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A Closed-Loop Supply Chain with Competitive Dual Collection Channel under Asymmetric Information and Reward–Penalty Mechanism Wenbin Wang 1 , Shuya Zhou 1,2 , Meng Zhang 1 , Hao Sun 3, * and Lingyun He 1,2 1

2 3

*

School of Management, China University of Mining and Technology, Xuzhou 221116, China; [email protected] (W.W.); [email protected] (S.Z.); [email protected] (M.Z.); [email protected] (L.H.) Jangsu Province’s Energy Economics and Management Base, Xuzhou 221116, China School of Business, Qingdao University, Qingdao 266071, China Correspondence: [email protected]; Tel.: +86-0532-85952399

Received: 27 May 2018; Accepted: 19 June 2018; Published: 22 June 2018







Abstract: We investigate a closed-loop supply chain (CLSC) where the retailer and the third-party recycler compete against each other to collect waste electrical and electronic equipment (WEEE) given that collection effort is their private information. Using the principle-agent theory, we develop a CLSC model with dual collection channel without the government’s reward–penalty mechanism (RPM). An information screening contract is designed for the manufacturer to attain real information on collection effort levels; meanwhile, the optimal decision-making results of other decision variables are derived. Next, we take RPM into account to further examine the efficacy of the government’s guidance mechanism in improving collection rate and profits of CLSC members. Our results indicate that (i) the collection competition reduces the total collection quantity and the expected profits of all the CLSC members without RPM; (ii) all CLSC members’ expected profits are improved if both two collection agents select a high collection effort level without and with RPM; (iii) RPM increases buyback price, collection price, collection quantity, and franchise fee but decreases wholesale price and retail price; with the reward–penalty intensity increasing, the manufacturer’s expected profit first decreases and then increases, while the expected profits of H-type retailer and H-type third-party recycler continue to increase. We find that RPM may ultimately stimulate the collection agents to collect more WEEEs, while the intense collection competition reduces the profits of CLSC members. Keywords: closed-loop supply chain; information screening contract; dual collection channel; collection competition; reward–penalty mechanism; asymmetric information

1. Introduction Due to the development of the economy and technology, there are more and more demands for various electronic products that bring people a more convenient life but also create a huge amount of electronic waste. According to a report by the United Nations University, electronic products such as mobile phones and computers have produced 12.3 million tons of e-waste during 2010 to 2015 in Asia. In this period, the quantity of e-waste produced by China has more than doubled to 6.7 million tons. Wu et al. [1] showed that the value of recycling has reached about $286 billion, which accounts for 8.89% of total sales in the United States, compared to only $100 billion in 2006. These data indicate that such a huge amount of e-waste can be a tremendous resource if recycled and reused properly. If it is adequately utilized, resource waste and environment pollution will be reduced a lot. Previous studies have proposed various CLSC models to find out how to increase the amount of returned products, and then improve the environmental performance and profits of CLSC members in Sustainability 2018, 10, 2131; doi:10.3390/su10072131

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different scenarios. Savaskan et al. [2] indicated the importance of remanufacturing used products and developed a model in which the manufacturer as the Stackelberg leader has three options for collecting WEEE. They also designed some simple coordination mechanisms so that the retailer’s collection effort and the CLSC profit are achieved at the same level as in a centrally coordinated system. Giovanni et al. [3] developed a dynamic CLSC model consisting of one manufacturer and one retailer, with both players participating in a product recovery program to increase the collection rate of used products. Hammond and Beullens [4] developed a CLSC network model in which the manufacturers and consumer markets engage in a Cournot game with complete information. They suggested that legislation on the minimum collection quantity of new products can stimulate reverse chain activities in CLSC. Savaskan and Wassenhove [5] investigated the interaction between decisions in the forward channel and the reverse channel, and the influence of retail competition on CLSC profits. They indicated that channel profits are affected by the scale of return on collection efforts in a direct collection system, but in an indirect reverse channel, CLSC profits are affected by the competition intensity between the retailers. Hong and Yeh [6] showed that the third-party collection channel is strictly inferior to the retailer collection channel when it forms a non-profit organization for collection. He et al. [7] compared the centralized (integrated) collection channel CLSC with the decentralized collection channel CLSC. The conclusion indicates that the optimal collection price, the collection quantity, and the quantity of remanufactured products under a decentralized collection channel are always lower than those under a centralized collection channel due to the double marginalization effect. Atasu and Çetinkaya [8] indicated that the collection rate, return timing, and reusability rate should correspond to the active market supply and demand in order to obtain the highest profits from remanufactured products. Also, they found that the fastest reverse supply chain may not be the most efficient one. Gaur et al. [9] developed an integrated optimization model for addressing the CLSC configuration. Esenduran et al. [10] investigated a stylized model in which an original equipment manufacturer (OEM) competes with an independent remanufacturer in order to find appropriate collection and reuse targets for maximizing OEM profit. All of the above papers are based on symmetrical information. However, in many scenarios, some information is only available to one supply chain member, and the other members have to make decisions based on limited information. Voigt and Inderfurth [11] indicated that the efficiency losses caused by the strategic use of private information cannot be overcome if all agents refuse to share their information. An appropriate contract is vital because supply chain members prefer to pursuit their own profits without considering the total supply chain profit under asymmetric information. In a forward supply chain, some contracts have been designed to reduce negative effects as follows. Biswas et al. [12] investigated how the asymmetry information, market-share, and supply chain structures affect the contract choice of the supplier. They found that the cost information of any buyers is beneficial for the supplier to increase her own profit. Liu et al. [13] examined how to design contracts for two competitive heterogeneous suppliers dealing with one common retailer under asymmetric information of external demand volumes for the retailer. Cao et al. [14] designed an optimal wholesale contract in a dual-channel supply chain under asymmetric information. Çakanyýldýrým et al. [15] indicated that asymmetric information alone does not necessarily result in channel inefficiency. Moreover, they designed an optimal contract to coordinate the supply chain. Similar to the forward supply chain, asymmetric information has a negative effect on CLSC. Zhang et al. [16] investigated the pricing and collection decision problem of a CLSC when the real information on collection efforts is only available to the retailer. They indicated that the asymmetric information may mislead the manufacturer into increasing the wholesale price, which can result in a higher sale price and a lower collection rate. Then they designed optimal contracts for the manufacturer. Giovanni [17] designed two incentive games by a profit-sharing contract to find out how the sharing information should be determined to benefit all the players. Wei et al. [18] investigated optimal strategies in different game scenarios under symmetric and asymmetric information structures. They found that the manufacturer’s asymmetric information on manufacturing and remanufacturing costs may increase the retail price, while the

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private information of the retailer on the collection quantity and the size of the recycling market may increase the wholesale price. Zhang et al. [19] indicated that information sharing can be efficiently implemented through a bargaining mechanism when the collection efficiency of the manufacturer is moderate, but there must be no information sharing when the efficiency is low. Wang et al. [20] is the first to investigate the effect of RPM on the equilibrium decisions and profitability of the CLSC members with information asymmetry. They found that the RPM can reduce the negative effect of asymmetric information and improve the collection rate and profits of the manufacturers and retailers. In the prior studies mentioned above, collection was usually done by only the retailer, the recycler, or the manufacturer. Differing from prior studies, one of the key points of this research is the dual collection channel. Some research on dual collection channels has been done before. Huang et al. [21] studied optimal decisions of a dual collection channel CLSC with a retailer and a third-party recycler competing to collect WEEEs. Hong et al. [22] showed that, ceteris paribus, the most effective reverse channel structure for the manufacturer is a dual collection channel consisting of one manufacturer and one retailer. Feng et al. [23] investigated a two-echelon reverse supply chain with a dual collection channel where the retailer acts as a Stackelberg game leader and the recycler as a follower with consideration of consumer behavior. The results showed that the dual collection channel is always superior to its single channel counterparts. Huang and Wang [24] indicated that in a CLSC with cost disruptions, the manufacturer prefers the dual collection channel rather than the single collection channel only if the negative disruption of remanufacturing cost comes to a large size. Zhao et al. [25] compared three dual collection channels with three single collection channels for a CLSC. They found that the manufacturer’s optimal choice is to ensure that the retailer engages in collection irrespective of adopting single or dual collection channels. Additionally, the government has been playing an important role in CLSC operations (Xie and Ma. [26]). For example, the Japanese government releases various data to encourage CLSC activities [27]. Ma et al. [28] studied how a consumption-subsidy program affects dual channel CLSC. Heydari et al. [29] demonstrated that government-sponsored incentive mechanisms for manufacturers are superior to those for retailers. Rahman and Subramanian [30] found that government legislation is one of the main driving forces to stimulate computer recycling operations. He et al. [31] indicated that the government’s environmental policies increase the recycling proportion, but strengthen the reverse supply chain bullwhip effect. Wang et al. [32] found that the government’s RPM can effectively improve the collection rate and reduce the price of a new product in a single collection channel CLSC. The existing CLSC literature lays a solid foundation for this paper. However, no previous papers examined RPM in a CLSC except for those by Wang et al. [20] and Wang et al. [32]. Wang et al. [32] did not consider asymmetric information in collection. Moreover, both of them were confined to cases where only the third-party collector engages in collection; in actual operations, dual collection channels with competition are very common. For instance, ReCellular Inc., the largest mobile phone remanufacturer in the United States, collects used phones both from retailers and third-party recyclers [33,34]. Yi et al. [34] investigated a dual reverse channel in which both the retailer and the third-party collector collect the used products and assumed that the two collection agents take part in collection in different districts, so there is no competition between them. However, in this paper, we assume that the two agents engage in collection in the same district, so competition should not be overlooked. Such situations are not rare in reality. BYD Auto, China’s leading electric carmaker (backed by Warren Buffett), entrusts his authorized distributor and GEM Co., Ltd., a third-party recycling company in China, to collect electrical vehicle batteries together. The two agents often engage in battery collection in the same district, so inevitably collection competition occurs between them. Wang et al. [35] studied three alternative scenarios selected by the manufacturer in hybrid CLSCs with competitive collector agents but they did not consider asymmetric information and government policy. The contribution of this paper lies in that we investigate the efficacy of information screening contract and the RPM on a CLSC with competitive dual collection channel and asymmetric information. Specifically, it is assumed that the retailer and the third-party recycler are commissioned by the

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manufacturer to participate in the CLSC and compete with each other when they collect WEEEs. In addition, we consider that information on collection effort levels is available to the collection agents themselves but unknown to the manufacturer. In this context, we aim to answer the following questions: (1) (2) (3)

How does collection competition between the retailer and the third-party recycler affect the decisions and profits of CLSC members under information asymmetry? Can the manufacturer design a valid information screening contract to obtain the real collection effort levels of the two competitive collection agents with and without RPM? Can the RPM improve the collection rates and the profits of CLSC members with collection competition and asymmetric information?

Based on the above analysis, we design an information screening contract to reduce the negative impact of the asymmetric information. With a principal–agent theory, we propose two CLSC models with and without RPM. Numerical examples are provided to verify the efficiency of RPM and acquire more managerial insights. The rest of the paper is organized as follows. Section 2 presents the notations and assumptions. The CLSC model without the RPM is proposed and analyzed in Section 3. Section 4 builds the CLSC model with the RPM and gives the analysis results. Finally, Section 5 presents conclusions and future directions. 2. Notations and Assumptions In this paper, the collection effort levels of both the retailer and the third-party recycler can be divided into two types: high level and low level. The parameters with subscripts H and L represent high and low collection effort levels, respectively. Superscript * indicates the optimal solutions. Moreover, we will refer to the manufacturer as “he” and to the retailer/third-party recycler as “she” hereinafter. The following notations in Table 1 are used throughout the paper: Table 1. Notations. Symbol

Description

Model parameters cn

The cost of manufacturing one product with new materials.

cr

The cost of remanufacturing one product with recycling components.

∆

Unit cost savings from remanufacturing, ∆ = cn − cr .

ε

Competition intensity. It represents the degree of competition between the retailer and the third-party recycler when they collect WEEEs. ε ∈ (0, 1).

eri

Collection effort level of the retailer. i ∈ { H, L}, erH > erL .

eti

Collection effort level of the third-party recycler. i ∈ { H, L}, etH > etL .

Trj

The franchise fee that the manufacturer charges the retailer when she chooses contract Grj , j ∈ { H, L}.

Ttj

The franchise fee that the manufacturer charges the third-party recycler when she chooses contract Gtj , j ∈ { H, L}.

Qritj

Collection quantity of the retailer when she chooses contract Gri under her real collection effort level i, while the third-party recycler chooses contract Gtj under her real collection effort level j.

Qtirj

Collection quantity of the third-party recycler when she chooses contract Gti under her real collection effort level i, while the retailer chooses contract Grj under her real collection effort level j.

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Table 1. Cont. Symbol k Q0 v

Description Reward–penalty intensity decided by government. Target collection quantity set by government. Probability of the retailer or the third-party recycler adopting H collection effort level, which is available to both collection agents.

Decision variables wj

Wholesale price of the manufacturer when the retailer chooses contract Grj , j ∈ { H, L}.

pij

Retail price of the retailer with the choice of contract Grj when her real collection effort level is i, i ∈ { H, L}, j ∈ { H, L}.

rrij

Unit collection price of the retailer with the choice of contract Grj when her real collection effort level is i, i ∈ { H, L}, j ∈ { H, L}.

rtij

Unit collection price of the third-party recycler with the choice of contract Gtj when her real collection effort level is i, i ∈ { H, L}, j ∈ { H, L}.

brj

Buyback price paid by the manufacturer to the retailer for each collected WEEE with her choice of contract Grj , j ∈ { H, L}.

btj

Buyback price paid by the manufacturer to the third-party recycler for each collected WEEE with her choice of contract Gtj , j ∈ { H, L}.

Other notations Grj

Information screening contract designed for the manufacturer, which means the retailer opts for buy-back price brj , wholesale price w j and gives franchise fee Trj , j ∈ { H, L}.

Gtj

Information screening contract designed for the manufacturer, which means the third-party recycler opts for buy-back price btj , wholesale price w j and gives franchise fee Ttj , j ∈ { H, L}.

  E πmij

Expected profit of the manufacturer with the third-party recycler’s choice of contract Gti and the retailer’s choice of contract Grj , i ∈ { H, L}, j ∈ { H, L}.

  E πrij

Expected profit of the retailer with her choice of contract Grj under her real collection effort level i, i ∈ { H, L}, j ∈ { H, L}.

  E πtij

Expected profit of the third-party recycler with her choice of contract Gtj under her real collection effort level i, i ∈ { H, L}, j ∈ { H, L}.

πr0

Reserved profit of the retailer without contract.

πt0

Reserved profit of the third-party recycler without contract.

Assumptions (1) (2)

(3) (4) (5)

There is no difference between newly manufactured products and remanufactured products [2,3,5,20]. cr < cn represents that unit production cost cn is more than unit remanufacturing cost cr [2,20,21]. We also assume that the unit cost of remanufacturing used products is fixed regardless of their different quality levels, which can avoid complex calculations without changing the major conclusions of the CLSC model. It is assumed that collected WEEE materials and components take precedence over the new components in production [6,18,25]. In this model, we assume that all CLSC members are risk-neutral, without regard to risk preference or risk aversion. Their targets are to earn the maximum profits. The market demand function is D = φ − pij + θ [25,36,37], where φ is the size of potential market, pij is the retail price, and θ is a random variable that follows the uniform distribution U (0, a). We denote the probability density function as f (·) and probability distribution function of θ as F (·). So, ( 1/a, x ∈ (0, a) f (x) = . 0, else

distribution function of θ as F ( ⋅) . So,

1 a , x ∈ ( 0, a ) f ( x) =  . 0, else Sustainability 2018, 10, 2131

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(6) We assume the retailer’s collection quantity Qritj and the third-party recycler’s collection

quantity Qtirj are both collection-effort-sensitive and collection-price-sensitive. Specifically, in We assume the retailer’s collection quantity Qritj and the third-party recycler’s collection quantity this paper the linear functions of Qritj and Qtirj are employed by Qritj = eri + rrij − ε rtij and Qtirj are both collection-effort-sensitive and collection-price-sensitive. Specifically, in this paper [23,38]. That is, for either collection quantity increases as Q eti + rtijfunctions − ε rrij respectively tirj = the linear of Qritj and Qtirj are employed by Qparty, ritj = eri + rrij − εrtij and Qtirj = eti + rtij − εrrijcollection respectively [23,38]. is, for either collection quantity increases as the own the own effort level That or collection priceparty, increases, but decreases as the competitor’s collectionprice effortincreases. level or collection price increases, but decreases as the competitor’s collection collection price increases. In the following, we examine CLSC models without and with RPM, and compare the differences between the models. In the following, wetwo examine CLSC models without and with RPM, and compare the differences

(6)

between the two models. 3. CLSC Model without the RPM (Case 1) 3. CLSC Model without RPM (Case 1) of CLSC without RPM, which is comprised of a Figure 1 gives thethe general structure manufacturer, a retailer, a third-party and consumers. The issolid line and dotted line Figure 1 gives the general structure recycler, of CLSC without RPM, which comprised of the a manufacturer, represent forward flow direction the reverse flow direction, respectively. Stackelberg a retailer, the a third-party recycler, andand consumers. The solid line and the dotted As linethe represent the leader of CLSC, the manufacturer entrusts the retailer and the third-party recycler to collect WEEEs. forward flow direction and the reverse flow direction, respectively. As the Stackelberg leader of CLSC, According to assumptions, theretailer two collection agents choose hightoorcollect low collection effort levels the manufacturer entrusts the and the third-party recycler WEEEs. According to separately, denoted H-type agents or L-type retailers and or L-type third-party recyclers. The assumptions, the twoas collection choose high or lowH-type collection effort levels separately, denoted as third-party recycler collects collection price recyclers. consumers, andrecycler then transfers rtij from The H-type or L-type retailers andWEEEs H-typeatorthe L-type third-party third-party collects WEEEs the collection rtij from and then them at buyback price them atatbuyback price price to theconsumers, manufacturer. The transfers retailer acquires WEEEs at the bcollection btj back tj back to the manufacturer. The retailer acquires WEEEs at the collection price r from consumers, and then price rrij from consumers, and then resells them at buyback price brjrij back to the manufacturer. resells them at buyback price brj back to the manufacturer. The manufacturer uses recycled materials The manufacturer uses recycled materials and components in preference to new materials in and components in preference to new materials in production owing to the lower cost. The retailer production owing to the lower cost. The retailer purchases new products at wholesale price w j purchases new products at wholesale price w j from the manufacturer, and then sells them at the from manufacturer, and then sells them atthe thereal retail price pijeffort to final consumers. retail the price pij to final consumers. However, collection levels are only However, known to the the real collection levels are only themselves. known to theToretailer and third-party recycler retailer and theeffort third-party recycler enhance thethe efficiency of CLSC, wethemselves. investigate To enhance thean efficiency of CLSC, we investigate how design an information how to design information screening contract for thetomanufacturer to acquirescreening their realcontract private for the manufacturer to acquire their information. The process of manufacturer the screening information. The decision process ofreal the private screening information is decision as follows: (1) the information is as follows: (1) thecontracts manufacturer informationof screening based on designs information screening baseddesigns on the probability being ancontracts H-type retailer orthe an probability of being recycler; an H-type H-typeorthird-party recycler; (2) either the retailer or the H-type third-party (2)retailer either or theanretailer the third-party recycler chooses one contract; third-party recycler chooses onereal contract; (3) the manufacturer real collection effort levels (3) the manufacturer identifies collection effort levels of theidentifies two collection agents through their of the two collection agents through their contract choices. contract choices. wj

pij

brj

rrij

btj

rtij

Figure Figure 1. CLSC CLSC structure structure with with competitive retailer and third-party recycler without RPM.

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3.1. Model Description In this section, we examine the information screening contract for the manufacturer to obtain private information from the retailer and the third-party recycler. Figure 1 shows that both the transactions of WEEEs and finished products combine the manufacturer with the retailer; only the transactions of WEEEs combine the manufacturer with the third-party recycler. So, the screening contracts designed by manufacturer for the retailer and the third-party recycler can be expressed as { GrH (brH , w H , TrH ), GrL (brL , w L , TrL )} and { GtH (btH , TtH ), GtL (btL , TtL )}, respectively. Based on Assumptions (5) and (6), the expected profit of the manufacturer with the retailer’s choice of contract GrH and the third-party recycler’s choice of contract GtH under their real collection level H can be expressed as:

Rz Ra E(πmHH ) = 0 HH (φ − p HH + x )(w H − cr ) f ( x )dx + z (φ − p HH + x )(w H − cn ) f ( x )dx + HH Ra , ∆ z [erH + etH + (1 − ε)(rtHH + rrHH )] f ( x )dx − btH (etH + rtHH − εrrHH )− HH brH (erH + rrHH − εrtHH ) + TtH + TrH

(1)

where z HH = erH + etH + (1 − ε)(rtHH + rrHH ) − φ + p HH . If 0 < x ≤ z HH , products made of recycled components can meet market demand; however, if z HH < x < a, market demand is higher than the collection quantity of WEEEs, so it is met by products made of recycled materials and new materials together. Similarly, when the retailer chooses contract GrL under real collection level L and the third-party recycler chooses contract GtH under real collection level H, the expected profit of the manufacturer can be formulated as: Rz Ra E(πmHL ) = 0 HL (φ − p LL + x )(w L − cr ) f ( x )dx + z (φ − p LL + x )(w L − cn ) f ( x )dx HL Ra , (2) +∆ z HL [etH + erL + (1 − ε)(rtHH + rrLL )] f ( x )dx − btH (etH + rtHH − εrrLL )− brL (erL + rrLL − εrtHH ) + TtH + TrL where z HL = etH + erL + (1 − ε)(rtHH + rrLL ) − φ + p LL . If 0 < x ≤ z HL , the products made of recycled components can meet market demand; however, if z HL < x < a, market demand is higher than the collection quantity of WEEEs, so it is met by products made of recycled materials and new materials together. When the retailer chooses contract GrH under real collection level H and the third-party recycler chooses contract GtL under real collection level L, the expected profit of the manufacturer can be expressed as:

Rz Ra E(πmLH ) = 0 LH (φ − p HH + x )(w H − cr ) f ( x )dx + z (φ − p HH + x )(w H − cn ) f ( x )dx + LH Ra , ∆ z [etL + erH + (1 − ε)(rtLL + rrHH )] f ( x )dx − btL (etL + rtLL − εrrHH )− LH brH (erH + rrHH − εrtLL ) + TtL + TrH

(3)

where z LH = etL + erH + (1 − ε)(rtLL + rrHH ) − φ + p HH . If 0 < x ≤ z LH , products made of recycled components can meet market demand; however, if z LH < x < a, market demand is higher than the collection quantity of WEEEs, so it is met by newly manufactured products and remanufactured products together. When the retailer chooses contract GrL under real collection level L and the third-party recycler chooses contract GtL under real collection level L, the expected profit of the manufacturer can be formulated as: Rz Ra E(πmLL ) = 0 LL (φ − p LL + x )(w L − cr ) f ( x )dx + z (φ − p LL + x )(w L − cn ) f ( x )dx + LL Ra , (4) ∆ z [etL + erL + (1 − ε)(rtLL + rrLL )] f ( x )dx − btL (etL + rtLL − εrrLL )− LL brL (erL + rrLL − εrtLL ) + TtL + TrL

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where z LL = etL + erL + (1 − ε)(rtLL + rrLL ) − φ + p LL . If 0 < x ≤ z LL , the product made of recycled components can meet market demand; however, if z LL < x < a, market demand is higher than the collection quantity of WEEEs, hence newly manufactured products and remanufactured products together meet the market demand. In a case where the third-party recycler adopts H collection effort level with the choice of contract GtH , her expressed profit is: E(πtHH ) = (btH − rtHH ){etH + rtHH − ε[vrrHH + (1 − v)rrLL ]} − etH 2 /4 − TtH .

(5)

When the H-type third-party recycler chooses contract GtL , her expected profit is: E(πtHL ) = (btL − rtHL ){etH + rtHL − ε[vrrHH + (1 − v)rrLL ]} − etH 2 /4 − TtH .

(6)

In a case where the third-party recycler adopts L collection effort level with the choice of contract GtL , her expected profit is: E(πtLL ) = (btL − rtLL ){etL + rtLL − ε[vrrHH + (1 − v)rrLL ]} − etL 2 /4 − TtL .

(7)

When the L-type third-party recycler chooses contract GtH , her expected profit is: E(πtLH ) = (btH − rtLH ){etL + rtLH − ε[vrrHH + (1 − v)rrLL ]} − etL 2 /4 − TtH .

(8)

In the case that the retailer makes H level collection effort with the choice of contract GrH , her expected profit is: E(πrHH ) = (brH − rrHH ){erH + rrHH − ε[vrtHH + (1 − v)rtLL ]} − erH 2 /4+ Ra . ( p HH − w H ) 0 (φ − p HH + x ) f ( x )dx − TrH

(9)

If the H-type retailer chooses contract GrL , her expected profit is: E(πrHL ) = (brL − rrHL ){erH + rrHL − ε[vrtHH + (1 − v)rtLL ]} − erH 2 /4+ Ra . ( p HL − w L ) 0 (φ − p HL + x ) f ( x )dx − TrL

(10)

When the retailer makes L level collection effort with the choice of contract GrL , her expected profit is: E(πrLL ) = (brL − rrLL ){erL + rrLL − ε[vrtHH + (1 − v)rtLL ]} − erL 2 /4+ Ra . (11) ( p LL − w L ) 0 (φ − p LL + x ) f ( x )dx − TrL If the L-type retailer chooses contract GrH , her expected profit is: E(πrLH ) = (brH − rrLH ){erL + rrLH − ε[vrtHH + (1 − v)rtLL ]} − erL 2 /4+ Ra , ( p LH − w H ) 0 (φ − p LH + x ) f ( x )dx − TrH

(12)

where etj 2 /4 and erj 2 /4 denotes the cost of collection effort of the third-party recycler and the retailer, respectively. In the CLSC without government intervention under random demand and information asymmetry, the expected profit maximization problem of the manufacturer can be expressed as: maxE(πm ) = v2 E(πmHH ) + v(1 − v) E(πmHL ) + v(1 − v) E(πmLH ) + (1 − v)2 E(πmLL )

(13)

s.t. ∗ rtHH = argmaxE(πtHH )

(14)

∗ rtLL = argmaxE(πtLL )

(15)

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∗ rrHH = argmaxE(πrHH )

(16)

∗ rrLL = argmaxE(πrLL )

(17)

p∗HH = argmaxE(πrHH )

(18)

p∗LL = argmaxE(πrLL )

(19)

E(πtHH ) ≥ πt0

(20)

E(πtLL ) ≥ πt0

(21)

E(πrHH ) ≥ πr0

(22)

E(πrLL ) ≥ πr0

(23)

E(πtHH ) ≥ E(πtHL )

(24)

E(πtLL ) ≥ E(πtLH )

(25)

E(πrHH ) ≥ E(πrHL )

(26)

E(πrLL ) ≥ E(πrLH ).

(27)

The optimal profits of the retailer and the third-party recycler without contract are πr0 and πt0 respectively, which can be called conserved profits. Equations (20)–(23) can guarantee that the expected profits of both two collection agents are no less than their conserved profits when they accept the contract. We call these equations participation constraints. Equations (24)–(27) indicate that both two collection agents can make the maximum profit when they choose the right contracts corresponding to their own real collection effort levels. If not, they cannot get their maximum profit. In other words, these constraint conditions avoid the third-party recycler and the retailer telling lies, so we call these constraint equations incentive compatible constraints. Specifically, Equation (24) indicates the profit of the H-type third-party recycler when the choice of contract GtH is more than that with the choice of contract GtL . Meanwhile, Equation (25) shows that the profit of the L-type third-party recycler with contract GtL is higher than that with contract GtH . Equations (26) and (27) do the same for the retailer. It is difficult to calculate and analyze the model because it has too many constraints and its arithmetic formulas are very complicated. We will give the relevant parameters specific values, and then compute the optimal solutions with the help of a software tool of MATLAB. Finally, we will analyze the results. 3.2. Numerical Examples To verify the efficiency of the information screening contract and analyze the competition between the two collection agents on CLSC operations without RPM, we set the parameters as follows: cn = 60, cr = 45, a = 4, φ = 120, etH = erH = 10, etL = erL = 7, πro = 300, πto = 60; in addition, we specify v ∈ {0.1, 0.2, 0.3, 0.4, 0.5}, ε ∈ {0.1, 0.2, 0.3, 0.4, 0.5}. The optimal decision-making of CLSC with different v and ε is shown in Appendix A.
∗ b∗ (1) We find that when ε < 0.5, the buyback price btH rH
increases as the probability v increases.
∗ b∗ ∗ ∗ When ε = 0.5, both the buyback prices btH rH and btL brL decrease as the probability v increases.

∗ b∗ ∗ ∗ Both btH rH and btL brL decrease as the competition intensity ε increases. As shown in Figure 2, with the probability v of H level of collection effort increasing, the buyback price is not always increasing. This indicates that when the degree of collection competition between the retailer and recycler reaches a certain level, the manufacturer will still take the measure of reducing the buyback price, even if the probability v increases. This shows that competition is not advantageous to both collection agents. Buyback price under high collection effort level is always higher than that under

(( ))

(( ))

* b* * and decrease probability brH increases. Both Both bbtHtH and bbtLtL* bbrLrL decrease as as the the competition competition intensity intensity εε probability vv increases. rH increases. H level increases. As As shown shown in in Figure Figure 2, 2, with with the the probability probability vv of of H level of of collection collection effort effort increasing, increasing, the buyback price is not always increasing. This indicates that when the degree the buyback price is not always increasing. This indicates that when the degree of of collection collection competition between the retailer and recycler reaches a certain level, the manufacturer will competition between the retailer and recycler reaches a certain level, the manufacturer will still still take take the measure of reducing the buyback price, even if the probability increases. This shows that v Sustainability 2018, 10, 2131 10 of 31 the measure of reducing the buyback price, even if the probability v increases. This shows that competition competition is is not not advantageous advantageous to to both both collection collection agents. agents. Buyback Buyback price price under under high high collection collection effort level is always higher than that under low collection effort level when and are fixed. ε v effort level is always higher than thatvunder low This collection effortboth level when and v Hare fixed. ε choose low collection effort level when ε and are fixed. will make two agents level of H level of collection effort for a higher buyback price. This will make both two agents choose H level of collection effort for a higher buyback price. This will make both two agents choose collection effort for a higher buyback price.

(( ))

(( ))

*
* b** ∗ bbrH b**∗ bbrL** ∗
vs. Figure 2. buyback price v and ∗ and Figure 2. The The buyback price and andε. εε .. Figure 2. The buyback pricebtHtH btH rHbrH andbbtLtLtL brL vs. vs. vv and rL

* * * * *∗ , p∗* (2) Figures 33 and 4, the wholesale prices the retail prices ppHH w** ,∗, w L ∗ and (2) As As shown shown in in prices , pLL (2) in Figures Figures 3and and4,4,the thewholesale wholesale priceswHw w and the theretail retailprices prices pHH H H,w L L and LL HH , p LL increase with the probability competition intensity .. The can more vv and increase v and competition intensity ε. Theεεmanufacturer can get more profit by increase with withthe theprobability probability and competition intensity The manufacturer manufacturer can get get more profit the prices while reducing buyback prices. the retailer raising theraising wholesale prices while reducing buyback prices. Accordingly, the retailer will the will sale profit by by raising the wholesale wholesale prices while reducing buyback prices. Accordingly, Accordingly, theraise retailer will * * ∗ ∗ * is higher * when ε raise the sale price to get more profit. Wholesale price than and w w v price more price w L is higher wH whenthan ε andwHvH are fixed. raise to theget sale priceprofit. to getWholesale more profit. Wholesale price than higher when and shows are wLL is ε This v are H fixed. This shows that the retailer should choose level of collection effort for a lower wholesale that the retailer should choose H level of collection effort for a lower wholesale price and a higher fixed. This shows that the retailer should choose H level of collection effort for a lower wholesale price aa higher buyback price and andprice. higher buyback buyback price. price.

* * * ∗ *∗ Figure 3. wholesale price and w Figure 3. The wholesale price andw ε. εε .. Figure 3. The The wholesale price and vs. vvv and and wHHw Hand wwLL L vs.

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11 11 of of 31 31 11 of 31

* * Figure 4. The retail price p HH and pLL vs. v and ε . * * Figure 4. The retail price and andε. ε . p p ∗ Figure 4. The retail price HHp HH and pLL∗LL vs. vs. vv and

(3) From the computing results, it can be found that the collection price of the third-party * * found * * (3) From the computing results, it rcan be that price of5,the , that . the As collection shown thethird-party collection recycler is equivalent to theresults, retailer’s, rrHH rtLL =the rrLL (3) From the computing it cantHH be =found collection priceinofFigure the third-party recycler * * * * , . As shown in Figure 5, the collection recycler is equivalent to the retailer’s, r = r r = r ∗ ∗ ∗ ∗ tHH rHH tLL rLL price decreases the increase probability decreases in competition is equivalent towith the retailer’s, r in = r , r v=, and r .first As increases shown inthen Figure 5, the collection price tHH

rHH

tLL

rLL

price decreases with the in probability and then decreases in competition v , increases L first intensity sum up,increase the collection price levelincreases of collection effort is higher than theε. ε . Tothe decreases with increase in probability v, andunder first then decreases in competition intensity * * L intensity . To sum up, the collection price under level of collection effort is higher than the ε H sum level By analyzing find is that when = 0.1 if εof ≤ collection 0.3 , rtHH rtHH , we effort To up,ofthecollection collectioneffort. price under L level of collection higher thanv the H, level * * ∗ ∗ H level of collection effort. By analyzing , we find that when v = 0.1 , if ε ≤ 0.3 , r r * find that when v * effort. Byinanalyzing = 0.1, if ≤ , 0.3, in ε; if εin>ε 0.3, tHH decreases in ε tHH . When if εrtHH , rtHH increases ; if increases 0.3 ,, we rtHH v >ε 0.1 ≤ 0.2increases ε ; if ε >rtHH * * ∗ ∗When ∗*increases ; in if ε.ε >When decreases , 0.2 ifε;,εifif≤ε0.2 in εin; ifε. in 0.3 v > 0.1 rtHH rincreases decreases 0.1, if ε analyze ≤ in 0.2,ε r. tHH 0.2, decreases * * εdecreases εtHH > 0.2 , rtHH in, εvrtHH .> Now let’s . increases When v ≤in ε>≤, 0.3 , rrtHH rtLL tLL increases in ε ; ∗ ∗ ∗ * * * Now let’s analyze rtLL . in When v ≤ let’s 0.2, if ε ≤ 0.3, rtLL increases0.2 r increases decrease in*εε.; , r,tHH analyze if ifεε≤>0.30.3, , rtLL * decreases * in ,ε; > 0.3 rtLL decrease in ε ε. .Now When 0.2 < v < 0.5rtLL , if. When ε ≤ 0.2v, ≤rtLL in ; if ε > 0.2 ,inrtLL ifε >ε 0.2 ε tLL ∗ increases ∗ increases *v < 0.5, if ε ≤ 0.2, r * * When 0.2 < in ε; if ε > 0.2, r decreases in ε. When v =, 0.5, tLL 0.2 < v < 0.5*, if ε ≤ 0.2 , rtLL tLL increases in ε ; if ε > 0.2 in= 0.5 rtLL if ε > 0.3 , inrtLL .decrease ε . , When decreases When if , decreases in . Through an analysis of the v 0.1 ≤ ε ≤ 0.5 r ε ε ∗ tLL if 0.1 ≤ ε ≤ 0.5, rtLL decreases in ε. Through an analysis of the collection price, we know that when * decreases price, in ε . we When , if 0.1 decreases in an analysis of will the 0.5 when ≤ ε ≤ 0.5 , rtLL ε . Through collection knowv =that the intensifies, the collection price the collection competition intensifies, thecollection collectioncompetition price will decrease. Under the situation above, collection price, we that collection when collection competition the collection price will decrease. Under theknow situation above,thewhen the probability ofintensifies, a high effort leveland is when the probability of a high effort level is relatively small, thecollection third-party recycler decrease. Under the situation above, when the probability of a high collection effort level is relatively small, the third-party recycler and the retailer are still able to increase the quantity of the retailer are still able to increase the quantity of WEEEs by raising the collection price despite relatively small, the third-party recycler and the retailer are still able to increase the quantity of WEEEs by raising the collection price despite the buyback price falling. However, in order to deal the buyback price falling. However, in order to deal with the buyback price reduction caused by WEEEs raising thecompetition collection despite the buyback price falling. However, in the order to both deal with theby buyback price reductionprice caused by the level collection competition intensifying, the level of collection intensifying, both twoofcollection agents will reduce collection withcollection the buyback price caused by the level of collection competition intensifying, both two agents willreduction reduce the collection prices gradually. prices gradually. two collection agents will reduce the collection prices gradually.

* ∗ *∗ Figure 5. 5. The collection price and and ε.ε . Figure The collection pricertHH rtHH andrtLL rtLLvs. vs.vv and * * Figure 5. The collection price rtHH and rtLL vs. v and ε .

*∗ ∗* will decrease (4) As shown and decrease in the process of shown in in Figures Figures 66 and and 7, 7, the thefranchise franchisefee fee TTtLtL and TTrL rL will * * (4) As shown in Figures 6 and * * 7, the franchise fee TtL and TrL will decrease in the process of ∗ ∗ vv and TtH T and TrH increase in v, but in ε. Therefore, cases of competitive andε increasing; and in decrease in ε . in Therefore, in cases of TrH increase ε increasing; v , but decrease tH * * and increasing; and increase in , but decrease in . Therefore, in cases of T T v ε v ε collection, the franchise the fee thecharged manufacturer out to be turns lower out when competition tH charged rHby competitive collection, franchise fee by the turns manufacturer to the be lower when competitive collection, themore franchise fee In charged by the the franchise manufacturer turnsbyout be lower when the competition becomes intense. addition, fee paid thetoretailer is higher the competition becomes more intense. In addition, the franchise fee paid by the retailer is higher than that paid by the third-party recycler. than that paid by the third-party recycler.

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becomes more intense. In addition, the franchise fee paid by the retailer is higher than that paid by the Sustainability 2018, 10, x FOR PEER REVIEW 12 of 31 third-party recycler.

Figure 6. The franchise fee of the third-party recycler TtH* ∗and TtL* ∗ vs. v and ε . Figure 6. The franchise fee of the third-party recycler TtH and TtL vs. v and ε.

* * Figure 7. The franchise feefee of the retailer TrHT ∗and TrL ∗ vs. v and ε . Figure 7. The franchise of the retailer rH and TrL vs. v and ε.

* * * * (5) When Whene eti== eeri ,, QQ∗ tHrH eti is relatively high (or low) and eri is = QrHtH ∗ , QtLrL ∗= QrLtL ; when ∗ (5) ti ri tHrH = QrHtH , QtLrL = QrLtL ; when eti is relatively high (or low) and eri is * * * * ∗ , Q, Q∗= Q = Q ∗ . According to the expression of the collection price relatively low low (or (or high), high), QQ∗tHrL ==QQ relatively rHtL tHrL rHtLtLrH tLrH rLtH rLtH . According to the expression of the collection * * * ∗ * ∗ ∗ ∗ price , rtLL = rrLL can obtain the equivalence relationship betweenthe the collection collection and and , we can, we obtain the equivalence relationship between rtHH r=tHH rrHH = , rtLLrrHH = rrLL quantities of the retailer and third-party recycler. Let us analyze the third-party recycler’s collection quantities of the retailer and third-party recycler. Let us analyze the third-party recycler’s collection quantity. quantity. When When both both collection collection agents agents choose choose aa high high collection collection effort effort level, level, the the collection collection quantity quantity ∗* Q arrives at its maximum. When both of them choose a low collection effort level, the collection QtHrH tHrH arrives at its maximum. When both of them choose a low collection effort level, the collection quantity Q∗tLrL reaches its minimum. What will happen when they choose different collection effort * reaches its minimum. What will happen when they choose different collection effort quantity QtLrL levels? Now we analyze the case where the third-party recycler chooses a high collection effort level levels? Now we analyze the case where the third-party recycler chooses a high collection effort level ∗ and the retailer chooses a low collection effort level. When v = 0.1, if ε < 0.2, then Q∗tHrL >Q * * rLtH ; and the retailer chooses a low collection effort level. When v = 0.1 , if ε < 0.2 , then Q > Q ; if ∗ ∗ if ε > 0.2, then Q∗tHrL < QrLtH . When v = 0.2, if ε ≤ 0.3, then Q∗tHrL > QrLtH ; if ε tHrL >* 0.3,rLtH then * * * * * ε ∗> 0.20.2 ≤ 0.3 , then Q QtHrL > QrLtH ; if ε > 0.3 , then QtHrL < QrLtH ; ∗ ∗, if εregardless tHrL < Q Q QrLtH ; when vrLtH > .0.2, Q∗tHrL QrLtH of ε. tHrL * * whenFrom v > 0.2 of ε that . QtHrL > Qabove, the, analysis we can infer even though the third-party recycler makes a high rLtH regardless collection his collection quantity is not higher the than the retailer’s. Themakes relationship From effort, the analysis above, we can infer thatalways even though third-party recycler a high depends the probability of a high collection effort level.higher For instance, in the case that therelationship probability collectiononeffort, his collection quantity is not always than the retailer’s. The of high collection effort level is low, e.g., effort v ≤ 0.2, when collection is not depends on the probability of relatively a high collection level. Fortheinstance, in competition the case that the ∗ ∗ , intense, although the third-party recycler’s price rlow, is lower than that of the retailer r probability of high collection effort levelcollection is relatively e.g., , when the collection v ≤ 0.2 tHH rLL * competition is not intense, although the third-party recycler’s collection price rtHH is lower than

* , the third-party recycler can still collect more WEEEs than the retailer due to that of the retailer rrLL

her high collection effort level. However, as the collection competition intensifies the collection difficulties for both parties increase, resulting in the collection price playing a more important role

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Sustainability 2018, 10, x FOR PEER REVIEW the third-party recycler can still collect

of 31 more WEEEs than the retailer due to her high collection13effort level. However, as the collection competition intensifies the collection difficulties for both parties than the resulting collectionineffort level. So,price withplaying a moreaintense collectionrole competition, a highereffort collection increase, the collection more important than the collection level. price will make the retailer collect more WEEEs than the third-party recycler despite the lower So, with a more intense collection competition, a higher collection price will make the retailer collect collection effort. more WEEEs than the third-party recycler despite the lower collection effort. In the case thatthe theprobability probabilityofofH H collection effort is relatively , the v >the 0.2effect In the case that collection effort levellevel is relatively high,high, e.g., ve.g., > 0.2, effect of collection effort level outweighs that of collection price. Although the collection of collection effort level outweighs that of collection price. Although the collection competition competition intensifies and the retailer provides a higher price, recycler the third-party intensifies and the retailer provides a higher collection price,collection the third-party can stillrecycler acquire can still acquire more WEEEs than the retailer due to her higher collection effort level. As8,depicted more WEEEs than the retailer due to her higher collection effort level. As depicted in Figure the total in Figureof8,WEEEs the total quantity decreases as the collection competition intensity ε quantity decreases as of theWEEEs collection competition intensity ε increases. When both two H collection collection quantity effort level, the its total collection increases. When choose both two collectioneffort agents choose collection agents H collection level, the total reaches maximum in quantity reaches its maximum in the case where the two parties choose different collection the case where the two parties choose different collection effort levels; the minimum will be theeffort case levels; the minimum will beLthe case where both of them choose L collection effort level. where both of them choose collection effort level.

Figure The total collection quantity WEEEs and ε. . Figure 8. 8. The total collection quantity ofof WEEEs vs.vs.v v and ε

(6) As shown in Figure 9, when the third-party recycler and retailer choose different collection *∗ * ∗ * ∗ * ∗ levels, the theprofits profitsofofmanufacturer manufacturer EE((ππmHH ,E πmLH ) andEE(π(mLL π ) decrease effort levels, ininε ε.. ) , ),EE(π(π ) , )E (π(mLH ) and ) decrease mHH mHL mLL mHL ∗ ∗ ∗ ∗ * * * * EE((π ) , E ( π ) and E ( π ) increase in v. When v ≤ 0.2, E ( π ) increases in v; in contrast, and E (πmLH π mHH ) , E (π mHL E (π mLL ) increases in v ; in mHH mHL ) mLH ) increase in v . When v ≤ 0.2 , mLL ∗ ) decreases in v. That is, as the collection competition intensifies, although the when v > 0.2, E(πmLL * contrast, when v > 0.2 , E (π mLL ) decreases in v . That is, as the collection competition intensifies, manufacturer raises the wholesale price and cuts the buyback price, his expected profit will shrink although the manufacturer raises the wholesale price and cuts the buyback price, his expected owing to the collection quantity decreasing. Moreover, both the expected profits of the third-party profit will shrink owing to ∗the collection quantity decreasing. Moreover, both the expected profits ∗ recycler and the retailer E(πtHH ), E(πrHH ) reduce in the competition intensity ε and the probability of * * of the third-party recycler and∗ the retailer ∗ E (π tHH ), E (π rHH ) reduce in the competition intensity ε H collection effort level v. E(πtLL ) and E(πrLL ) always remain at the level of their reservation profits. * * and the probability of H that collection level vhas . Ea(detrimental always remain at and the π tLL ) and Eeffect (π rLL ) on The above results indicate intense effort competition both the retailer

level of their recycler. reservation profits. above results that intense competition has a the third-party Whether the The two collection agentsindicate should cooperate to mitigate the negative detrimental effect on deserves both the further retailerinvestigation. and the third-party recycler. Whether the two collection impact of competition agents should cooperate to mitigate the negative impact of competition deserves further investigation.

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* * * * Figure 9. The expected profits of manufacturer E (π mHH ) , E (π mHL ) , E (π mLH ) and E (π mLL ) vs. v * ∗ E (π)*, E)(,π ∗E (π *), E ∗ (π *) vs. Figure 9. The expected profits of manufacturer ) , E∗ (π ) and ) and ) vs. v ε. and . The ε 9. Figure expected profits of manufacturer E(πmHH E(πEmLL v and mHH mLL mHLmHL ( πmLHmLH and ε .

4. CLSC the RPM RPM (Case (Case 2) 2) 4. CLSC Model Model with with the 4. CLSC Model with the RPM (Case 2) With RPM, RPM, although although the the manufacturer manufacturer still still plays plays aa leading leading role role in in CLSC, CLSC, the the government government will will With Withmeasures RPM, although the manufacturer still plays a leading rolegovernment in CLSC, theintervention government will take some to stimulate WEEEs collection. Thus, we add to the take some measures to stimulate WEEEs collection. Thus, we add government intervention to the takemodel. some measures toinstimulate WEEEs collection. Thus, we add government intervention to thethe basic As shown Figure 10, the government sets a target collection quantity Q and basic model. As shown in Figure 10, the government sets a target collection quantity Q00 and the basic model. As shown in Figure 10, the government sets a target collection quantity Q0 and the reward–penalty intensity intensityk for manufacturer. is, the when the total quantity WEEEs k for the the manufacturer. That That is, when total quantity of WEEEsofcollected reward–penalty intensity for the manufacturer. That is, when the total quantity of WEEEs k collected by the third-party recycler and the retailer the targetquantity, collection the by the third-party recycler and the retailer exceeds theexceeds target collection thequantity, government collected by the third-party recycler and the retailer exceeds the target collection quantity, the government willmanufacturer reward the manufacturer for the exceeding part; thewill government will will reward the for the exceeding part; otherwise, theotherwise, government penalize him government will reward the manufacturer for the exceeding part; otherwise, the government will penalize him for theThe unmet part. The intensity of penalty reward and penalty to is be assumed to be k, for the unmet part. intensity of reward and is assumed the same, k, the for same, avoiding penalize him for the unmet part. The intensity of reward and penalty is assumed to be the same, k , for avoiding computation. complicated computation. of thescreening information screening contract this case complicated The details ofThe the details information contract in this case areinsimilar to for avoiding complicated computation. The details of the information screening contract in this case are similar those of the basic model. those of theto basic model. are similar to those of the basic model. wj wj

k ,kQ, Q o

bbrj rj

o

bbtjtj

p

pij ij

rrrijrij rtijrtij

Figure The CLSCstructure structurewith withcompetitive competitive retailer retailer and RPM. Figure 10. The CLSC retailer andthird-party third-partyrecycler recyclerwith with RPM. Figure 10.10. The CLSC structure with competitive and third-party recycler with RPM.

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4.1. Model Description The manufacturer designs the information screening contracts similar to the basic model. The screening contracts designed for the retailer and the third-party recycler can be expressed as { GrH (brH , w H , TrH ), GrL (brL , w L , TrL )} and { GtH (btH , TtH ), GtL (btL , TtL )}, respectively. Based on their choices of the screening contracts, we can develop the model as follows: When the third-party recycler chooses contract GtH and the retailer opts for contract GrH corresponding to their real collection level H, the expected profit of the manufacturer can be expressed as:

Rz Ra E(πmHH ) = 0 HH (φ − p HH + x )(w H − cr ) f ( x )dx + z (φ − p HH + x )(w H − cn ) f ( x )dx + HH Ra , (28) ∆ z [etH + erH + (1 − ε)(rtHH + rrHH )] f ( x )dx − btH (etH + rtHH − εrrHH )− HH brH (erH + rrHH − εrtHH ) + TtH + TrH + k [etH + erH + (1 − ε)(rtHH + rrHH ) − Q0 ] where z HH = etH + erH + (1 − ε)(rtHH + rrHH ) − φ + p HH . If 0 < x ≤ z HH , the remanufactured products made of recycled components can meet market demand; however, if z HH < x < a, market demand exceeds the collection quantity of WEEEs, it is met by products made of recycled materials and new materials together. Similarly, when the third-party recycler opts for contract GtH with her real collection level H and the retailer chooses contract GrL under her real collection level L, the expected profit of the manufacturer can be formulated as: Rz Ra E(πmHL ) = 0 HL (φ − p LL + x )(w L − cr ) f ( x )dx + z (φ − p LL + x )(w L − cn ) f ( x )dx + HL Ra , (29) ∆ z [etH + erL + (1 − ε)(rtHH + rrLL )] f ( x )dx − btH (etH + rtHH − εrrLL )− HL brL (erL + rrLL − εrtHH ) + TtH + TrL + k[etH + erL + (1 − ε)(rtHH + rrLL ) − Q0 ] where z HL = etH + erL + (1 − ε)(rtHH + rrLL ) − φ + p LL . If 0 < x < z HL , the remanufactured products are enough to meet market demand; however, if z HL < x < a, market demand exceeds the collection quantity of WEEEs, so it is met by the newly manufactured products and remanufactured products together. When the third-party recycler chooses contract GtL with her real collection level L and the retailer opts for contract GrH with her real collection level H, the expected profit of manufacturer can be formulated as: Rz Ra E(πmLH ) = 0 LH (φ − p HH + x )(w H − cr ) f ( x )dx + z (φ − p HH + x )(w H − cn ) f ( x )dx + LH Ra , (30) ∆ z [etL + erH + (1 − ε)(rtLL + rrHH )] f ( x )dx − btL (etL + rtLL − εrrHH )− LH brH (erH + rrHH − εrtLL ) + TtL + TrH + k[etL + erH + (1 − ε)(rtLL + rrHH ) − Q0 ] where z LH = etL + erH + (1 − ε)(rtLL + rrHH ) − φ + p HH . If 0 < x ≤ z LH , the remanufactured products can meet the market demand; however, if z LH < x < a, the market demand exceeds the collection quantity of WEEEs, so it is met by the new-manufactured products and remanufactured products together. When the third-party recycler chooses contract GtL with her real collection level L and the retailer chooses contract GrL under her real collection level L, the expected profit of the manufacturer can be expressed as:

Rz Ra E(πmLL ) = 0 LL (φ − p LL + x )(w L − cr ) f ( x )dx + z (φ − p LL + x )(w L − cn ) f ( x )dx + LL Ra , ∆ z [etL + erL + (1 − ε)(rtLL + rrLL )] f ( x )dx − btL (etL + rtLL − εrrLL )− LL brL (erL + rrLL − εrtLL ) + TtL + TrL + k[etL + erL + (1 − ε)(rtLL + rrLL ) − Q0 ]

(31)

where z LL = etL + erL + (1 − ε)(rtLL + rrLL ) − φ + p LL . If 0 < x ≤ z LL , the remanufactured products can meet market demand; however, if z LL < x < a, market demand exceeds the collection quantity

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of WEEEs, so newly manufactured products and remanufactured products together satisfy the market demand. In a case where the third-party recycler with collection effort level H chooses contract GtH , her expected profit is given as follows: e2 E(πtHH ) = (btH − rtHH ){etH + rtHH − ε[vrrHH + (1 − v)rrLL ]} − tH − TtH . (32) 4 When the H-type third-party recycler chooses contract GtL , her expected profit can be formulated as: E(πtHL ) = (btL − rtHL ){etH + rtHL − ε[vrrHH + (1 − v)rrLL ]} −

e2tH − TtL . 4

(33)

In a case where the third-party recycler with collection effort level L opts for contract GtL , her expected profit is given as follows: e2 E(πtLL ) = (btL − rtLL ){etL + rtLL − ε[vrrHH + (1 − v)rrLL ]} − tL − TtL . (34) 4 When the L-type third-party recycler chooses contract GtH , her expected profit can be formulated as: E(πtLH ) = (btH − rtLH ){etL + rtLH − ε[vrrHH + (1 − v)rrLL ]} −

e2tL − TtH . 4

(35)

When the retailer makes H level collection effort with the choice of contract GrH , her expected profit is given as follows: E(πrHH ) = (brH − rrHH ){erH + rrHH − ε[vrtHH + (1 − v)rtLL ]} − Ra ( p HH − w H ) 0 (φ − p HH + x ) f ( x )dx − TrH

2 erH 4 +

.

(36)

If the H-type retailer opts for contract GrH , her expected profit can be expressed as: 2 erH 4 +

E(πrHL ) = (brL − rrHL ){erH + rrHL − ε[vrtHH + (1 − v)rtLL ]} − Ra ( p HL − w L ) 0 (φ − p HL + x ) f ( x )dx − TrL

.

(37)

When the retailer makes L level collection effort with the choice of contract GrL , her expected profit is given as follows: E(πrLL ) = (brL − rrLL ){erL + rrLL − ε[vrtHH + (1 − v)rtLL ]} − Ra ( p LL − w L ) 0 (φ − p LL + x ) f ( x )dx − TrL

2 erL 4 +

.

(38)

If the L-type retailer opts for contract GrH , her expected profit can be expressed as: E(πrLH ) = (brH − rrLH ){erL + rrLH − ε[vrtHH + (1 − v)rtLL ]} − Ra ( p LH − w H ) 0 (φ − p LH + x ) f ( x )dx − TrH

2 erL 4 +

.

(39)

In the CLSC with RPM imposed on the manufacturer by government under random demand and information asymmetry, the expected profit maximization problem of the manufacturer can be formulated as follows: maxE(πm ) = v2 E(πmHH ) + v(1 − v) E(πmHL ) + v(1 − v) E(πmLH ) + (1 − v)2 E(πmLL )

(40)

s.t. ∗∗ rtHH = argmaxE(πtHH )

(41)

∗∗ rtLL = argmaxE(πtLL )

(42)

∗∗ rrHH = argmaxE(πrHH )

(43)

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∗∗ rrLL = argmaxE(πrLL )

(44)

p∗∗ HH = argmaxE ( πrHH )

(45)

p∗∗ LL = argmaxE ( πrLL )

(46)

E(πtHH ) ≥ πt0

(47)

E(πtLL ) ≥ πt0

(48)

E(πrHH ) ≥ πr0

(49)

E(πrLL ) ≥ πr0

(50)

E(πtHH ) ≥ E(πtHL )

(51)

E(πtLL ) ≥ E(πtLH )

(52)

E(πrHH ) ≥ E(πrHL )

(53)

E(πrLL ) ≥ E(πrLH ).

(54)

Equations (47)–(50) are participation constraints. These equations ensure that the expected profits of both two collection agents are no less than their conserved profits if they accept the contract. Equations (51)–(54) are incentive compatibility constraints, which ensure that both two collection agents will get higher profits when they select the same type contracts as their real collection effort levels. We will give the relevant parameters specific values and compute these optimal solutions with the aid of a software tool of MATLAB. 4.2. Numerical Example We assumed that cn = 60, cr = 45, a = 4, φ = 120, etH = erH = 10, etL = erL = 7, πro = 300, πto = 60, ∆ = cn − cr , v = 0.5; moreover, we specify ε ∈ {0.1, 0.2, 0.3, 0.4, 0.5}, k ∈ {10, 20, 30, 40} and Q0 = 32. The optimal decisions of this model (given in Appendix B) vary when the competition intensity ε and the reward–penalty intensity k have different values. ∗∗ (1) As shown in Figures 11–13, we know that both the buyback prices b∗∗ H and b L , all the collection ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ prices rtHH , rrHH , rtLL and rrLL , and all the collection quantities QtHrH , QrHtH , Q∗∗ tHrL , QrHtL , QtLrH , ∗∗ , Q∗∗ and Q∗∗ increase in the reward–penalty intensity k, while r ∗∗ ∗∗ ∗∗ ∗∗ QrLtH tLrL rLtL tHH = rrHH , rtLL = rrLL ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ and QtHrH = QrHtH , QtHrL = QrHtL , QtLrH = QrLtH , QtLrL = QrLtL . So, in a case where collection competition exists, the total collection quantity of the two collection agents will increase in the reward–penalty intensity with RPM. From these figures, we also see the relationship between these parameters: buyback price, collection price, collection quantity, the reward–penalty intensity, and competition intensity. When both the third-party recycler and the retailer choose collection effort ∗∗ level H, their own collection quantities Q∗∗ tHrH and QrHtH will be the highest. In contrast, when both ∗∗ choose collection effort level L, their collection quantities Q∗∗ tLrL and QrLtL will be the least. When one of them chooses collection effort level H while the other chooses collection effort level L, the one choosing H can collect more WEEEs than the other choosing L. By comparison with the results in Appendix A, ∗ ∗∗ ∗ the buyback prices with RPM are higher than without RPM, i.e., b∗∗ H > b H , b L > b L . It is the same ∗∗ > r ∗ ∗∗ ∗ ∗∗ ∗ with the collection prices and collection quantities, namely rtHH tHH , rtLL > rtLL , rrHH > rrHH , ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ rrLL > rrLL and QtHrH > QtHrH , QtHrL > QtHrL , QtLrH > QtLrH , QtLrL > QtLrL , QrHtH > QrHtH , ∗∗ ∗ ∗∗ ∗ ∗∗ > Q∗ . The RPM makes the manufacturer raise the buyback QrHtL > QrHtL , QrLtH > QrLtH , QrLtL rLtL prices, and then both the collection agents increase the collection prices accordingly. So, the collection quantities are boosted.

** > bb*L* .. L > bbL** L ** * ** > r* rrtLL > rtLL tLL

tLL

It It ,,

is the the same same is ** * ** > r* rrrHH > rrHH ,, rHH

rHH

with the the with ** * ** > r* rrrLL > rrLL rLL

rLL

collection prices prices and and collection collection collection ** * ** * ** * ** * QtHrH >Q QtHrH QtHrL >Q QtHrL and Q > > and ,, Q tHrH

tHrH

tHrL

**

**

tHrL

** * ** > r* quantities, namely namely rrtHH tHH , quantities, tHH > rtHH , ** * ** * ** * ** > Q* QtLrH >Q QtLrH QtLrL > > QtLrL ,, ,, Q ,, Q tLrH

tLrH

tLrL

tLrL

** * ** * ** * ** * ** * ** * ** * ** > Q* QrHtH > QrHtH > QrHtL > QrLtH , QrHtL , QrLtH , QrLtL rLtL . The RPM makes the manufacturer raise the Q rHtH > QrHtH , QrHtL > QrHtL , QrLtH > QrLtH , QrLtL > QrLtL . The RPM makes the manufacturer raise the buyback prices, prices, and and then then both both the the collection collection agents agents increase increase the the collection collection prices prices accordingly. accordingly. So, So, buyback Sustainability 2018, 10, 2131 18 of 31 the collection collection quantities quantities are are boosted. boosted. the

Figure 11. 11. TheThe buyback price and b** andε. εε .. ∗∗ ∗∗vs. H b and L bbH** Figure 11. The buyback price and Figure buyback price vs. kkk and H andbLb L vs.

** **

** **

Figure 12. 12. The The collection collection price price rtHH∗∗ and and rtLL∗∗vs. vs. k and and εε .. Figure 12. The collection pricertHH rtHH andrtLL rtLL vs.kk and ε. Sustainability 2018, 10, x FORFigure PEER REVIEW

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Figure 13.13. The total collection quantity of of WEEEs vs.vs.k k and and ε.ε . Figure The total collection quantity WEEEs ** (2) As shown in Figures 14 and 15, the wholesale prices wH** and ∗∗ , w L , and the retail prices (2) As shown in Figures 14 and 15, the wholesale prices w∗∗ and w and the retail prices p∗∗ H L HH ** ** ∗∗ p p and decrease in the reward–penalty intensity . By comparison with the results in k HH p LL and LL decrease in the reward–penalty intensity k. By comparison with the results in Appendix A, * ∗ i.e., ∗∗ w** ∗< w* , w** same Appendix A, the wholesale prices with RPM lowerRPM, than i.e., without RPM, the wholesale prices with RPM are lower than are without w∗∗ L < wL . H < w H , w L < Hw L . ItH is the ** * p∗ . ** * with thesame retailwith prices, p∗∗ p∗HH andpHH p∗∗ pHH It is the thenamely retail prices, namely HH < LL< < LLand pLL < pLL .

w**H** and w**L** ,, and (2) As As shown shown in in Figures Figures 14 14 and and 15, 15, the the wholesale wholesale prices prices w and w and the the retail retail prices prices (2) H L ** ** and ppLL decrease decrease in in the the reward–penalty reward–penalty intensity intensity kk .. By By comparison comparison with with the the results results in in and

** ** HH ppHH LL w**H** TtL , TrH > TrH , TrL > TrL . In addition, the manufacturer can get more profit by raising the franchise fee under RPM. ∗∗ TrH

tH

tL

** ** and TTrLrL**** of of the the retailer retailer charged charged by by the the manufacturer manufacturer increase increase in in the the reward–penalty reward–penalty and TTrH and rH and intensity kk .. By By comparison comparison with with the the results results of of Appendix Appendix A, A, we we see see that that the the franchise franchise fees fees charged charged intensity by the the manufacturer manufacturer on on the the two two collection collection agents agents with with RPM RPM are are more more than than without without RPM, RPM, i.e., i.e., by ** ** ** ** ** ** ** ** ** ** ** ** > TTrH TrLrL >> TTrLrL .. In In addition, addition, the the manufacturer manufacturer can can get get more more profit profit by by raising raising TTtHtH >> TTtHtH ,, TTtLtL >> TTtLtL ,, TTrH rH > rH ,, T

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the franchise franchise fee fee under under RPM. RPM. the

**

**

** ∗∗ ∗∗vs. Figure 16.16. TheThe franchise feefee of the the third-party recycler and vs. kk and and εε .. TTtHtH**TtH Figure 16. The franchise fee of third-party recycler and tL Figure franchise of the third-party recycler andTTtLT tL vs. k and ε.

**

**

** ** Figure 17.17. TheThe franchise feefee of the the retailer and vs. kk and and εε .. ∗∗ TTrHrH Figure 17. The franchise fee of retailer and rL ∗∗vs. Figure franchise of the retailer TrH andTTrLT rL vs. k and ε.

(4) As As shown shown in in Figure Figure 18, 18, as as the the reward–penalty reward–penalty intensity intensity k increases, increases, the the expected expected profits profits (4) (4) As shown in Figure 18, as the**reward–penalty intensity**k kincreases, the expected profits of ** ** ** ** ** ** E((ππ)mHH ) ∗∗E E((π)π,mHL ) ∗∗ E()(ππand Efirst of the the manufacturer manufacturer , E and first decrease, decrease, then increase. ((ππmLL )) first of then increase. ∗∗E ∗∗ )E mHH mHL mLH ))E (and mLL mLH the manufacturer E(πmHH , E() π,, mHL E()π,mLH πmLL decrease, then increase. Specifically, ≤ 0.3 0.3 Specifically, when ifexpected the expected expected profit of of the thedecreases manufacturer decreases in the the 20 ,, profit Specifically, when ,, if the profit manufacturer in kk ≤≤ 20 when ε ≤ 0.3, if k ≤ε ≤ 20, the of the manufacturer in thedecreases reward–penalty = 0.4 reward–penalty intensity ; but if , his expected profit increases in . When , if if k k > 20 k ε = 0.4 reward–penalty intensity ; but if , his expected profit increases in . When , k k > 20 k intensity k; but if k > 20, his expected profit increases in k. When ε = 0.4, if k ≤ 30, his expected , his expected profit decreases with rising; if , the changing trend of his expected k ≤ 30 k k > 30 , his expected decreases if k >of30his , the changing trend of the his expected k ≤ 30decreases k rising;trend profit with profit k rising; if k > 30,with the changing expected profit is just opposite. ≥ 0.5 profit is just the opposite. When , his expected profit is always decreasing with rising. k rising. ε ≥ 0.5 profit is just the opposite. When , his expected profit is always decreasing with k When ε ≥ 0.5, his expected profit is always decreasing with k rising. We can deduce that under We can deduce that under moderate collection competition intensity between the third-party We can deduce thatcompetition under moderate collection intensity the third-party moderate collection intensity between competition the third-party recyclerbetween and the retailer, there is recycler and the thereward–penalty retailer, there there is isintensity large enough enough reward–penalty intensity to make the manufacturer manufacturer recycler and retailer, aa large reward–penalty intensity make the a large enough to make the manufacturer betterto off. However, in the case better off. off. However, in the the case case without without RPM, thealways manufacturer’s expected profits always always decrease better However, in RPM, the manufacturer’s profits decrease without RPM, the manufacturer’s expected profits decrease expected as the competition intensity rises. as the competition intensity rises. Therefore, the RPM can motivate the manufacturer, which serves as the competition rises.the Therefore, the RPM canserves motivate theleader manufacturer, which serves Therefore, the RPMintensity can motivate manufacturer, which as the of the CLSC, to collect as the theWEEEs leader of of the CLSC, toand collect more WEEEsrecycler. via the the retailer retailer and and the the third-party third-party recycler. recycler. as leader to collect WEEEs via more viathe theCLSC, retailer themore third-party

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21 of 31 21 of 31

∗∗ ∗∗(π ), E ∗∗(π ) and ∗∗ E (π mHH ) (, πE ) and E (π)mLL Figure 18. The Theexpected expectedprofits profits manufacturer Figure 18. of of manufacturer E(πmHH ), E) (, πE E(πmLL vs.) kvs. and kε. mHLmHL mLHmLH and ε . **

**

**

**

By comparing the manufacturer’s expected profits under RPM with those in the absence of By the manufacturer’s expected ∗∗ profits ∗ ∗∗ ) those ∗ the ∗∗ ) of RPM, wecomparing find that when ε ≤ 0.2, if k ≤ 30, E(πmHH ) < E(under πmHH )RPM , E(πwith < E(πin ), Eabsence (πmLL < mHL mHL ** * ** * ∗ ∗∗ ∗ ∗∗ ∗ ∗∗ ∗ ε ≤ 0.2 E ( π ) < E ( π ) E ( π ) < E ( π ) , , if , , RPM, we find that when k ≤ 30 E(π ); if k > 30, E(π ) > E(π ), E ( π ) > E(π mHH ), E(π mHH ) > E(π )mHL . When ε mHL > 0.2, mLL

mHH

mHH

mHL

mHL

mLL

mLL

** * ** ∗∗ ∗ ; if), E ∗∗ , E (π **( π ∗) > E)(, πE*( π ∗∗ ∗> E)(.π * ) , E (π ** ) > E (π * ) . When π mHH ) , )Eπ30 EE((π )E 0.2 π mHH ) are equal to collection the conserved when choose collection level ∗ H),, while ∗∗ their ∗ E(πtHH E(πrHH ) > expected E(πrHH );profits when they choose effortprofits level L, theirthey expected profits with effort level L . By comparison with the results in Appendix A, the expected profits of the two collection agents with RPM are higher than without RPM when they choose collection effort level ** * ** * H , i.e., E (π tHH ) > E (π tHH ) , E (π rHH ) > E(π rHH ) ; when they choose collection effort level L , their

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∗∗ ) = E ( π ∗ ) = π 0 , RPM are equal to without RPM, which are their conserved profits, i.e., E(πtLL t tLL ∗∗ ∗ 0 E(πrLL ) = E(πrLL ) = πr .

5. Conclusions and Future Research In this paper, we study a CLSC with dual collection channel, in which the manufacturer entrusts one retailer and one third-party recycler with collecting WEEEs in competition. The collection effort levels of both collection agents are only known to themselves. The manufacturer provides information screening contracts for the two collection agents in order to attain real information about their collection effort levels. In this context, we focus on verifying the efficiency of the information screening contracts and exploring the influence of the RPM on the CLSC with competitive dual collection channel and information asymmetry. The contract parameters and optimal decision-making results are obtained by numerical simulation and the main findings are as follows: (1)

(2)

(3)

The information screening contract can help the manufacturer acquire the real collection effort levels effectively because the two collection agents are induced to choose the same type of contract as their collection effort type for profit maximization. That is, the screening contract can prevent them from lying and improve the efficiency of the CLSC system. The retailer and the third-party recycler will earn more profit by choosing a high level collection effort when competing against each other. The collection competition reduces the total collection quantity and the expected profit of the manufacturer, while the expected profits of both two collection agents first increase and then decrease as the competition intensity increases. In addition, the more intense the collection competition is, the more losses they will suffer. Therefore, the CLSC channel members should make efforts to come to a cooperation agreement for mitigating the negative effect of the competition. The RPM has a positive effect on CLSC with collection competition. First, RPM increases the collection price, buyback price, franchise fee, and total collection quantity; secondly, it can encourage initiatives of the collectors in collecting WEEEs, and then the environmental benefits to society will improve. What is more, the RPM can ensure that the profits of all the CLSC members are superior to without RPM.

This paper is among the first efforts to investigate the impact of RPM on a CLSC with competitive dual collection channel and information asymmetry. Several possible extensions deserve future research. First, all the conclusions we have obtained are based on a case where the manufacturer delegates the collection task to the mutual competitive retailer and third-party recycler. However, as Savaskan et al. [5] have noted, the manufacturer may choose to collect the WEEEs itself. So, other competition forms, such as mutual competitive manufacturer and retailer (or mutual competitive manufacturer and the third-party recycler) can also be examined. Secondly, we assume that there is no difference between the new product and the remanufactured product. In reality, however, there are many differences between the two types of products. For instance, the price of a remanufactured product may be lower than that of a new product, so the product differentiation needs to be considered in the future. Finally, this paper assumes that all the CLSC members are risk-neutral and profit maximizers. We may need to incorporate the risk attitudes of the decision-makers into the CLSC model. Author Contributions: Conceptualization, W.W. and L.H.; Formal analysis, W.W. and S.Z.; Investigation, S.Z. and M.Z.; Writing—original draft, S.Z. and M.Z.; Writing—review & editing, H.S.; Funding acquisition, H.S. Funding: This research was funded by the Postgraduate Education & Teaching Reform Research & Practice Innovation Program of Jiangsu Province (No. JGLX16_064) and the Natural Science Foundation of Shandong Province of China (ZR2017MG015). Conflicts of Interest: The authors declare no conflict of interests.

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Appendix A Table A1. The optimal CLSC decision results vs. v and ε without RPM. v ε

0.1

0.2

0.3

0.4

0.5

16.870 16.390 15.820 15.120 14.170

16.890 16.420 15.860 15.140 14.160

16.910 16.450 15.890 15.170 14.150

16.920 16.480 15.930 15.190 14.130

16.940 16.510 15.960 15.210 14.120

∗ ,b∗ brL tL 0.1 0.2 0.3 0.4 0.5

18.510 18.150 17.660 16.960 15.940

18.250 17.860 17.330 16.580 15.480

17.920 17.490 16.910 16.100 14.910

17.470 17.000 16.360 15.470 14.190

16.830 16.300 15.590 14.620 13.230

w∗H 0.1 0.2 0.3 0.4 0.5

64.070 65.120 66.320 67.700 69.300

64.090 65.160 66.370 67.760 69.380

64.120 65.190 66.410 67.810 69.440

64.150 65.230 66.450 67.850 69.500

64.180 65.260 66.480 67.890 69.540

65.260 66.550 68.030 69.710 71.660

65.450 66.760 68.240 69.930 71.880

65.680 67.000 68.490 70.180 72.130

65.990 67.300 68.790 70.480 72.410

66.400 67.720 69.190 70.860 72.770

∗ rtHH 0.1 0.2 0.3 0.4 0.5

3.726 3.788 3.808 3.744 3.496

3.718 3.764 3.763 3.656 3.349

3.711 3.740 3.713 3.575 3.205

3.698 3.717 3.670 3.490 3.059

3.691 3.694 3.622 3.407 2.922

∗ rtLL 0.1 0.2 0.3 0.4 0.5

6.046 6.168 6.228 6.164 5.880

5.898 5.984 5.998 5.876 5.509

5.716 5.760 5.723 5.540 5.085

5.473 5.477 5.385 5.130 4.589

5.136 5.089 4.937 4.612 3.978

∗ rrHH 0.1 0.2 0.3 0.4 0.5

3.726 3.788 3.808 3.744 3.496

3.718 3.764 3.763 3.656 3.349

3.711 3.740 3.713 3.575 3.205

3.698 3.717 3.670 3.490 3.059

3.691 3.694 3.622 3.407 2.922

∗ rrLL 0.1 0.2 0.3 0.4 0.5

6.046 6.168 6.228 6.164 5.880

5.898 5.984 5.998 5.876 5.509

5.716 5.760 5.723 5.540 5.085

5.473 5.477 5.385 5.130 4.589

5.136 5.089 4.937 4.612 3.978

∗ ,b∗ brH tH

0.1 0.2 0.3 0.4 0.5

w∗L

0.1 0.2 0.3 0.4 0.5

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Table A1. Cont. v ε

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5

93.035 93.560 94.160 94.850 95.650

93.045 93.580 94.180 94.880 95.690

93.060 93.600 94.200 94.900 95.720

93.080 93.620 94.220 94.920 95.750

93.090 93.630 94.240 94.940 95.770

p∗LL 0.1 0.2 0.3 0.4 0.5

93.630 94.280 95.020 95.860 96.830

93.720 94.380 95.120 95.960 96.940

93.840 94.500 95.240 96.090 97.060

94.000 94.650 95.400 96.240 97.200

94.200 94.860 95.600 96.430 97.380

∗ TtH 0.1 0.2 0.3 0.4 0.5

60.880 48.364 35.494 22.517 9.269

61.943 50.046 37.849 25.262 12.460

63.108 51.846 40.218 28.262 15.814

64.326 53.819 42.886 31.374 19.259

65.961 56.113 45.769 34.789 23.127

∗ TtL 0.1 0.2 0.3 0.4 0.5

83.109 71.318 58.443 44.295 28.946

80.319 68.789 56.172 42.317 27.166

76.694 65.334 52.899 39.261 24.276

71.674 60.523 48.204 34.670 19.924

64.507 53.433 41.238 27.912 13.359

∗ TrH 0.1 0.2 0.3 0.4 0.5

659.860 617.190 570.560 519.640 463.590

660.340 617.740 571.530 520.760 464.680

660.630 618.690 572.780 522.400 466.450

660.980 619.530 574.340 524.430 468.330

661.750 620.970 576.380 526.760 471.140

∗ TrL 0.1 0.2 0.3 0.4 0.5

647.970 599.990 546.630 487.860 422.470

639.800 591.650 538.710 480.140 415.170

629.680 581.580 528.730 470.590 406.030

615.950 568.550 516.030 458.250 394.720

597.350 550.010 498.460 441.740 379.260

∗ ,Q∗ QtHrH rHtH 0.1 0.2 0.3 0.4 0.5

13.353 13.030 12.666 12.246 11.748

13.346 13.011 12.634 12.194 11.674

13.340 12.992 12.599 12.145 11.602

13.330 12.974 12.569 12.094 11.530

13.320 12.955 12.535 12.044 11.461

∗ Q∗tHrL ,QrHtL 0.1 0.2 0.3 0.4 0.5

13.120 12.550 11.940 11.280 10.560

13.130 12.570 11.960 11.310 10.590

13.140 12.590 12.000 11.360 10.660

13.150 12.620 12.050 11.440 10.760

13.180 12.680 12.140 11.560 10.930

p∗HH

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Table A1. Cont. v ε

0.1

0.2

0.3

0.4

0.5

12.670 12.410 12.090 11.670 11.130

12.530 12.230 11.870 11.410 10.830

12.340 12.010 11.610 11.110 10.480

12.100 11.730 11.280 10.730 10.060

11.770 11.350 10.850 10.250 9.517

12.440 11.930 11.360 10.700 9.940

12.310 11.790 11.200 10.530 9.754

12.140 11.610 11.010 10.320 9.542

11.930 11.380 10.770 10.080 9.294

11.620 11.070 10.460 9.767 8.989

∗ Q∗tHrH +QrHtH 0.1 26.710 0.2 26.060 0.3 25.330 0.4 24.490 0.5 23.500

26.690 26.020 25.270 24.390 23.350

26.680 25.980 25.200 24.290 23.200

26.660 25.950 25.140 24.190 23.060

26.640 25.910 25.070 24.090 22.920

∗ ∗ Q∗tHrL +QrHtL , Q∗tLrH +QrLtH 0.1 25.790 25.650 0.2 24.960 24.800 0.3 24.030 23.830 0.4 22.940 22.720 0.5 21.690 21.430

25.480 24.600 23.610 22.470 21.140

25.250 24.360 23.340 22.170 20.820

24.940 24.030 22.990 21.810 20.450

∗ Q∗tLrL +QrLtL 0.1 0.2 0.3 0.4 0.5

∗ Q∗tLrH ,QrLtH

0.1 0.2 0.3 0.4 0.5

∗ Q∗tLrL ,QrLtL 0.1 0.2 0.3 0.4 0.5

24.880 23.870 22.720 21.400 19.880

24.620 23.570 22.400 21.050 19.510

24.290 23.220 22.010 20.650 19.080

23.850 22.760 21.540 20.160 18.590

23.240 22.140 20.910 19.530 17.980

∗ E(πmHH ) 0.1 0.2 0.3 0.4 0.5

788.550 774.670 760.750 747.460 736.050

790.150 777.180 764.290 752.050 741.810

791.890 779.930 768.090 756.950 747.900

794.010 783.020 772.260 762.290 754.370

796.730 786.790 777.080 768.220 761.460

∗ E(πmHL ) 0.1 0.2 0.3 0.4 0.5

788.440 772.310 755.130 737.300 719.400

789.610 774.310 758.050 741.090 724.050

790.740 776.240 760.790 744.570 728.330

791.810 778.020 763.190 747.640 731.940

792.760 779.420 765.070 749.890 734.420

∗ E(πmLH ) 0.1 0.2 0.3 0.4 0.5

789.270 773.500 756.840 739.650 722.600

790.390 775.420 759.570 743.100 726.770

791.440 777.180 761.990 746.180 730.390

792.320 778.650 763.990 748.600 733.130

792.760 779.430 765.070 749.850 734.410

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Table A1. Cont. v ε

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5

788.820 771.260 751.710 729.930 705.920

789.050 771.880 752.630 731.020 707.040

788.830 771.820 752.620 730.950 706.680

787.780 770.650 751.190 729.060 704.220

785.000 767.330 747.160 724.230 698.430

∗ ) E(πtHH 0.1 0.2 0.3 0.4 0.5

86.893 85.446 83.797 81.887 79.678

86.556 85.128 83.497 81.611 79.412

86.113 84.688 83.061 81.180 78.974

85.491 84.068 82.425 80.521 78.303

84.584 83.133 81.459 79.524 77.257

∗ ) E(πtLL 0.1 0.2 0.3 0.4 0.5

60.000 60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000 60.000

∗ E(πrHH ) 0.1 0.2 0.3 0.4 0.5

326.880 325.450 323.800 321.890 319.680

326.550 325.130 323.490 321.610 319.410

326.110 324.690 323.060 321.180 318.980

325.490 324.060 322.420 320.520 318.290

324.580 323.130 321.470 319.530 317.260

∗ ) E(πrLL 0.1 0.2 0.3 0.4 0.5

300.000 300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000 300.000

∗ ) E(πmLL

Appendix B Table A2. The optimal CLSC decision results vs. k and ε with RPM. ” k ∗∗ ,b∗∗ btH rH

10 20 30 40

∗∗ ,b∗∗ btL rL 10 20 30 40

0.1

0.2

0.3

0.4

0.5

21.310 25.680 30.050 34.420

20.920 25.320 29.730 34.130

20.400 24.850 29.290 33.730

19.700 24.180 28.670 33.160

18.660 23.190 27.730 32.270

21.200 25.570 29.940 34.310

20.700 25.110 29.510 33.920

20.030 24.480 28.920 33.360

19.100 23.590 28.080 32.570

17.770 22.310 26.850 31.390

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Table A2. Cont. ” k

0.1

0.2

0.3

0.4

0.5

10 20 30 40

58.780 53.380 47.980 42.580

60.150 55.040 49.940 44.830

61.710 56.940 52.160 47.390

63.500 59.110 54.720 50.330

65.590 61.650 57.700 53.750

w∗∗ L 10 20 30 40

61.000 55.600 50.200 44.800

62.610 57.500 52.400 47.290

64.420 59.650 54.880 50.100

66.470 62.080 57.690 53.300

68.820 64.870 60.920 56.980

∗∗ rtHH 10 20 30 40

5.991 8.291 10.590 12.890

6.144 8.589 11.040 13.480

6.234 8.851 11.460 14.070

6.212 9.013 11.820 14.630

5.949 8.970 12.000 15.020

∗∗ rtLL 10 20 30 40

7.436 9.736 12.040 14.340

7.534 9.984 12.430 14.880

7.549 10.170 12.780 15.390

7.412 10.220 13.020 15.830

7.004 10.030 13.060 16.080

∗∗ rrHH 10 20 30 40

5.991 8.291 10.590 12.890

6.144 8.589 11.040 13.480

6.234 8.851 11.460 14.070

6.212 9.013 11.820 14.630

5.949 8.970 12.000 15.020

10 20 30 40

7.436 9.736 12.040 14.340

7.534 9.984 12.430 14.880

7.549 10.170 12.780 15.390

7.412 10.220 13.020 15.830

7.004 10.030 13.060 16.080

p∗∗ HH 10 20 30 40

90.390 87.690 84.990 82.290

91.080 88.520 85.970 83.420

91.860 89.470 87.080 84.700

92.750 90.560 88.360 86.160

93.800 91.820 89.850 87.880

p∗∗ LL 10 20 30 40

91.500 88.800 86.100 83.400

92.300 89.750 87.200 84.640

93.210 90.820 88.440 86.050

94.240 92.040 89.840 87.650

95.410 93.440 91.460 89.490

∗∗ TtH 10 20 30 40

118.890 180.390 250.450 329.090

104.340 160.060 223.630 294.670

88.739 138.510 194.870 257.930

72.353 115.410 164.290 218.790

54.769 90.868 131.630 177.050

∗∗ TtL 10 20 30 40

117.210 178.480 248.310 326.720

101.100 156.560 219.530 290.350

83.532 132.620 188.310 250.690

64.350 106.550 154.430 207.940

43.654 78.548 117.980 162.070

w∗∗ H

∗∗ rrLL

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Table A2. Cont. ” k

0.1

0.2

0.3

0.4

0.5

10 20 30 40

878.080 1117.500 1380.200 1666.000

820.690 1041.000 1281.800 1543.400

757.460 956.710 1174.300 1409.600

687.920 864.200 1055.900 1263.000

610.290 761.400 925.250 1101.600

∗∗ TrL 10 20 30 40

807.460 1040.700 1297.100 1576.700

742.890 956.620 1190.600 1445.700

672.400 864.500 1074.600 1303.100

595.250 764.150 948.380 1147.900

510.680 654.510 810.670 978.970

∗∗ Q∗∗ tHrH ,QrHtH 10 15.392 20 17.462 30 19.531 40 21.601

14.915 16.871 18.832 20.784

14.364 16.196 18.022 19.849

13.727 15.408 17.092 18.778

12.974 14.485 16.000 17.510

∗∗ Q∗∗ tHrL ,QrHtL 10 20 30 40

15.250 17.320 19.390 21.460

14.640 16.590 18.550 20.500

13.970 15.800 17.630 19.450

13.250 14.920 16.610 18.300

12.450 13.960 15.470 16.980

∗∗ Q∗∗ tLrH ,QrLtH 10 20 30 40

13.840 15.910 17.980 20.050

13.310 15.270 17.220 19.180

12.680 14.510 16.340 18.170

11.930 13.610 15.290 16.980

11.030 12.540 14.060 15.570

∗∗ Q∗∗ tLrL ,QrLtL 10 20 30 40

13.690 15.760 17.840 19.910

13.030 14.990 16.940 18.900

12.280 14.120 15.950 17.770

11.450 13.130 14.810 16.500

10.500 12.020 13.530 15.040

∗∗ Q∗∗ tHrH +QrHtH 10 30.780 20 34.920 30 39.060 40 43.200

29.830 33.740 37.660 41.570

28.730 32.390 36.040 39.700

27.450 30.820 34.180 37.560

25.950 28.970 32.000 35.020

∗∗ ∗∗ ∗∗ Q∗∗ tHrL +QrHtL ,QtLrH +QrLtH 10 29.080 27.940 20 33.220 31.860 30 37.370 35.780 40 41.510 39.690

26.650 30.310 33.970 37.620

25.170 28.540 31.900 35.280

23.480 26.500 29.530 32.550

∗∗ Q∗∗ tLrL +QrLtL 10 20 30 40

∗∗ TrH

∗∗ ) E(πmHH 10 20 30 40

27.380 31.520 35.670 39.810

26.050 29.970 33.890 37.810

24.570 28.240 31.890 35.550

22.890 26.260 29.620 33.000

21.000 24.030 27.060 30.080

749.410 743.440 778.980 855.890

729.820 712.030 733.340 793.690

709.240 677.950 683.350 725.290

688.080 641.510 628.660 649.550

667.100 603.030 569.160 565.640

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Table A2. Cont. ” k

0.1

0.2

0.3

0.4

0.5

10 20 30 40

745.050 738.730 773.810 850.340

721.570 702.800 723.230 782.720

695.630 662.750 666.450 706.790

667.150 618.080 602.690 620.940

636.310 568.460 530.920 523.600

∗∗ ) E(πmLH 10 20 30 40

745.050 738.680 773.850 850.360

721.570 702.830 723.240 782.700

695.630 662.770 666.460 706.770

667.150 618.080 602.590 620.950

636.330 568.460 530.920 523.640

∗∗ ) E(πmLL 10 20 30 40

736.900 730.180 764.920 841.070

708.460 688.860 708.360 766.960

676.040 641.610 643.700 682.320

638.890 587.300 569.220 585.010

596.610 525.080 483.780 472.700

∗∗ ) E(πtHH 10 20 30 40

90.792 96.999 103.210 109.420

88.993 94.878 100.740 106.630

86.944 92.440 97.932 103.410

84.562 89.619 94.666 99.719

81.797 86.340 90.882 95.426

∗∗ ) E(πtLL 10 20 30 40

60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000

60.000 60.000 60.000 60.000

∗∗ ) E(πrHH 10 20 30 40

330.790 337.060 343.200 349.390

329.000 334.850 340.730 346.700

326.940 332.440 337.910 343.400

324.560 329.620 334.710 339.660

321.800 326.340 330.880 335.390

∗∗ ) E(πrLL 10 20 30 40

300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000

300.000 300.000 300.000 300.000

∗∗ ) E(πmHL

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