Dual recycling channel decision in retailer oriented closed-loop supply chain for construction machinery remanufacturing

Journal of Cleaner Production 137 (2016) 1393e1405

Contents lists available at ScienceDirect

Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Dual recycling channel decision in retailer oriented closed-loop supply chain for construction machinery remanufacturing Pengxing Yi*, Min Huang, Lijun Guo, Tielin Shi School of Mechanical Science & Engineering, Huazhong University of Science & Technology, 1037 Luoyu Road, Hongshan District, Wuhan, 430074, Hubei, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 November 2015 Received in revised form 22 June 2016 Accepted 19 July 2016 Available online 30 July 2016

This paper targets on the optimum strategies of the collection decision for a retailer oriented closed-loop supply chain with dual recycling channel in the construction machinery industry. In the forward channel of this system, the manufacturer produces the new products, the retailer is contracted to remanufacture the used ones, and then sells both the new ones and remanufactured ones to the customers. In the reverse channel, the retailer and the third party collector simultaneously collect the used products. Based on several valid assumptions, we propose a special closed-loop supply chain model with dual recycling channel within the framework of game theory, and explore how the remanufacturer should properly allocate the collection efforts to the retailer and the third party. Furthermore, we conduct performance analysis to investigate the optimal strategies for the supply chain members. Our research confirms that the remanufacturer can gain more used product returns and profits with dual recycling channel, and the optimal allocation of the collection efforts to the retailer and the third party is determined by the relationship of the reverse logistics cost coefficients. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Closed-loop supply chain Retailer oriented Dual recycling channel decision Pricing Remanufacturing

1. Introduction In order to enhance resource utilization and reduce environmental pollution, many manufacturing and servicing enterprises are engaged in remanufacturing (Xiang et al. 2008). Studies have indicated that firms could have 40%e65% cost savings by conducting products remanufacturing strategies, which not only economize the raw materials for manufacturing new parts but also avoid the resources wasting (Kerr and Ryan 2001). Since remanufacturing has a very lucrative prospect, both the original equipment manufacturers (OEMs) and the independent remanufacturers focus their attention on this field (Ferguson and Toktay, 2006). In the construction machinery industry, Caterpillar has firstly shifted its strategy from solely manufacturing and selling new construction equipment to leasing and remanufacturing (Gutowski et al., 2001), and expanded its market to the contractors who cannot afford a new product. Such strategy is imitated by many construction equipment retailers in China, because remanufacturing can be a strategy to attract these low-end consumers through discounting

* Corresponding author. E-mail addresses: [email protected] (P. Yi), [email protected] (M. Huang), [email protected] (L. Guo), [email protected] (T. Shi). http://dx.doi.org/10.1016/j.jclepro.2016.07.104 0959-6526/© 2016 Elsevier Ltd. All rights reserved.

when they face a competitive threat in the market (Atasu et al., 2008; Guide and Li, 2010). It is widely accepted that the market activities involving remanufacturing are more complicated than the traditional manufacturing and selling process, and there exist a lot of different features, such as the uncertainty of sources of used products, or the complexity of their supply chains which involve both the forward and reverse logistic process (Agrawal et al., 2015). Therefore, for those firms engaged in remanufacturing, one of the urgent problems to be solved is how to establish a profitable closed-loop supply chain to collect the used products efficiently and distribute both the new products and remanufactured ones simultaneously. Closed-loop supply chains (CLSCs) for remanufacturing, which involve the movement of the products from the upstream suppliers to the downstream customers and the flow of used ones back to the remanufacturers, combine the forward logistics with the reverse logistics. In real-world industries, the ability to preannounce the production decision, managerial delegation and information management policies distinguishes the leader and the follower (Wang and Wang, 2010). Owing to the differentiation in the market structure, any one of the OEM, the retailer and the third party collector can hold the dominant position in a CLSC involving remanufacturing (Choi et al., 2013). As some studies

1394

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

pointed out, in order to comply with the correlative regulations, many OEMs who concentrated on the core business had to transfer the dominating position in the used product recovery to independent remanufacturers, such as retailers, or other third party firms, rather than set up their own reverse supply chain (Hauser and Lund, 2008; EL korchi and Millet, 2011). Actually, the advantages of being close to the market and convenient for providing the after-sale service make the retailer outperform the OEM in developing remanufacturing activities. And Karakayali et al. (2007) further concluded that the agent who was in charge of the collection or the processing activity in a CLSC tended to assume the leadership power. However, few people paid attention to the mechanism of retailer oriented closed-loop supply chains (ROCLSCs) where the retailer took charge of remanufacturing, though many recent studies investigated the manufacturer oriented closed-loop supply chains (MOCLSCs), and discussed how to establish, model and optimize them (Ahn, 2009; € Shi et al., 2011; Ozkır and Bas¸lıgıl, 2012; and Huang et al., 2013). To complement this shortage, we focus on the situation where a retailer is authorized by the OEM to remanufacture used products, and hope to obtain new insights on how to model and optimize the ROCLSCs for collecting and remanufacturing used products. As is well known, for the CLSCs about products return and remanufacturing, the establishment of the suitable reverse channels is essential (Guide and Van Wassenhove, 2006, and Souza, 2009). In general, three options, named manufacturer collection, retailer collection and third-party collection respectively, are all available for the remanufacturer to collect the used products from customers (Savaskan et al., 2004). The recovery of used products is generally difficult to be conducted due to the complexity of the source of used products, the variability of the quality of returned ones, the participation by the customers, and the uncertainty of market requirements. In particular, it is very hard to collect a sufficient amount of used ones to realize the economies of scale through a single recycling channel under such complicated conditions. To overcome this obstacle, many remanufacturers have adopted more than one recycling channel to increase the return rate of used products. For example, ReCellular Inc., the largest cell phone remanufacturer in the USA, chooses to collect the used phones both from the retailers and the third party collectors (Teunter and Flapper, 2011). For those firms applying CLSCs with dual or multi recycling channel, how to properly allocate the collection efforts to the partners due to the different environment for conducting end-of-life product collection activities, and how to correctly handle the relationship between products recovery and products selling, are also outstanding issues. Many papers about reverse channel decision within CLSCs have been recently published. Savaskan et al. (2004) modelled product return rates as a function of the investment of the collection activities, analyzed the pricing decision and supply chain members' profits in the supply chain in the meantime, and concluded that the agent, who was closer to the customer, was the best choice. Considering the economies of scale and diseconomies of scale in collection cost in real-life industries, Atasu et al. (2013) used models similar to the ones proposed by Savaskan et al. (2004) to investigate the optimal reverse channel choice of the manufacturer. They analyzed manufacturer-, retailer-versus third party-managed collection, and explored which one among them would maximize the manufacturer's profit under different collection cost structures. Nevertheless, these works only provided models and insights to decision-maker on how to choose the most suitable single recycling channel, and most of them talked about this issue within MOCLSC. Actually, for the ROCLSC case, where at least two recycling channels are adopted to collect the used products for the

remanufacturer, the decision-makers should consider not only the choice of recycling channel but also their relationship. To fill in this gap, one goal of this paper is to provide the remanufacturer with guidelines in a ROCLSC with dual recycling channel, in which both the retailer and the third party collector are engaged in collecting used products. The literature on the optimal strategies of CLSCs with dual recycling channel for product remanufacturing is quite scarce. Savaskan and Van Wassenhove (2006) designed a reverse channel for the case of competing retailers, modeled a manufacturermanaged collection system and a retailer-managed collection system, and looked into the dominant factors that influenced the reverse channel choice. But the recycling channel adopted by the retailer-managed collection system could be regarded as the singular way of retailer collection. Huang et al. (2013) investigated optimal strategies of a MOCLSC with dual recycling channel and came up with macro-control policy based on exhaustive numerical analysis. They discussed the conditions when the dual recycling channel was more effective than the single recycling channel for the remanufacturer. Hong et al. (2013) investigated three reverse hybrid collection channel structures in a manufacturer-oriented CLSC, namely the manufacturer and retailer hybrid collection channel, the manufacturer and third party hybrid collection channel, and the retailer and third party hybrid collection channel. They concluded that the manufacturer and the retailer hybrid collection channel was the most effective one. These intensive studies on the dual recycling channel puzzle mainly focused on systems where the OEMs undertook the products remanufacturing responsibility, and gave the firms advice on how to choose the optimum design of reverse channel structure. However, they didn't study how the firms should allocate the different collection efforts to the agents under various circumstances when a dual recycling channel was chosen to collect the used products. Moreover, the collection cost structure in these works could not be applied to the case of construction machinery remanufacturing. And when the retailer is in charge of remanufacturing, the reverse flow of the used products is different from that when the OEM is in charge of remanufacturing. In addition, the assumptions of these works were restrictive. For example, the authors held the views that there was no obvious discrimination between the new products and the remanufactured ones except for the cost of production, and the production and marketing of all the products were in the same period. In this paper, aiming to obtain a solution for the dual recycling channel puzzle existing in a ROCLSC for construction machinery remanufacturing, a two-period method is adopted to handle the differentiation of the new products and remanufactured ones, and applied to determine the optimized collection efforts in each recycling channel and the optimal price decision within the framework of game theory. On the whole, the contribution of this research is threefold. Firstly, considering the fact that the retailer conducts the remanufacturing business for construction machinery with low-budget operation, a special ROCLSC model with dual recycling channel was established, which revealed the combination possibility of different recycling channels. With this model, we solved how to properly allocate the collection efforts to the retailer and the third party in the CLSC to gain more product returns and profits for the remanufacturer. Secondly, the characteristic of the ROCLSC was exhaustively explored and the key factors that influenced the performance of the ROCLSC were detailed illustrated. Finally, the research work was significantly meaningful to engineering practice, as well as the important instruction for enterprises (especially the retailers) aiming to collect and remanufacture the construction machinery. To the best of our knowledge, this is the first paper that thoroughly

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

1395

Fig. 1. The retailer oriented system with dual recycling channel.

investigates the reverse channel decision in the ROCLSC, in which both the retailer (remanufacturer) and the third party take efforts on used products collection simultaneously in the remanufacturing context. The rest of this paper is as follows. Section 2 formulates the dual recycling channel problem in the ROCLSC motivated by a supply chain managerial example in construction machinery industry. Section 3 presents a two-period ROCLSC model and method for reverse channel decisions of the remanufacturer. Section 4 explores the optimal strategies for the remanufacturer on retailer collection and third party collection, and conducts the performance analysis. Section 5 concludes, highlights limitations, and investigates possible directions for the future. 2. Problem description In this paper, some methodologies are followed to model a CLSC with an OEM, a retailer (who also acts as a remanufacturer) and a third party collector motivated by an actual case in China. In China, in order to strengthen the industrial management of remanufacturing, standardize the market competition, and ensure the quality of remanufactured products, the Ministry of Industry and Information Technology has formulated the List of Electromechanical Products Remanufacturing Pilot Enterprises and the Catalog of Remanufactured Products (Ministry of Industry and Information Technology of the PRC, 2014). Actually, only the enterprises included in the list can get authorization to remanufacture, and only the remanufactured products that belong to the above catalog can be produced and sold in the market. Therefore, some local retailers in the construction machinery field in China, who are close to the market and provide the after-sale service, have the advantages in collecting the used products and doing the remanufacturing business over the OEMs. In this actual supply chain, there exist three members, namely, the retailer, the OEM, and the third party. Among these companies, the retailer (the SEVALO Construction Machinery Group Co., LTD, China), is the leading green supply chain facilitator of construction machinery in China. The retailer has years of experience in retailing the construction machinery products which cover multiple brands, and has already established lots of company-operated outlets, which are mainly distributed in Hubei Province, Xinjiang Province, Guangxi Province, Sichuan Province and Chongqing in China. Owing to the advantages in being close to the customer and convenient for providing after-sale service, the retailer owns the information of the customers and the used products (the OEMs and other retailers do not have these information), and is approved by

the Ministry of Industry and Information Technology (the other members in the market don't get the authorization) to remanufacture the end of life excavators which produced by the OEM (Doosan Infracore Construction Equipment). The remanufactured excavators produced by the retailer nearly have no difference with the original excavators produced by the OEM, and are printed on the retailer's independent remanufactured product trademarks. As the retailer dominates the distributing business, after-sales service, collection activities, remanufacturing business, and the pricing capacity in the market of China, the leadership power of this CLSC is assumed by the retailer. When the retailer sells the new excavators and remanufactured ones to the customers, he signs buyback contracts with them. If the customers return the used excavators to the retailer, he pays refunds to them. Because the excavators are bulky and hard to transport, the retailer would like to collect them from the customers closer to his outlets for the consideration of avoiding huge logistics cost. In addition, to collect sufficient amount of used excavators, the retailer also subcontracts part of the collection activities to the third party (a subcontracted third party collector, such as a local second-hand market of construction machinery in a different region) through paying transfer price for the returns. The retailer has already established a perfect forward distribution channel, and sells both the new excavators and remanufactured ones to the customers simultaneously in China. This type of supply chain can be represented by a ROCLSC model with dual recycling channel, in which the retailer/remanufacturer plays the leading role, the OEM/manufacturer concentrates on producing new products, and both the retailer and the third party collector are engaged in used product collection activities. The formulation of this ROCLSC with dual recycling channel is illustrated in Fig. 1. Through modeling this special CLSC system, we aim to explore how the decision-maker should properly allocate the collection efforts to the retailer and the third party, and analyse the decisive factors that drive the optimal strategies of the members in ROCLSC. As mentioned in Section 1, when we model and analyse this ROCLSC, we consider the differentiation of public perception on the new products and remanufactured ones. Herein, a two-period model is adopted to deal with this trouble. 2.1. Definition of symbols For the development of the mathematical model for the ROCLSC shown in Fig. 1, the following notations are defined and summarized. In the above symbols, qt is the decision variable of the third

1396

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

Symbol Definition cm cr

u1 u2

m1 m2 p1 p2n p2r q1 q2n q2r

d b A qT qR

t I

h1 h2

pkij

unit cost of producing a new product with the raw materials unit cost of producing a remanufactured product from the returns unit wholesale price in the first period unit wholesale price in the second period unit profit of the retailer by selling the new product to the customer in the first period unit profit of the retailer by selling the new product to the customer in the second period unit retail price of the new product in the first period, then p1 ¼ u1 þ m1 unit retail price of the new product in the second period, then p2n ¼ u2 þ m2 unit retail price of the remanufactured product in the second period demand for the new products in the market in the first period demand for the new products in the market in the second period amount of remanufactured products produced by the retailer in the second period public perception of the remanufactured products compared with the brand new one, and d2[0,1] unit transfer price for returning product from the third party to the retailer average recycling price for unit used product the amount of used products collected by the third party the amount of used products collected by the retailer the total collection rate investment in collection activities reverse logistics cost coefficient of the retailer collection reverse logistics cost coefficient of the third party collection profit function of party i in the period j of model k, i ¼ M,R,T denotes the manufacturer, the remanufacturer/retailer and the third party separately j ¼ 1, 2 denotes the first period and the second period separately, and k ¼ S,D denotes the closed-loop supply chain with retailer collection alone and dual recycling channel separately.

party, u1 and u2 are the decision variables of the manufacturer, and m1, m2, q2r and b are the decision variables of the retailer.

2.2. Modeling assumptions To handle the case stated in the above subsection, we propose some key assumptions, which are mainly based on the works of Savaskan et al. (2004), Ferguson and Toktay (2006), and Atasu et al. (2013). (1). Both the new excavators and remanufactured ones just have one period life cycle, and the used excavators can be remanufactured for only once. In the first period, the new excavators are produced by the OEM, then they are sold by the retailer to the customers. In the second period, the retailer first formulates the production plan and schedule of remanufacturing. After that, both the retailer and the third party collect the used excavators for the retailer. Finally, the retailer engages in remanufacturing, and sells both the new products and remanufactured ones to the customers simultaneously. If the length of the periods is appropriately chosen, this assumption is reasonable and the customer purchase decisions are independent across periods (Ferguson and Toktay, 2006). (2). Remanufacturing through used parts is less costly than manufacturing through raw materials, i.e., cr < cm. (3). The remanufactured excavator is a natural low-cost alternative to the brand new one, but it has the same functionality. It is assumed that the consumer willingness-to-pay (WTP, namely the valuation) is heterogeneous and uniformly distributed in the interval [0, 1], each consumer's WTP for a remanufactured product is a fraction d of their WTP to a new one, and the market size is normalized to 1 (Ferguson and Toktay, 2006). And Ferguson and Toktay (2006) pointed out that the remanufacturer could estimate the parameter d through operating under an existing bias, such as a judicious choice of packaging, warranties, and marketing. It is obvious that the demand functions in the two periods are given by p1 ¼ 1q1 (the first period), p2 n¼ 1q2ndq2r and p2 r¼ d(1q2nq2r) (the second period). Submitting

p1 ¼ m1 þ u1 and p2 ¼ m2 þ u2 into the above equations, we can obtain that q1 ¼ 1m1u1, q2n ¼ 1u2m2dq2r, and p2r ¼ d(u2þm2þdq2rq2r). (4). According to our investigation, the target company adopts a remanufacture-to-order system and collects the amount of used products he plans to remanufacture. Therefore, we assume that all the end of life excavators collected in the second period are remanufactured (namely q2r ¼ qRþqT). Then, the total collection rate can be formulated as t ¼ q2r/q1. When t ¼ 0, it implies that the retailer does not remanufacture any products, and the retailer and the third party collect nothing in the second period. When t ¼ 1, it implies that the retailer remanufactures all the products sold in the first period. Since the reverse logistics cost is generally high for the excavators and it is impossible for the retailer to collect and remanufacture all the used excavators in the market, we assume that the condition 0 < t < 1 is satisfied to avoid the discussion of the above two special cases. (5). Given that the end-of-life excavators is bulky and hard to be transported, the firm generally gives priority to collecting from the resource which is closer and the collection cost is comparably cheaper. Consequently, the remanufacturer should collect from progressively more distant region to increase the collection volume. Hence, the total collection cost of one agent can be characterized as a convex increasing function of his collection volume q, and is given by C(q) ¼ Aq þ hq2, which exhibits the diseconomies of scale (Ferguson and Toktay, 2006; Atasu et al., 2013). For the retailer and the third party, the reverse logistics cost coefficients are symbolized as h1 and h2, which are varying with the change of the circumstance for collecting the used products. h1 and h2 characterize the degree of difficulty for the retailer and third party to take part in the used products collection activities. As the retailer and the third party collect from different regions, the reverse logistics cost coefficients h1 and h2 vary according to the circumstance for collecting the used products, such as the situation of the reverse logistics network and the service of transportation. (6). There exists a Stackelberg game among the manufacturer, the retailer and the third party in this ROCLSC. In this game, the retailer plays as the market leader, and the manufacturer

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

and the third party play as the followers. In the first period, the retailer first decides the profit m1 by selling the new products, then the manufacturer decides the wholesale price u1 of the new products. In the second period, the retailer first decides the profit m2 by selling the new products, the total amount of the remanufactured products q2r and the transfer price b paid to the third party for the collecting activities. Then, the manufacturer decides the wholesale price u2 of the new products. Finally, the third party collects qT used products for the retailer.

1397

pSM2 ¼ ðu2  cm Þð1  u2  m2  dq2r Þ

(3)

pSR2 ¼ m2 ð1  u2  m2  dq2r Þ þ dðu2 þ m2 þ dq2r  q2r Þq2r  ðA þ cr Þq2r  h1 q22r (4) s:t: 0 < q2r < 1  u1  m1

(5)

Then the total profit of the manufacturer and the retailer can be calculated by

3. Optimal strategies and methods In this section, we use the game theory to analyse the optimal decisions of the members in the ROCLSC, and acquire the optimal collection efforts of the retailer and the third party. Before conducting the analysis, we note that the ROCLSC with dual recycling channel is simplified to the one with single channel (only the retailer/remanufacturer takes the collection efforts) provided that the unit transfer price paid to the third party by the retailer is not higher than the unit recycling price for used products paid to the customers. When b*  A, the third party is unwilling to take any collection effort for no guaranteed economically profits. In the following scenarios, we will use the first model as a benchmark, analyse these two models in detail within the game theory, and make a comparison between them. 3.1. Simplified model of ROCLSC only considering retailer collection As illustrated in Fig. 2, in the ROCLSC model with single recycling channel of retailer collection, the retailer plays as the Stackelberg leader to decide the profits of selling new products in these two periods and the amount of remanufactured products. The manufacturer is the follower, who decides the wholesale prices of new products in these two periods. Profits of the manufacturer and the retailer in the two periods are separately given by:

pSM1 ¼ ðu1  cm Þð1  u1  m1  dq2r Þ

(1)

pSR1 ¼ m1 ð1  u1  m1 Þ

(2)

pSM ¼ ðu1  cm Þð1  u1  m1 Þ þ ðu2  cm Þð1  u2  m2  dq2r Þ (6)

pSR ¼ m1 ð1  u1  m1 Þ þ m2 ð1  u2  m2  dq2r Þ þ dðu2 þ m2 þ dq2r  q2r Þq2r  ðA þ cr Þq2r  h1 q22r (7) To obtain the optimal values of the decision variables that maximize the profits of the retailer and the manufacturer, we apply the backward induction method to conduct the analysis in the two periods. In the first period, we first calculate the best-response function of the manufacturer for a given m1. Then, we substitute the manufacturer's best response u1(m1) into the objective function of the retailer, and deduce the optimal value of m1. In the second period, the calculation is conducted by characterizing the bestresponse function of the manufacturer. Subsequently, by substituting the manufacturer's best response u2(m2,q2r) into the retailer's objective function, the optimal values of the retailer are calculated. Proposition 1. In the ROCLSC model with retailer collection, if

h1 >

dð1 þ cm Þ  2ðA þ cr Þ 1  cm



dð2  dÞ 2

;

then in the first period, the optimal wholesale price of the manufacturer, denoted as uS* 1 , and the optimal profit of the retailer, denoted as mS* , are 1

uS* 1 ¼

1 þ 3cm 4

(8)

mS* 1 ¼

1  cm 2

(9)

and in the second period, the optimal wholesale price of the manufacturer, denoted as uS* 2 , the optimal profit of the retailer, denoted as mS* 2 , and the optimal amount of remanufactured products, denoted as qS* 2r , are given by

uS* 2 ¼

1 þ 3cm d2 ð1 þ cm Þ  2dðA þ cr Þ  8h1 þ 4dð2  dÞ 4

(10)

mS* 2 ¼

1  cm 2

(11)

qS* 2r ¼ Fig. 2. The simplified model of ROCLSC only considering retailer collection.

dð1 þ cm Þ  2ðA þ cr Þ 4h1 þ 2dð2  dÞ

Hence, the total collection rate can be calculated by

(12)

1398

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

tS* ¼

2dð1 þ cm Þ  4ðA þ cr Þ ð1  cm Þ½2h1 þ dð2  dÞ

(13)

pS* R ¼

ð1  cm Þ2 þ 4

2

 cr q2r  bqT  Aðq2r  qT Þ  h1 ðq2r  qT Þ2

d 2 ð1 þ cm Þ  ðA þ cr Þ

4h1 þ 2dð2  dÞ

" #2 ð1  cm Þ2 1  cm d2 ð1 þ cm Þ  2dðA þ cr Þ þ  ¼ 8h1 þ 4dð2  dÞ 16 4

(20)

(14) s:t: 0 < q2r < 1  u1  m1

The profit of the manufacturer is

pS* M

(19)

pDR2 ¼ m2 ð1  u2  m2  dq2r Þ þ ½dðu2 þ m2 þ dq2r  q2r Þ

The profit of the retailer is




pDM2 ¼ ðu2  cm Þð1  u2  m2  dq2r Þ

(15)

Proposition 1 includes the necessary condition h1 > d(1þcm) 2(Aþcr)/1cmd(2d)/2. Because the logistic limitation that the amount of remanufactured products in the second period should not exceed the new products sold in the first period must be S* satisfied. In Appendix A, we set qS* 2r < q1 , and obtain the condition h1 > d(1þcm)2(Aþcr)/1cmd(2d)/2. This condition signifies that the reverse logistics cost coefficient h1 should be large enough, and the collection ratio should not exceed 1. Indeed, in the field of construction machinery remanufacturing, the cost in collecting the used excavators generally exhibits the diseconomies of scale, which indicates that these used products are difficult to be collected, and huge expanse of collection cost is needed, therefore, the scalar parameters are pretty large to satisfy the above criterion. So, throughout this paper, we give tacit consent to satisfaction of the logistic limitation to avoid the unnecessary discussion. Similar definitions also can be found in the previous works, such as Savaskan et al. (2004) and Huang et al. (2013). From Proposition 1, we can conclude that the optimal wholesale price of the manufacturer falls in the second period. Because the retailer participates in the remanufacturing business in the second period, fewer new products are sold in this period, and the manufacturer has to lower the wholesale price to guarantee the profit. In addition, uS* 2 is monotonic increasing with the increase of the coefficient h1, and is monotonic decreasing with the increase of the parameter d. Because the larger h1 is, the more reverse logistics cost is needed to invest in used product collection activities. This means that the retailer would take more efforts to sell the new products, and the manufacturer can raise the wholesale price accordingly. Moreover, larger d signifies more profits in selling the remanufactured products for the retailer, thus the manufacturer has to lower the uS* 2 . In addition, we can find that the retailer would collect more used products with the decrease of the coefficient h1 or with the increase of the parameter d. Moreover, the unit profit of the retailer by selling the new product to the customer in the second period S* mS* 2 is the same to the m1 . Proof. See Appendix A.

(21)

Then the total profits of the manufacturer and the retailer can be calculated by

pDM ¼ ðu1  cm Þð1  u1  m1 Þ þ ðu2  cm Þð1  u2  m2  dq2r Þ (22)

pDR ¼ m1 ð1  u1  m1 Þ þ m2 ð1  u2  m2  dq2r Þ þ ½dðu2 þ m2 þ dq2r  q2r Þ  cr q2r  bqT  Aðq2r  qT Þ  h1 ðq2r  qT Þ2 (23) To obtain the optimal values of the decision variables that maximize the profits of the retailer and the manufacturer, we conduct the analysis similar to that in Section 3.1. In the first period, for a given m1, the manufacturer's problem is to maximize the profit pDM1 . Then, considering the best-response function u1(m1), the retailer's objective is to maximize pD R1 . In the second period, for a given b, the objective of the third party is to determine his collection quantities qT to maximize pD T . For given m2 and q2r, the objective of the manufacturer is to determine his wholesale prices u2 to maximize pDM2 . Then, considering the best-response functions qT(b) and u2(m2, q2r), the retailer's objective is to maximize pD R2 by determining the optimal values of b, m2 and q2r. Proposition 2. In the ROCLSC model with dual recycling channel, if

4h1 h2 2dð1 þ cm Þ  4ðA þ cr Þ >  dð2  dÞ; 1  cm h1 þ 2h2 then the optimal amount of remanufactured products collected by the third party, denoted as qD* T , is


qD* T ¼

h1



d 2 ð1 þ cm Þ  ðA þ cr Þ

4h1 h2 þ ðh1 þ 2h2 Þdð2  dÞ

(24)

Proposition 2 confirms that the optimal amount of used products collected by the third party qD* T is monotonic increasing with the increase of the coefficient h1, and is monotonic increasing with the decrease of the coefficient. Moreover, the third party can collect more used products by promoting the public perception of the remanufactured product d.Proof. See Appendix B.

3.2. Retailer oriented CLSC model with dual recycling channel

Proposition 3. In the CLSC model with dual recycling channel, if

Based on the problem description in Section 2, profits of the supply chain members are as follows:

4h1 h2 2dð1 þ cm Þ  4ðA þ cr Þ >  dð2  dÞ; 1  cm h1 þ 2h2

pDT ¼ ðb  AÞqT  h2 qTT2

(16)

pDM1 ¼ ðu1  cm Þð1  u1  m1 Þ

(17)

then in the first period, the optimal wholesale price of the manufacturer, denoted as uD* 1 , and the optimal profit of the retailer, denoted as mD* 1 , are

pDR1 ¼ m1 ð1  u1  m1 Þ

(18)

uD* 1 ¼

1 þ 3cm 4

(25)

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

mD* 1 ¼

1  cm 2

(26)

and in the second period, the optimal wholesale price of the manufacturer, denoted as uD* 2 , the optimal profit of the retailer, denoted as mD* 2 , the optimal transfer price paid to the third party, denoted as bD* , and the optimal amount of remanufactured products, denoted as qD* 2r , are given by




uD* 2 ¼

1 þ 3cm  4

mD* 2 ¼

1  cm 2

bD* ¼

qD* 2r ¼

dðh1 þ 2h2 Þ

 d 2 ð1 þ cm Þ  ðA þ cr Þ

8h1 h2 þ 2ðh1 þ 2h2 Þdð2  dÞ

(27)

(28)


 2h1 h2 2d ð1 þ cm Þ  ðA þ cr Þ 4h1 h2 þ ðh1 þ 2h2 Þdð2  dÞ

þA

(29)


 ðh1 þ 2h2 Þ 2d ð1 þ cm Þ  ðA þ cr Þ (30)

4h1 h2 þ ðh1 þ 2h2 Þdð2  dÞ

Hence, the collection rates of the third party and the retailer can be calculated by

tD* T ¼

2dð1 þ cm Þ  4ðA þ cr Þ h1
$ h1 þ 2h2 4h1 h2 ð1  cm Þ h þ2h þ dð2  dÞ 1

tD* R

(31)

2

2dð1 þ cm Þ  4ðA þ cr Þ 2h2
$ ¼ h1 þ 2h2 4h1 h2 ð1  cm Þ h þ2h þ dð2  dÞ 1

(32)

2

Then the total collection rate of the supply chain is

tD* ¼

2dð1 þ cm Þ  4ðA þ cr Þ
 1 h2 ð1  cm Þ h4hþ2 ð2 Þ  þ d d h 1

pD* T ¼

(36)

Corollary 2. The ratio of collection efforts the retailer and third party taking in the dual recycling channel can be represented as 2h2/ h1 þ 2h2 and h1/h1 þ 2h2 respectively, which indicates that there is a logical choice for the remanufacturer to minimize the collection cost depended on the parameters h1 and h2.

2 d 2 ð1 þ cm Þ  ðA þ cr Þ

(34)

½4h1 h2 þ ðh1 þ 2h2 Þdð2  dÞ2

Substituting Eq. (25), Eq. (26) and Eq. (30) to pD M yields

pD* M ¼

ð1  cm Þ2 16 " þ




1  cm  4

dðh1 þ 2h2 Þ

d

2 ð1

 þ cm Þ  ðA þ cr Þ #2

4h1 h2 þ ðh1 þ 2h2 Þdð2  dÞ

Substituting Eq. (27) ~ Eq. (30) to pD R yields

pD* R ¼

ð1  cm Þ2 þ 4


2 ðh1 þ 2h2 Þ 2d ð1 þ cm Þ  ðA þ cr Þ 8h1 h2 þ 2ðh1 þ 2h2 Þdð2  dÞ

Corollary 1. The retailer could gain more profit in the ROCLSC model with dual recycling channel, when compared with the model with only the retailer collecting the used products. And the total collection rate in the dual channel is larger than that in the single one, which indicates that the dual recycling channel generally has better performance for the remanufacturer (retailer) in the retailer oriented CLSC.

(35)

2




the same as that in the first period of the ROCLSC with retailer D* collection. In addition, uD* 2 is smaller than u1 . As the retailer takes part in remanufacturing activities in the second period, the manufacturer has to lower down the wholesale price to guarantee the sale of the new products. In addition, we can find that the optimal transfer price bD* is monotonic increasing with the increase of the coefficients h1, h2 and the parameter d, and the optimal amount of remanufactured products produced by the retailer qD* 2r is monotonic decreasing with the increase of the coefficient h1 and h2, and is monotonic increasing with the increase with the parameter d. Because the coefficients h1 and h2 characterize the difficulty in collecting the used products, and the parameter d characterizes the relative WTP of a remanufactured product to a brand new one, the retailer should set a high transfer price to motivate the third party to collect the used products if h1, h2 and d are large. The analysis of the D* D* optimal profits pD* T , pM and pR is omitted herein, as we will conduct a performance analysis in the next section. Moreover, from this proposition, we can provide management insight to the practitioners that the retailer can gain more product returns and profits with the aid of scheduling plan for transportation in implementation of collaborative logistic network, and the retailer oriented mode can guarantee more product returns. Both Proposition 2 and Proposition 3 include the necessary condition 4h1h2/h1þ2h2 > 2d(1þcm)4(Aþcr)/1cmd(2d) to hold. Following the discussion in Section 3.1, as the condition 4h1h2/ h1þ2h2 > 2d(1þcm)4(Aþcr)/1cmd(2d) is quite easy to be satisfied in the field of construction machinery (the reverse logistics cost coefficients h1 and h2 should be large enough). Consequently, the physical constraint 0 < tD* < 1 holds. Proof. See Appendix B.

Proof. See Appendix C. This corollary indicates that it is lucrative for the remanufacturer (retailer) to adopt a dual recycling channel in the ROCLSC, and this conclusion differs from the work of Huang et al. (2013). In the work of Huang et al. (2013), they investigated a MOCLSC, assumed that the collection cost was characterized by a function of the collection rate, and the retailer and the third party compete in collecting the used products in the same region. However, in the case we investigate, the retailer and the third party collect the used products in different regions. Moreover, the collection cost structure for collecting construction machinery exhibits diseconomies of scale in volume, this collection cost structure indicates that each additional used product is more and more difficult to acquire. Hence, adding the third party to collect the returns brings benefit to the remanufacturer. In addition, we further find that when the collection cost is concave in number of units collected, the single sourcing is the best (see Appendix D).

(33)

Substituting Eq. (24) and Eq. (29) to pD T yields

h21 h2

1399

From Proposition 3, we can draw the similar conclusion with that from Proposition 1. The wholesale price set by the manufacturer in the first period of the ROCLSC with dual recycling channel is

This corollary confirms that there is an optimum allocation of the collection efforts to the retailer and the third party according to the reverse logistics cost coefficients of them.

1400

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

The management insight of the above corollaries can be summarized as follows. For the retailer, when the collection cost is convex in number of units collected, it is lucrative to assign himself and the third party both to collect the used products in different region, and when collection cost is concave in number of units collected, the single sourcing is the best. Consequently, in the field of construction machinery remanufacturing, the retailer oriented mode can guarantee more product returns and bring benefit to the environmental sustainability. Moreover, the retailer and the third party should strengthen cooperation with each other, such as building the reverse logistics network together, sharing the information about the geographical location of the used products, and collaborative transportation. 4. Results and discussion In this section, a numerical study is conducted to explore the optimal strategies of the remanufacturer on the retailer collection and third party collection, and analyse the profits within the ROCLSC with dual recycling channel for construction machinery remanufacturing. 4.1. Optimal collection efforts allocation on retailer collection and the third party collection From Section 3, it is obvious that the optimal ratio of collection efforts allocated to the retailer and third party in the dual recycling channel can be represented as 2h2/h1 þ 2h2 and h1/h1 þ 2h2 respectively, and the profits of the supply chain members decrease monotonically with the increase of the collection efforts scalar parameter h1 and h2. Larger parameters h1 and h2 broadly imply that more cost (the transportation cost, used products information gathering cost, reverse channel building cost and so on) is needed to collect the returns. The collection efforts taken by the retailer and third party depend on the relationship between the collection efforts scalar parameters h1 and h2. To simplify the problem, we assume that the relationship between the collection efforts scalar parameters h1 and h2 can be formulated as h1 ¼ ah2. Herein, the coefficient a refers to the relative difficulty between the retailer collection and the third party collection, and a varies according to the circumstance for the used products collection, whereby Fig. 3 is obtained through numerical simulations in Matlab. As shown in Fig. 3, the remanufacturer is supposed to make the

Fig. 3. The ratio of collection efforts taken in dual reverse channels.

third party take more efforts on used products collection as the coefficient a increases, since a larger a indicates that it is much more difficult for the retailer to collect the returns compared with the third party. Especially, when h1 ¼ 2h2, the retailer and the third party may collect the same amount of used products. In fact, the case we focus on is such a unique one that the retailer is in charge of the remanufacturing in the ROCLSC, and the reverse channel is extended to be a dual one. For the decision-maker, the mode that the retailer dominates the collection and remanufacturing would make full use of the forward distribution channel and provide better understanding of the customers’ requirements. Moreover, the retailer could pay more attention to the remanufacturing business, lower the product recycling management cost, and transfer the risk caused by the uncertainty in the market through the third party collection. Therefore, the retailer should properly allocate the collection efforts to the retailer and the third party according to their reverse logistics cost coefficients in the ROCLSC. 4.2. Performance analysis for ROCLSC with dual recycling channel In this section, we aim to investigate the effects of the parameters h1, h2, and the relative WTP d of a remanufactured product to a brand new one of the public on the performance of the supply chain members. 4.2.1. Effect of reverse logistics cost coefficients on supply chain performance Herein, we will investigate the effects of reverse logistics cost coefficients on supply chain performance under the following settings: Cm ¼ 0.2,d¼0.8, C r¼ 0.1, A¼0.05. In this scenario, the remanufacturing cost is medium, the recycling price is low, and the customer has a relative high WTP for the remanufactured products. As the retailer and the third party collect the used products from different regions, the reverse logistics cost coefficients h1 and h2 vary according to the circumstance for collecting the used products, and these two parameters may be positive correlation or negative correlation. To show the effect of reverse logistics cost coefficients on supply chain performance in different circumstance, we make contour plots of the profits and collection rates as functions of h1 and h2, and obtain Fig. 4 and Fig. 5 in the Matlab. As we can see in Fig. 4, the retailer faces a particularly low collection rate when the expected reverse logistics cost coefficients h1 is relatively large, while the cost coefficients h2 has litter influence on retailer's collection rate (for example, when h1 ¼ 4, and h2 varies from 1 to 15, the retailer's collection rate is still around 0.18). In addition, for the third party, his collection rate is particularly low when the expected reverse logistics cost coefficients h2 is relatively large, while the cost coefficients h1 has litter influence on retailer's collection rate. Moreover, the remanufacturer can obtain a high total collection when h1 or h2 is rather small. Because, in this condition, the decision-maker can make more investment in the supply chain agent which is easier to conduct the collection activities. As depicted by Fig. 5, with the increase of both the scalar parameters h1 and h2, the profits of the retailer is decreasing (from the maximum 0.18 to minimum 0.16, about 11.1% decrease). However, the profit of the manufacturer increases in a certain degree (from the minimum 0.072 to maximum 0.0798, about 8.1% increase). Because larger values of the scalar parameters generally indicate higher cost for the remanufacturing activities, remanufacturing is no longer a very lucrative market for the retailer, while the production marketing of the new products is becoming his core business. As the remanufacturing activities in the second period deprive the manufacturer of a certain profit, arising difficulties in used products collection activities result in more market for the new

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

1401

Fig. 4. Effect of reverse logistics cost coefficients on the collection rates.

products selling, namely profitable growth for the manufacturer. And for the third party, when the scalar parameter h1 decreases and the scalar parameter h2 increases, the profit drops sharply (from the maximum 0.004 to minimum 0.0005, dropping 87.5%). Based on the above analysis, we note that the remanufacturer can generate high collection rate of used products when it is easy for the retailer or the third party to invest in used product collection activities. But the increasing sales volume of the remanufactured products grabs the market share in a certain degree, and leads to profit lose for the manufacturer. In addition, the third party can gain more profit if it is easy for the third party to invest in used product collection activities or it is hard for the retailer to invest in used product collection activities. Consequently, the largest system profits would be implemented by some mechanisms, such as sharing the collecting responsibilities and the profits of remanufactured products in the ROCLSC. 4.2.2. Effect of the public perception of the remanufactured products compared with the brand new one on supply chain performance To illustrate the influence of the public perception of the

remanufactured products compared with the brand new one on supply chain performance, we give the following numerical assumption: Cm ¼ 0.2, h1 ¼ 4, h2 ¼ 3, C r¼ 0.1, A ¼ 0.05. In this scenario, the remanufacturing cost is medium, the recycling price is low, and the difficulty for the retailer and the third party to collect the used products is medium. Fig. 6 and Fig. 7 are obtained from numerical simulation in Matlab. As shown in Fig. 6, both the retailer and the third party would have high used products return rates when the public perception of the remanufactured products goes up. Moreover, it can be observed from Fig. 7 that the profits of the third party and the retailer will increase with the increase of the public perception d (if d varies from 0.5 to 1, the retailer's profit increases from 0.162 to 0.1778, growing about 9.8%, and the third party's profit increases from 0.00035 to 0.0029, about 728.6% growth), while the profit of the manufacturer is decreasing accordingly. Furthermore, the parameter d has a more widely influence on the third party than the retailer. Indeed, high public perception of the remanufactured products brings both the retailer and third party high profit margin in remanufacturing business. Hence the decision-maker has an incentive to invest in reverse supply chain network, and both the

1402

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

Fig. 5. Effect of reverse logistics cost coefficients on the profits of the supply chain members.

Fig. 6. Effect of the public perception d on the collection efforts of the supply chain members.

Fig. 7. Effect of the public perception d on the profits of the supply chain members.

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

retailer and the third party are willing to collect more used products for them. But for the manufacturer, the growth in sales volume of the remanufactured products cannibalizes the profit of the new products, which implies that more cooperation with the retailer is needed to protect profit under this circumstance, as it is illustrated in Fig. 7. Hence, to enhance the profit, the retailer should strengthen cooperation with the OEM in improving the design of the new products and the public perception of the remanufactured ones. This can be realized through advertisements, providing on site customer training, trading in allowance, feedback regarding the market and customer demand, and revenue sharing of the remanufactured products. As for the governments, to promote the development of the dual recycling channel for used construction machinery, what they can do is to adopt some feasible approaches such as guidelines on quality assurance and quality information provision, the tax subsidies, giving publicity to the use of remanufactured construction equipment and improving general public environmental awareness.

1403

Acknowledgements This research is supported by the National High Technology Research and Development Program “Reuse and Remanufacturing Technologies of Retired Construction Machinery: Study and Applications” of the P.R. China under Grant No. 2013AA040206, and the Fundamental Research Funds for the Central Universities, HUST under Grant No. CXY12Q025. Appendix A. The proofs of Proposition 1 First period analysis By Eq. (1), the first and second order derivatives of pSM1 to u1 can be calculated by

vpSM1

¼ 1  2u1  m1 þ cm ;

vu1

v2 pSM1 vu21

¼ 2:

Then, the optimal response function of the manufacturer is

1  m1 þ cm : 2

5. Conclusion

b S1 ¼ u

In this paper, we develop insights for remanufacturers who plan to conduct remanufacturing and establish a ROCLSC with both the retailer and the third party involved in collecting used products from different regions in the construction machinery field. Motivated by an actual case in China, we consider a scenario where the retailer is the market leader engaged in the remanufacturing activities, and the remanufactured products are valued less than the new ones in the market. According to the above analysis and discussion, conclusions can be summarized as:

By Eq. (2), the first and second order derivatives of pSR1 to m1 can be calculated by

(1) For the remanufacturer (retailer), when the collection cost is convex in number of units collected, it is lucrative to assign himself and the third party both to collect the used products in different region, and when collection cost is concave in number of units collected, the remanufacturer should choose the most suitable single recycling channel according to the reverse logistics cost coefficients of the retailer and the third party. (2) In the ROCLSC with dual recycling channel for construction machinery remanufacturing, it is very important for the retailer to allocate the collection efforts to the retailer and the third party according to the environment in different regions for collecting the used products. To gain more profits, the retailer should cooperate with the third party in the collection activities and help the OEM with the product design and marketing. (3) For the firms engaged in construction machinery remanufacturing, to gain more product returns and profits, the decision-maker can adopt the retailer oriented mode to meet the need of the market, assign the collection activities to the dual recycling channel, reduce the reverse logistics cost coefficients and improve the public perception of the remanufactured products. However, our research is restricted and there are two potential future extensions to improve our model. One would be to analyse the competition among multiple retailers in distributing and collecting multiple brands of construction machinery. The other potential direction is to consider the fuzziness and uncertainty associated with the market demand, and take the uncertainty in collecting and remanufacturing cost of the used products into account.

vpSR1 vm1

2 S

¼

1  2m1  cm v pR1 ; ¼ 1: 2 vm21 vpSR

1cm By setting vm11 to zero, we can obtain that mS* 1 ¼ 2 . S 1þ3c S* m b 1 , we can calculate that u1 ¼ 4 . Substituting it into u

Second period analysis By Eq. (3), the first and second order derivatives of pSM2 to u2 can be calculated by

vpSM2

¼ 1  2u2  m2 þ cm  dq2r ;

vu2

v2 pSM2 vu22

¼ 2:

Then, the optimal response function of the manufacturer is

b S2 ¼ u

1  m2 þ cm  dq2r : 2

By Eq. (2), the first and second order derivatives of pSR2 to m2 and q2r can be calculated by

vpSR2 vm2 vpSR2 vq2r

2 S

¼

¼

1  2m1  cm v pR2 ; ¼ 1; 2 vm22

d½1 þ cm þ 2ðd  2Þq2r  2

 ðA þ cr Þ  2h1 q2r ;

v2 pSR2 vq22r

¼ dð2  dÞ  2h1 : The resulting Hessian matrix of pSR2 is given by




HpS ¼ R2

1 0

0 dð2  dÞ  2h1

It is obvious that HpS

R2

 :

is negative definite, namely, HpS

concave with respect to (m2,q2r). By setting

vpSR 2 vm2

and

vpSR 2 vq2r

R2

is

to zero

simultaneously, Eq. (11) and Eq. (12) can be obtained. Substituting b S1 and u b S2 , Eq. (8) and Eq. (10) can be obtained. As them into u

1404

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405

1cm q1 ¼ 1m1u1, we can calculate that qS* 1 ¼ 4 . Substituting Eq.

(8) ~ Eq. (12) to pSR yields Eq. (14), and substituting Eq. (8) ~ Eq. (12) to pSM yields Eq. (15). We notice that the logistic limitation that the amount of remanufactured products in the second period should not exceed the new products sold in the first period should be satisfied. By S* setting qS* 2r < q1 , we can calculate that the condition h1 > d(1þcm) 2(Aþcr)/1cmd(2d)/2 should hold. If this condition is not satisfied, then the amount of used products remanufactured in the second period is equal to the amount of new products sold in the first period. We give tacit consent to satisfaction of the above logistic limitation to avoid the unnecessary discussion. Then Proposition 1 is proved.

vpD R2 vm2

vpD R2 vb vpD R2 vq2r

By Eq. (17), the first and second order derivatives of pD M1 to u1 can be calculated by

¼ 1  2u1  m1 þ cm ;

v2 pD M1 vu21

¼ 2:

Then, the optimal response function of the manufacturer is

1  m1 þ cm : ucD1 ¼ 2

vpDR

1cm By setting vm11 to zero, we can obtain that mD* 1 ¼ 2 . D 1þ3c D* m b 1 , we can calculate that u1 ¼ 4 . Substituting it into u

Second period analysis By Eq. (16), the first and second order derivatives of pD T to qT can be calculated by. vpDT v2 pDT vqT ¼ b  A  2h2 qT and vq2T ¼ 2h2 < 0, which implies the concavity of. pD T: vpD Setting vqTT to zero, then the optimal response function of the third party is D ¼ b  A: qc T 2h2

  2 D h1 b  A v pR2 1 h q2r  ; ¼   12 2h2 h2 h2 2h2 vb2

d½1 þ cm þ 2ðd  2Þq2r  2

h1 ðb  AÞ ; h2

 ðA þ cr Þ  2h1 q2r

v2 pD R2 vq22r

2

¼ 1  2u2  m2 þ cm  dq2r ;

1

6 6 0 6 HpD ¼ 6 R2 6 4 0

0 

1

h2



3

0

h1 2h22

h1 h2

h1 h2

dð2  dÞ  2h1

7 7 7 7: 7 5

The principal minor sequences of the discrimination matrix are             h 2h HpD  ¼ h12 þ 2h12 > 0, HpD  ¼  h21  d HpD  ¼ 1 < 0, R2

1

2

R2

2

3

ð2  dÞ 2h22hþ2h1 < 0. Which implies that the pD R2 is a concave function to 2

(m2, b, q2r). By setting

vpDR vpDR vm2 , vb

and

vpDR vq2r

to zero simultaneously, Eq.

D (30) to pD M yields Eq. (35), and substituting Eq. (27) ~ Eq. (30) to pR yields Eq. (36). Following the discussion in Appendix A, the physical constraint 0 < tD* < 1 holds, as the condition 4h1h2/h1þ2h2 > 2d(1þcm) 4(Aþcr)/1cmd(2d) is quite easy to be satisfied in the field of construction machinery. Then Proposition 2 and Proposition 3 are proved.

Appendix C. The proof of Corollary 1

By Eq. (19), the first and second order derivatives of pD M2 to u2 can be calculated by

vu2

h2

þ

cD and qc D, (28) ~ Eq. (30) can be obtained. Substituting them into u T 2 Eq. (24) and Eq. (25) can be obtained. Then substituting Eq. (24) and Eq. (29) to pD T yields Eq. (34), substituting Eq. (25), Eq. (26) and Eq.

2 D

1  2m1  cm v pR1 ; ¼ ¼ 1: vm1 2 vm21

vpD M2

¼

bA

¼ dð2  dÞ  2h1 :

R2

By Eq. (18), the first and second order derivatives of pD R1 to m1 can be calculated by

vpD R1

¼

The resulting Hessian matrix of pD R2 is given by

First period analysis

vu1

1  2m1  cm v pR2 ; ¼ 1: 2 vm22

þ

Appendix B. The proofs of Proposition 2, and 3

vpD M1

2 D

¼

v2 pD M2 vu22

Following the discussion in Appendix A and Appendix B, we tacitly approve that the condition m Þ4ðAþcr Þ m Þ4ðAþcr Þ > 2dð1þc > 0 is satisfied. 1  cm > 2dð1þc 4h1 h2 2h þdð2dÞ

h1 þ2h2 þdð2dÞ

¼ 2:

Setting the first derivatives to zero, we can obtain the optimal response function of the manufacturer as follow:

1  m2 þ cm  dq2r : ucD2 ¼ 2 For constructing the Hessian matrix of pD R2 , we carry out the following calculations to acquire the first and second order derivatives of pD R2 to m2, b and q2r.

1

By Eq. (14) and Eq. (36),

pDR  pSR ¼


2 ðh1 þ 2h2 Þ 2d ð1 þ cm Þ  ðA þ cr Þ 8h1 h2 þ 2ðh1 þ 2h2 Þdð2  dÞ
2 d 2 ð1 þ cm Þ  ðA þ cr Þ :  4h1 þ 2dð2  dÞ

P. Yi et al. / Journal of Cleaner Production 137 (2016) 1393e1405


Let A ¼

collection activities (h1 < h2) or making the third party alone take the collection activities (h1 > h2).

2

ðh1 þ 2h2 Þ 2d ð1 þ cm Þ  ðA þ cr Þ

8h1 h2 þ 2ðh1 þ 2h2 Þdð2  dÞ
2 d ð1 þ c Þ  ðA þ c Þ m r 2 ¼ : 4h1 þ 2dð2  dÞ

and B

2

S thenpD R > pR :

By Eq. (13) and Eq. (33). 2dð1þcm Þ4ðAþcr Þ
 ð1cm Þ

tD* ¼ tS*

4h1 h2 þdð2dÞ h1 þ2h2

2dð1þcm Þ4ðAþcr Þ ð1cm Þ½2h1 þdð2dÞ

¼

2h1 þdð2dÞ

4h1 h2 h1 þ2h2 þdð2dÞ

In summary, we can conclude that if the collection cost is concave in number of units collected, the single sourcing is the best. References

A 4h þ 2dð2  dÞ 8h1 h2 ¼ 8h h1 ; it is obvious that 4h1 > ; 1 2 B h 1 þ 2h2 h þ2h þ 2dð2  dÞ 1

1405

> 1; then tD* > tS* : So Corol-

lary 1 is proved.

Appendix D. Different collection cost structures on the management insights In this paper, the collection cost is formulated as C(q) ¼ Aqþhqk. If k > 1, the collection cost exhibits diseconomies of scale, and if 0 < k < 1, the collection cost exhibits economies of scale (Atasu et al., 2013). As the end-of-life construction machinery is bulky and hard to be transported, we assume that the collection cost exhibits diseconomies of scale in volume. Subsequently, we set k ¼ 2 to strike a balance between the model realism and problem tractability. In addition, we conclude in the Corollary 1 that it is best to recover used products using the dual reverse channel. In this section, we will explore the management insight if the collection cost is concave in number of used products. Firstly, the profit function of the third party can be written as pDT ¼ ðb  AÞqT  h2 qkT ð0 < k < 1Þ. Then the first and second order derivatives of pD T to qT can be calculated by

vpD v2 pD T T ¼ b  A  kh2 qk1 ¼ h2 kðk  1Þqk2 > 0: T and T vqT vq2T vpD

Hence, the stationary point calculated by vqTT ¼ 0 is not a maximizer of the function pD T , and there are two possible solutions for the third party. One is collecting nothing, the other one is collecting as many as he can. (1) If the third party chooses to collect nothing, the CLSC with dual recycling channel is simplified to the one with retailer collection. (2) If the third party chooses to collect as many as he can, the retailer has two choices: making the retailer alone take the

Agrawal, S., Singh, R.K., Murtaza, Q., 2015. A literature review and perspectives in reverse logistics. Resour. Conser. Recycl. 97, 76e92. Ahn, H., 2009. On the profit gains of competing reverse channels for remanufacturing of refillable containers. J. Serv. Sci. 1 (2), 147e189. Atasu, A., Sarvary, M., Van Wassenhove, L.N., 2008. Remanufacturing as a marketing strategy. Manag. Sci. 54 (10), 1731e1746. Atasu, A., Beril Toktay, L., Van Wassenhove, L.N., 2013. How collection cost structure drives a manufacturer's reverse channel choice. Prod. Oper. Manag. 22 (5), 1089e1102. Choi, T., Li, Y., Xu, L., et al., 2013. Channel leadership, performance and coordination in closed loop supply chains. Int. J. Prod. Econ. 146 (1), 371e380. EL korchi, A., Millet, D., 2011. Designing a sustainable reverse logistics channel: the 18 generic structures framework. J. Clean. Prod. 19 (6), 588e597. Ferguson, M.E., Toktay, L.B., 2006. The effect of competition on recovery strategies. Prod. Oper. Manag. 15 (3), 351e368. Guide Jr., V.D.R., Li, J., 2010. The potential for cannibalization of new products sales by remanufactured products. Decis. Sci. 41 (3), 547e572. Guide Jr., V.D.R., Van Wassenhove, L.N., 2006. Closed-loop supply chains: an introduction to the feature issue (Part 1). Prod. Oper. Manag. 15 (3), 345e350. Gutowski, T.G., Murphy, C.F., Allen, D.T., et al., 2001. WTEC Panel Report on: Environmentally Benign Manufacturing (EBM). International Technology Research Institute, World Technology (WTEC) Division, Baltimore, Maryland. Hauser, W., Lund, R., 2008. Remanufacturing: Operating Practices and Strategies. Boston University, Boston, MA. Huang, M., Song, M., Lee, L.H., et al., 2013. Analysis for strategy of closed-loop supply chain with dual recycling channel. Int. J. Prod. Econ. 144 (2), 510e520. Hong, X., Wang, Z., Wang, D., et al., 2013. Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection. Int. J. Adv. Manuf. Technol. 68 (5e8), 1851e1865. Kerr, W., Ryan, C., 2001. Eco-efficiency gains from remanufacturing: a case study of photocopier remanufacturing at Fuji Xerox Australia. J. Clean. Prod. 9 (1), 75e81. Karakayali, I., Emir-Farinas, H., Akcali, E., 2007. An analysis of decentralized collection and processing of end-of-life products. J. Oper. Manag. 25 (6), 1161e1183. € Ozkır, V., Bas¸lıgıl, H., 2012. Modelling product-recovery processes in closed-loop supply-chain network design. Int. J. Prod. Res. 50 (8), 2218e2233. Savaskan, R.C., Bhattacharya, S., Van Wassenhove, L.N., 2004. Closed-loop supply chain models with product remanufacturing. Manag. Sci. 50 (2), 239e252. Savaskan, R.C., Van Wassenhove, L.N., 2006. Reverse channel design: the case of competing retailers. Manag. Sci. 52 (1), 1e14. Shi, J., Zhang, G., Sha, J., 2011. Optimal production and pricing policy for a closed loop system. Resour. Conserv. Recycl. 55 (6), 639e647. Souza, G.C., 2009. Remanufacturing in closed-loop supply chains. Prod. Inventory Manag. J. 45 (1), 56e65. Teunter, R.H., Flapper, S.D.P., 2011. Optimal core acquisition and remanufacturing policies under uncertain core quality fractions. Eur. J. Operational Res. 210 (2), 241e248. The Ministry of Industry and Information Technology of the People’s Republic of China, 2014. The announcement of the Ministry of Industry and Information Technology.http://www.miit.gov.cn/n11293472/n11293832/n11293907/ n11368223/16100075.html. Wang, L.F., Wang, Y.C., 2010. Stackelberg real-leader in an insider trading model. Stud. Econ. Finance 27 (1), 30e46. Xiang, Yonghua, Xu, Binshi, Lv, Yaohui, Xia, Dan, Liu, Cunlong, 2008. Role of resource recovery of waste machinery and electronic products in sustainable development. Int. Conf. Bioinforma. Biomed. Eng. 4333e4335.