesale price and return rates. The retailer sets retail price. Thus, the proble of Model M can be written as ω,, M ( Max = ω c + B B A A ( ω M s. t. Max = p p (5 Proposition 5. In Model M, the optial values of the retail price, the wholesale price, and return rates are given by ( α ( A M α B c p = ( 4B, ( α ( A M α B c ω = ( 4B, and = = 4 ( ( α B ( A M M A c ( M M M Proposition 5 states that we can find the optial solutions ( p, ω,,. M of Model M. oparing equilibriu channel profits in Table 3, we see that the central planner s profit in Model M is greater than the total profit of the central planner and recycler in Model M (i.e., +. Additionally, the retailer s profit in Model M is also greater than that in M M M Model M (i.e.,. Therefore, the total profit in Model M is greater than that in M M Model M (i.e., M M. Moreover, the central planner s profit is also greater than the total profit of the anufacturer, recycler and recycler in Model (i.e., + +. The M M retailer s profit is also greater than that in Model (i.e., (see Appendix. It shows M that cooperation strategy aong the anufacturer and recyclers can increase both the alliance s profit and the retailer s profit. Hence, the anufacturer and the recyclers are willing to cooperate with one another M-- cooperative odel (Model M In Model M (as shown in Figure f, the anufacturer and the retailer can ally with either of

13 recyclers. Here we also just take the alliance aong the anufacturer, the retailer and recycler for exaple. Wholesale price is irrelevant in this odel. The central planner decides transfer price, retail price and recycler s return rate. ecycler deterines recycler s return rate. Hence, the proble of Model M is given by s. t. Max = b B A M ( ( ( M Max = M + + = p c + A + b B b, p, (6 Proposition 6. In Model M, the optial values of the retail price, the unit transfer price, and return rates are as follows: ( α 4B c M α p =, b ( 8B 3( A M ( ( α + A A c M =, =, and 8B 3 ( ( α A c M =. 8B 3 ( A ( A M M M Proposition 6 states that there exist the optial solutions ( p, b,, M, which axiize the profit functions in Model M. oparing equilibriu channel profits in Table 3, we can find that the central planner s profit in Model M is greater than the total profit of the central planner and the retailer in Model M (i.e., also greater than that in Model M (i.e., +. Additionally, recycler s profit is. Thus, the total profit in Model M is M M greater than that in Model M (i.e., M M. Moreover, the central planner s profit is greater than the total profit of the central planner s profit and recycler s profit in Model M (i.e., +. ecycler s profit is also greater than in Model M (i.e., M M M. M M Therefore, the total profit in Model M is greater than that in Model M (i.e., M M (see Appendix. It indicates that cooperation strategy aong the anufacturer, the retailer and one recycler can increase both the alliance s profits and the other recycler s profit. Therefore, the anufacturer, the retailer and the recycler would like to cooperate with one another. In the following section, we perfor a detailed coparative analysis of these odels. 5 oparison of Various ooperative Models In this section, we ake a detailed analysis and careful coparison of the results in various cooperative odels. The ain objective is to develop a general understanding of each coalition

14 structure. The results are suarized in Table, Table and Table 3. The optial decisions in Model and Model are displayed in Table, which provides benchark scenarios for coparing with other odels. Table shows optial decisions in various cooperative odels such as Model M, Model M, Model M, and Model M. Additionally, the channel ebers profits in various odels for different coalition structures are shown in Table Analytical esults By coparative analysis of the results in Table, Table and Table 3, we ake soe interesting observations to reveal the relationships of different coalition structures in LSs. All proofs are provided in the Appendix. Proposition 7. When A, total channel profits in various odels are related as M M li = li = li, A A A M M li = li = li, and A A A Note that if A, then M M 3 li = = =. A M M 4 0, because the recyclers have no profit and ay not be willing to collect any used products. Thus the reverse channel would no longer exist. When A, we copare the two groups of odels and deterine that the profit ratios equal 3 4. In this situation, there exists only the forward supply chain in LSs. Model M and Model M have a structure siilar to that of Model, and Model M and Model M have a structure siilar to that of Model. In particular, when the anufacturer and the retailer establish cooperation with one another, the increased profit equals a quarter of the total channel profits. Proposition 7 states that the total channel profits in LSs ainly coe fro the forward supply chain. Hence, the anufacturer and the retailer ought to establish a good cooperative relationship. Many observations in the industry epirically corroborate the findings of the proposition, as in the case of the partnership between P&G and Wal-Mart [4].

15 Table oparison of optial decisions in Model and Model hannel decision and profits Model Model ( α ( B c ( B A α B ( α c p B ( A ( ( α ( B c ( B A ( 4 B ( A B ( α c ( B ( A 8 ( α B α c ( 8 B ( A ( B α c ( 8 B ( A ( A ( α c B ( A ( ( A ( α c ( 8 B ( A ( A ( α c B ( A ( ( A ( α c ( 8 B ( A α 4 B ( α c ω N/A ( 8 B ( A b A + N/A

16 Table oparison of optial decisions in cooperative odels hannel decision and profits Model M Model M Model M Model M ( 48 B 5 ( A B ( α c ( 6 B 3 ( A α 4 B ( α c p 6 B 3 ( A ( ( 6 B ( A B ( α c ( B ( A 4 ( ( α B α c ( 4 B A ( 8 B ( A B ( α c ( B ( A 4 ( ( α B α c ( 4 B A ( 6 5 ( ( α B B A c ( 8 B 3 ( A ( α α 4 B c ( 8 B 3 ( A ( A ( α c 6 B 3( A ( A ( α c 4 B ( A ( ( A ( α c 4 B ( A ( ( A ( α c 8 B 3( A ( A ( α c B ( A 6 3 ( A ( α c 4 B ( A ( ( A ( α c 4 B ( A ( ( A ( α c ( 8 B 3 A + 3 ( A ( α c B ( A 6 3 ( A ( α c 4 B ( A ( A ( α c 4 B ( A 3 ( A ( α c ( 8 B 3 A α 8 B ( α c ω ( 6 B 3 ( A ( ( α B α c ( 4 B A N/A N/A b A + N/A A + + A

17 Table 3 oparison of channel ebers profits in the decentralized odel and cooperative odels Profits Model M Model M Model Model M Model M M 6 B ( α c ( 6 B 3 ( A ( α B c 3 B ( α c ( 4 B ( A 8 B ( A B ( α c 8 B ( A ( 4 ( α B c ( 8 B ( A ( α B c ( 8 B ( A ( ( α B A c ( 6 B ( A ( α ( B c ( 4 B A ( ( ( 8 B ( A B A α c ( α B c ( 8 B 3 ( A B ( A ( α c ( 6 B 3 ( A ( ( α B A c ( 6 B ( A ( ( ( 8 B ( A B A α c ( ( α B A c ( 8 B 3 ( A

18 Proposition 8. In Model, Model M, Model M and Model M, the anufacturer sets all ( A b = +. The reverse supply chain consists of the anufacturer and the recyclers. The incentive for reanufacturing is directly driven by b, and the incentive of the recyclers to recycle is directly driven by b A. The transfer price affects the gae between the anufacturer and recyclers. Naely, the transfer price varies fro the iniu of quantity A to the highest. If the anufacturer chooses a large transfer price, the recyclers would increase return rate. However, the anufacturer s net savings fro reanufacturing products would diinish (i.e., b decreases, and the anufacturer s profits would decrease as the transfer price approaches the saving cost fro reanufacturing. We obtain equilibriu between the anufacturer s profit and the recycler s profit, and the balance point is b ( A = +. Proposition 8 iediately iplies that for different coalition structures, the transfer price paid by the anufacturer to recyclers is stable. The proposition will help recyclers to choose the proper investent level in the collection of used products. Proposition 9. The optial return rates are related as M M M M =. Note that the recycler j s total profit is ( b A j ( p ( w B j, in which retail price is deterined by the retailer, transfer price is deterined by the anufacturer, and return rate is deterined by recycler. Because b A, we know that the arginal benefit is M ( b A ( A ( b A ( A + in Model, Model M, Model M and Model. To increase profits, these cooperative structures would oderately increase the investent in the M M collection of used products and iprove the return rate (. Moreover, we also find that M M. The alliance of anufacturer and retailer can increase the deand of the arket, which ay indirectly influence the aount of used products in the reverse channel. etail price can be strategically deterined to ake used-product collection ore profitable, a result of a second-degree effect on return rate. Proposition 9 contains soe potentially interesting results. In LSs, ore ebers in an alliance are associated with higher return rates. Specifically, the cooperation between the anufacturer

19 and the retailer could increase return rates. Hence, the governent should encourage the anufacturer and retailer to participate in collecting used products. Proposition 0. Wholesale prices and retail prices in various odels are related as M M ω ω ω, and M M M M p p p p p p. onsequently, M M M M, where = α p. Fro the above proposition, the wholesale price and the retail price would be influenced by various coalition structures. Moreover, wholesale price is deterined by the anufacturer and retail price is deterined by the retailer. Fro Proposition 9, we know that the alliance of anufacturer and M M recycler would increase the investent in the collection of used product ( and collect ore used products fro the arket. The anufacturer setting a lower wholesale price to increase the deand and increasing the cost savings fro reanufacturing ay cause the wholesale M M price to decrease ( ω ω ω. When the anufacturer establishes an alliance with the retailer, wholesale price would be irrelevant in these odels (Model M, Model M, and Model. The retail price in the copletely centralized odel is lower than that of the others because the lower price can increase both deand and profits. The iplication of Proposition 0 is that the ore the ebers enter into an alliance aong the anufacturer and recyclers, the lower the wholesale prices are. In addition, the cooperation between the anufacturer and the retailer ight decrease retail prices and be beneficial to consuers. Proposition. The retailer s profits and total channel profits in various odels are related as > > and M M M M. The results reveal the varying of profits aong various cooperative odels. When the anufacturer allies with the retailer, the retail price is reduced and ore products are sold into the arket. When the anufacturer builds alliances with recyclers, ore used products are collected fro the arket. In short, cooperative strategies can increase the yield of products in LSs and proote the selling of products to obtain ore profit at the best price. The iplication of Proposition is that the alliance aong the anufacturer and recyclers would iprove the retailers profit, and cooperation strategy can iprove supply chain efficiency. The anufacturer ay be apt to cooperate with the retailer rather than the recycler.

20 5.. Nuerical Study Because recycling fee and scaling paraeter cannot be solved analytically, a nuerical exaple is provided to exaine the effect of the autocorrelation coefficients A and B on return rates, retail prices, deand and total channel profits in various odels. We assue that α = 0000, = 40, c = 00, and = 00 []. And Matlab software is utilized to calculate optial channel decisions and profits. The results are shown in the Figure, Figure 3, Figure 4, and Figure 5. In Figure, we focus on how recycling fee and scaling paraeter affect return rates in various cooperative odels. In Figure a, we first plot changes in return rates when A is increased fro 5 to 00 with an increent of. Figure a validates Proposition 9. We find that these return rates are negatively related to the recycling fee, which increases at the sae rate. Additionally, the relationship between the recycling fee and the return rates are alost linearly dependence. In Figure b, we plot these return rates when scaling paraeter B is increased fro 75,500 to,800,000 in increents of 000. We find that return rates are also negatively related to the scaling paraeter and that the growth inflection is 500,000. In other words, value B also has a great influence on the return rates when value B is increased fro 75,500 to 500,000. When B increases fro 500,000 to,800,000, value B has a slight effect on the return rates in these odels. (a Effect of A on return rates (b Effect of B on return rates Figure Effect of soe factors on the return rate in the supply chain Figure shows that the ore the ebers enter into an alliance, the higher the return rates are in various cooperative odels. Hence, cooperative strategies have a ajor ipact on the return rate in a LS. Specifically, when the anufacturer and the retailer establish cooperation with one another, the return rate will increase proinently.

21 (a Effect of A on retail prices (b Effect of A on deand Figure 3 Effect of the recycling fee on retail prices and deand In Figure 3, we perfor sensitivity analysis of retail prices and deand with respect to recycling fee. We plot changes in retail prices and deand when recycling fee A changes fro 5 to 00 with an increent of. Figure 3 validates Proposition 0. We find that wholesale price and retail price are positively related to recycling fee, and deand is negatively related to recycling fee, which increases at the sae rate. In Figure 4, we investigate the effect of scaling paraeter on retail prices and deand. We plot changes in retail price and deand when B is increased fro 75,500 to,800,000 in increents of 000. Figure 4 confirs Proposition 0. In Figure 4, we find that retail price is positively related to scaling paraeter, and deand is negatively related to scaling paraeter. These curves have the sae growth inflection, which is 500,000. When B increases fro 75,500 to 500,000, value B has a great influence on retail prices and deand. When B increases fro 500,000 to,800,000, value B has a slight effect on retail prices and deand. (a Effect of B on retail prices (b Effect of B on deand Figure 4 Effect of the scaling paraeter on retail prices and deand

22 Both in Figure 3 and Figure 4, the retail price in the copletely centralized odel is saller than that in other odels. In addition, we see that the anufacturer and the retailer are ore likely to choose low-price strategy when the value of scaling paraeter is saller. However, when the scaling paraeter is big enough, the anufacturer and retailer ay choose stable prices, i.e., their cooperative strategies are no longer affected by scaling paraeter. To further study the effects of recycling fee and scaling paraeter on total channel profits, we plot the varying of profits when A increases fro 5 to 00 with an increent of in Figure 5a, which indicates that profits are negatively related to value A, which increases at the sae rate. In Figure 5b, we plot the varying of profits when B increases fro 75,500 to,800,000 in increents of 000. In Figure 5b, we find that profits are negatively related to value B, which increases at the sae rate as does value B. When B increases fro 75,500 to 500,000, value B changes slightly, whereas profit varies significantly. When B increases fro 500,000 to,800,000, value B has a slight effect on profits. These curves have the sae growth inflection of 500,000. (a Effect of A on total channel profits (b Effect of B on total channel profits Figure 5 Effect of soe factors on profits Figure 5 depicts the intuitive effect of recycling fee and scaling paraeter on total channel profits in various cooperative odels. We see that total channel profits fall off rapidly with the increasing in scaling paraeter. In addition, the total channel profit in the copletely centralized odel doinates total channel profits in other odels, because forward and reverse supply chain decisions are integral coordinated in a LS. Specifically, cooperation structures in the forward supply chain are better than that in the reverse supply chain. Hence, the anufacturer should pay ore attention to the relationship with the retailer.

23 6 Suary In this paper, we consider a three-echelon supply chain consisting of a single anufacturer, a single retailer and two recyclers. We investigate interactions between the different parties in LSs and present four cooperative odels: Model M, Model M, Model M and Model M. And we solve these cooperative odels and ake a detailed analysis and careful coparison of the results in various cooperative odels. In particular, the following results are of anagerial relevance. First, cooperative strategies have an ipact on return rates of used products, and return rates increase with the nuber of alliance ebers. Specially, the cooperation between the anufacturer and the retailer would proinently increase return rates. Second, wholesale prices would decrease with the nuber of ebers in an alliance aong the anufacturer and recyclers. The cooperation between the anufacturer and the retailer would decrease retail prices and be beneficial to consuers. Third, cooperative strategies can lead to win-win outcoes and increase the total channel profit. Total channel profits in the forward supply chain are larger than that in the reverse supply chain. In future research, we ay reove soe assuptions to develop ore coprehensive supply chain systes, such as a case in which recyclers copete against one another in the sae arket. Both consuer utility and governent subsidy echaniss affecting the supply chain should be considered. The odeling fraework in this paper can be easily extended to consider such questions. Acknowledgents We are grateful to the associate editor and the two anonyous reviewers for their valuable coents and useful suggestions, which are all valuable and very helpful for revising and iproving our paper. Appendix A Proof of the profit functions of supply chain ebers are concave in the decision variables. Proof. onsider Model. To have an interior point solution for 0 + [, 9, 4], j ( should satisfy j 0 and + ( = j calculate the Hessian atrix as follows:. That is, B ( α c ( A ( A 0 +. Then, we

24 ( A ( A p p p H = p = ( A B 0 p ( A 0 B Since A, 0, and B 0 H 0, we can obtain ( = <, H = B ( A and H 4 B B ( A 4 0 ( 3 = 0. Hence, is jointly concave in p, and. onsider Model. To have an interior point solution for j ( 0 +, ust satisfy j 0 and ( 0. That is, B ( α c ( A. j j + = j j is concave in p since = 0. p is concave in j since j = B 0 j j. For A b, M is jointly concave in ω and b since ( ( B ( b A( b ( B M = ω ( 8B ( A 0 and 4 ( w ( ( + ( ( M B A M M α M 0 =. ω b b ω b ω B 3 b A b onsider Model M. M is concave in p since M p = 0. is concave in since M = B 0. In addition, we calculate the Hessian atrix as follows: M ( ( b A( b B ( w ( A b + M M M 4 α ( A b b ω b 4B 4B M M M ( w ( A b α + ( α w H = 0 = b ω ω ω 4B 4B M M M ( A 0 B b ω Since b A, 0, and B 0, we can obtain ( H = ( 4B + ( b A( b 6B + ( A 0, 4B 4B ( ( ( ( ( ( H = α w 4B A + 3 b A b 4B 0, and

25 ( w ( ( A B ( b( b A α H3 = B Hence, M is jointly concave in ω, b and. onsider Model M. is concave in j since M j = B 0. For A b, M j j M is concave in ω and b since ( α p M = b B 0 and ( p ( + B 3 ( b A( b M M M M 4 B A α 0 =. b p b p b p onsider Model M. M is concave in p since M p = 0. In addition, we calculate the Hessian atrix as follows: M M M ω ω ( ( ω A A M M M H = = ( A B 0 ω M M M ( A 0 B ω Since b A, 0, and B 0 H 0, we can obtain ( =, H = 8B ( A 0 and H B B ( A 4 ( 3 = Hence, M is jointly concave in ω, b and. onsider Model M. is concave in since M = B 0. In addition, we calculate the Hessian M atrix as follows: ( ( b A( b B ( p ( A b + M M M α ( A p b p p B B M M M ( p ( A b α + ( α p H = 0 = b p b b B B M M M ( A 0 B p b Since b A, 0, and B 0, we can obtain

26 H H = ( B + ( b A( b 0, B ( p ( B ( A + ( b A( b α = 3 0, and B ( p ( ( A B ( b( b A α H3 = B Hence, M is jointly concave in p, b and. Appendix B Proof of Proposition. In Model, the central planner axiizes ( ( ( ( Max M, p c A B p, = = Because the objective function is jointly concave in p, and (see Appendix A, the first-order condition ( ( characterizes the unique best response, p α B ( α c B ( A ( ( ( A( c B ( A = =. α p = and Proof of Proposition. In Model, for a given wholesale price ω, the retailer s proble is ( ω Max = p. Because the objective function is concave in p (see Appendix A, it follows that p ( α ω ( = +. Given p, recyclers axiize Max = b B A. Fro j j j j j the concavity of the objective function in j, it follows that j (( b A( α ω ( 4B =. Given p and, the anufacturer axiizes ( j Max = ω c + b. Because the objective ω, b function is jointly concave in ω and b, the first-order condition characterizes the unique best response, b ( A p = + and ω = α 4B ( α c 8 B A. M ( ( ( ( Proof of Proposition 3. In Model M, for a given wholesale price ω, the retailer axiizes M ( ω Max = p. Fro the concavity of the objective function in p (see Appendix A, it M follows that p ( α ω ( = +. Given M p, recycler axiizes ( Max b A B M =. Fro the concavity of the objective function in (( b A( ( B = α ω. Given M 4 ω, b, M ( ( M p and M, it follows that, the central planner axiizes Max = ω c + + b B A. Because the objective function is jointly

27 concave in ω, b and, the first-order condition characterizes the unique best response, ( ( ( 8B ( c 6B 3 ( A M =, b ( A M ω α α ( ( ( A( c B ( A M α = 6 3. = +, and Proof of Proposition 4. In Model M, for a given retail price p, recyclers axiize Max = b B A. Because the objective function j M j j j j M M Appendix A, it follows that (( A( c 4B ( A and M is concave in j (see M j ( ( = = α. Give M, the central planner axiizes ( ( b, p M Max = p c + b. Because the objective function is jointly concave in p and b, the first-order condition characterizes the unique best ( ( M response, ( ( 4 ( M p = α B α c B A and b ( A p = +. Proof of Proposition 5. In Model M, for a given wholesale price ω, the retailer axiizes M ( ω Max = p. Fro the concavity of the objective function in p (see Appendix A, it M follows that p ( α ω ( = +. Given M p, the central planner axiizes ω,, M ( ω ( ( Max = c + + B B + A. Because the objective function is jointly concave in,, and ω, the first-order condition characterizes the unique best response, ( (( A( c B ( A = = 8 and M M α ( ( ( B ( c 4B ( A =. M ω α α Proof of Proposition 6. In Model M, the recycler s proble can be stated as Max b B A M =. Fro the concavity of the objective function in (see Appendix M A, it follows that (( b A( α p ( B =. Given M, the central planner axiizes ( ( ( = + + = + +. Because the objective M Max M p c A b B b, p, function is jointly concave in b, p and ( ( ( 4 ( 8 3 ( M p B c B A M, it follows that b ( A = +, = α α, and (( ( ( A( c B ( A = 8 3. M α

28 Appendix Because the deand is nonnegative, i.e., 0, we obtain an equivalent B ( A oparison of the supply chain profit between Model M and Model. Note the following: ( + M M ( α c ( 6B ( A ( A ( B ( A ( B ( A B = M ( ( = B A α c = M Then, we can obtain ( M M ( α c 0. ( 6B 3( A 6B ( A ( 4B + 0, ( 3 8B 0, M ( A 8B ( A 0, and M oparison of the supply chain profit between Model M and Model. Note the following: ( + = M M 3 6B ( α c ( 8B ( A 4B ( A ( M ( ( = B A α c M. ( 8B ( A 6B ( A ( M ( ( = B A α c Then, we can obtain ( M M M + 0, ( 8B ( A 6B ( A ( M 0, and 0. oparison of the supply chain profit between Model M and Model / Model M. Note the following:

29 ( c ( 8B ( A ( A ( B ( A B ( A B α M M M ( + = ( M M B ( α c = ( 4B ( A 3 4B ( A 4 ( + + M M = B ( α c ( A ( 4B ( A 8B ( A ( M B ( α c = ( 4B ( A 4B ( A Then, we can obtain ( + 0, M M M 0, M M M M, ( + + 0, and M M 0, M oparison of the supply chain profit between Model M and Model / Model M/ Model M. Note the following: ( + = M M M ( ( α 3 8B ( α c ( 6B 3( A 8B 3( A ( M M = B A c ( M M M ( 8B 3( A 6B 3( A ( 8 ( ( ( ( ( B α c B A A + = ( ( α ( 8B 3 A ( 4B ( A M M = B A c Then, we can obtain ( 8B 3( A 8B ( A ( ( + 0, M M M 0, M M M M, ( + 0, M M M 0, and M M M M. Appendix

30 Proof of Proposition 9. We can obtain fro the optial values of ( j, Table. Note the following: = in Table and 3 3 B A 4B A 4B A 8B A 8B A ( ( ( ( ( 3 3 B A B A 4B A 4B A 8B A 4 4 ( ( ( ( ( Then, we can obtain ( ( ( ( ( ( ( ( j ( ( A α c A α c A α c A α c A α c B ( A 3 ( 4 ( 3 4B A B A 8B ( A 8B ( A ( ( ( ( ( ( ( ( ( ( A α c A α c A α c A α c A α c B ( A 3 ( 4 ( 3 B A B A 4B ( A 8B ( A 4 4 Hence, = and M M M M =, M M M M then, we obtain M M M M =, where = +. Proof of Proposition 0. Note the following: 3 B ( A B ( A B ( A B ( A 4B ( A 4B ( A 4 3 B ( A B ( A B ( A 4 Then, we can obtain ( ( ( α B α c α B α c α B α c ( 3 ( B A B A B ( A 4 8 ( ( ( ( A α B α c α B α c α B α c 3 4B ( A 4B ( A ( 4B 4 α B ( α c α B ( α c α B ( α c 3 B ( A B ( A ( B ( A 4 Hence, M M ω ω ω and M M M M p p p p p p. We also obtain M M M M, where = α p. Proof of Proposition. Fro Appendix, we obtain

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