INTRODUCTION

The rapid developments in high technology lead to higher production efficiency, shorter product lifecycle and more severe market competition. Plentiful products come into the market, which means that several used products need to be processed. The processing of used products is usually performed in four ways: product repair (returning the product to a functional condition), product recovery (recovering product parts that may be reused), product recycling (returning the product to the raw material state) and product remanufacturing (a process where worn-out products are restored to an almost new condition). Many firms now take back their products in order to recycle the material into new products. However, there may be greater economic benefit in remanufacturing these items instead of recycling them. A Boston University study (Lund, 1996) on the remanufacturing industry studied 11,000 firms in eight industry sectors: automotive, compressors, electrical equipment, machinery, office furniture, tires, toner cartridges and valves. It concluded that the remanufacturing industry is a $53bn industry in the US alone, on a par with the steel industry. The direct employment in 73,000 remanufacturing firms in the US was 480,000, equal to the consumer durables industry. Remanufacturing is an environmentally and economically sound way to achieve sustainable development and economic efficiency. Remanufacturing growth is recognised as a prevalent manufacturing system trend in the 21st century (Coates, 2000).

However, there is a baffling question in China: many scientists, manufacturers and government officers explicitly understand that remanufacturing is useful for protecting the environment, saving natural resources and increasing profits, but only a few manufacturers carry out remanufacturing. As a result, there exists a huge gap between the reality and requirements of the utilisation of resources and environmental protection. What are the reasons for this baffling question?

In order to find the answer, we conducted a survey on the collection of used mobile phones and their batteries, used electronic appliances and used engines. The results of our survey were as follows:

1. The capacity of the used-products market is large enough: To date, so many used products are waiting to be processed in China. As such, in the electronic industry, the quantity of electronic products is becoming larger and larger.
2. Some legislations and policies have been implemented: In order to enhance the reuse of used products and protect the environment, the Chinese government has implemented some related legislations and policies. For example, the manufacturer should take back their used products from the end-customers.
3. There are three collection channel formats in China: the manufacturer, the retailer and the third party for collection. For example, in China, Motorola and Nokia collect used mobile phones or the batteries at service centres (retailer) using a collection box. Gome collects used electronic appliances at its stores or via third parties. Jinan Fuqiang Power Co. Ltd collect used engines by themselves, through retailers and through third parties. These collection channel formats are the same as in other countries.
4. The quantity of the returned used products is not enough: As the used products are materials for remanufacture, if the supply is short, remanufacture cannot be carried out efficiently. Obviously, the means to obtain a plenty of returned used products are very important.
5. The quantity of the returned used products is affected by the end-customers' willingness to return their used products, and the end-customers' willingness to return their used products is affected by the collecting price. In China, when the collector (manufacturer, retailer or third party) collects the used products from the end-customers, the end-customers hope to receive a payment (the collecting price), and the higher the collecting price, the larger the return rate of the used products. It is obvious that the collecting price is a key factor that must not be neglected.

Motivated by this issue, this paper aims to study the pricing decisions of the collecting price. In fact, when used-product remanufacturing and new-product manufacturing are carried out in the meantime, the manufacture must manage a closed-loop supply chain that combines the forward and the reverse supply chain. In a closed-loop supply chain, the wholesale price and the retail price of the new products will also be affected by the collecting price of the used products. Hence, this paper will study the retail price and the wholesale price decisions while studying the collecting price decisions of the closed-loop supply chain.

LITERATURE REVIEW

Nowadays, there is an increasing amount of research on recycling issues (ie reverse logistics, reverse supply chain and closed-loop supply chain) (Schrady, 1967; Pasternack, 1985; Mabini and Gelders, 1991; Pohlen and Farris II, 1992; Johnson and Wang, 1995; Jahre, 1995; Kroon and Vrijens, 1995; Fleischmann et al., 1997; Van der Laan and Salomon, 1997; Padmanabhan and Png, 1997; Emmons and Gilbert, 1998; Van der Laan et al., 1999a, 1999b; Donohue, 2000; Shih, 2001; Hu et al., 2002; Dennis and Sheu, 2002; Daniel et al., 2002; White et al., 2003; KiesmÄuller, 2003; Inderfurth, 2004; Savaskan et al., 2004; Sheu et al., 2005; Tang and Grubbström, 2005; Gu and Ji, 2006), but, it is noteworthy that the previous literature appears to be devoted mainly to the reverse distribution planning, inventory control of return flows, production planning with reuse of parts and materials and optimal contract design of product return. In general, collection of used products in recycling issues may include purchasing, except transportation and storage activities. However, with our literature review, even in optimal contract design, studies specifically addressing purchasing (namely, the pricing decision of the returns) (Gu et al., 2005; Gu and Ji, 2005; Nagurney and Toyasaki, 2005) are rare. In view of the lack of research on the pricing decision of the returns, we assume that the customer's willingness to return a used product is related to the collecting price, and the return rate of the used product is an increasing function of the collecting price. We will focus on the collecting price, the retail price and the wholesale price decisions based on the closed-loop supply chain models.

In the optimal contracts literature, Pasternack (1985), Emmons and Gilbert (1998) and Donohue (2000) determine optimal product return contracts for short lifecycle products. The returns considered in these studies occur at the end of the selling season due to demand uncertainty and the retailer's overstocking of inventory. Related to this group of work, Padmanabhan and Png (1997) explore how ordering flexibility from buy-back contracts affects the retail-level competition. Savaskan et al. (2004) consider used products, which are returned from consumers for remanufacture, and discuss contract forms, which jointly coordinate the reverse and the forward channels. In his study, the decision variables are the wholesale price, the retail price and the product return rate. It assumes that each customer who returns a used product receives a payment per unit and the payment is fixed. In contrast, in this paper, we consider used products, too. In contrast, we consider the payment as a decision variable.

In the price decisions of material literature, Anna Nagurney and Fuminori Toyasaki (2005) consider the price of a recycled material based on the electronic waste. They develop an integrated framework for the modelling of reverse supply chain management of electronic waste, which includes recycling. They describe the behaviour of the various decision-makers, consisting of the sources of electronic waste, the recyclers, the processors and the consumers associated with the demand markets for the distinct products. They construct the multitiered e-cycling network equilibrium model and establish the variational inequality formulation, whose solution yields the material flows as well as the prices. In their paper, the price of a recycled material is affected by the amount of the recycled material. In contrast, we assume that the amount (the return rate) of the used products is affected by the collecting price.

In the price decisions of used-products literature, Gu et al. (2005), Gu and Ji (2005) study the pricing decisions of recycled used products based on the reverse supply chain by game theory. In their paper, the authors consider only the reverse supply chain, and study only the collecting price decisions. In contrast, in this paper, our study will focus on the closed-loop supply chain and study the wholesale price decisions, the retail price decisions and the collecting price decisions at the same time.

PROBLEM DESCRIPTION

Figure 1 illustrates the closed-loop supply chain Model CMRC. Model CMRC has two members: the manufacturer and the retailer. The manufacturer collects the used products from the end-customers directly.

Figure 1.

Model CMRC

Full figure and legend (44K)

In the forward supply chain of Model CMRC, the manufacturer produces new products with the unit manufacturing cost c_m or with the unit remanufacturing cost c_rm, sells the new products to the retailer with the unit wholesale price and the retailer sells the new products to the end-customers with the unit retail price p. Herein, c_rm<c_m, c_m-c_rm is the unit cost saving from remanufacturing.

In the reverse supply chain of Model CMRC, the manufacturer will pay a unit collecting price f to the end-customer for a used product, and the unit average operational cost of collecting a used product is c, including inventory cost, transportation cost, etc.

In this model, the manufacturer will decide the collecting price f of the used products and the wholesale price of the new products to maximise its profit _M^CMRC, and the retailer will decide the retail price p of the new products to maximise its profit _R^CMRC. Let ^CMRC denote the total profit of Model CMRC.

Figure 2 illustrates the closed-loop supply chain model CRMRC. Model CRMRC has two members: the manufacturer and the retailer. The retailer engages in collecting of the used products. One characteristic of this channel format is that the ownership of used products initially rests with the retailer after the collection. To take the products back, the manufacturer must pay a transfer price per used product returned from the retailer.

Figure 2.

Model CRMRC

Full figure and legend (53K)

The forward supply chain of Model CRMRC is similar to Model CMRC.

In the reverse supply chain of Model CRMRC, the manufacturer will take back all the returned used products from the retailer with the unit transfer price b, and c<bc_m-c_rm. The retailer will pay a unit collecting price f to the end-customer for a used product, and the unit average operational cost of collecting a used product is c, including inventory cost, transportation cost, etc.

In this model, the manufacturer will decide the wholesale price to maximise its profit _M^CRMRC, and the retailer will decide the collecting price f of the used products and the retail price p of the new product to maximise its profit _R^CRMRC. Let ^CRMRC denote the total profit of Model CRMRC.

Figure 3 illustrates the closed-loop supply chain model CTMRC. Model CTMRC has three members: the manufacturer, the retailer and the third party. The third party engages in collecting the used products. One characteristic of this channel format is that the ownership of the used products initially rests with the third party after the collection. To take the used products back, the manufacturer must pay a transfer price per used product returned to her from the third party.

Figure 3.

Model CTMRC

Full figure and legend (51K)

The forward supply chain of Model CTMRC is similar to Model CMRC.

In the reverse supply chain of Model CTMRC, the manufacturer will take back all the returned used products from the third party with the unit transfer price b, and c<bc_m-c_rm. The third party should pay a unit collecting price f to the end-customer for a used product, and the unit average operational cost of collecting a used product is c, including inventory cost, transportation cost, etc.

In this model, the manufacturer will decide the wholesale price of the new products to maximise its profit _M^CTMRC, the retailer will decide the retail price p of the new product to maximise its profit _R^CTMRC and the third party will decide the collecting price f of the used products to maximise its profit _T^CTMRC. Let ^CTMRC denote the total profit of Model CTMRC.

According to our survey results, the following assumptions are postulated: (1) the return rate of the used products is an increasing function of the collecting price, =f^k, (0<1, >0, 0<k<1); (2) the manufacturer produces only one kind of product that is manufactured or remanufactured. Namely, there is no difference between the remanufactured products and the manufactured products; (3) the new product demand D(p) is a function of retail price, D(p)=-p, with and being positive parameters and >c_m; and (4) the manufacturer is the Stackelberg leader, and all the supply members share the same information.

OPTIMAL RESULTS

Proposition 1

In Model CMRC, the optimal value of the wholesale price ^*CMRC, the collecting price f^*CMRC and the retail price p^*CMRC are as follows:

In Model CMRC, the retailer's problem is

The objective function is concave in p as ²_R^CMRC/p²=-2<0. Hence, the retailer's first-order condition characterises the unique best response,

The derived demand function of the new products is given by D()=(-)/2.

The manufacturer's problem can be stated as

The objective function (3) is concave in and f. It is easy to obtain ^*CMRC and f^*CMRC by the manufacturer's first-order condition. Replacing with ^*CMRC in equation (2), p^*CMRCcan be obtained.

Proposition 2

In Model CRMRC, the optimal value of the wholesale price ^*CRMRC, the retail price p^*CRMRC and the collecting price f^*CRMRC are as follows:

In Model CRMRC, the retailer's problem is

The objective function (4) is concave in p and f, and hence, the retailer's first-order condition characterises the unique best response,

The derived demand function of the new products is given by D()=(-)/2+k^k(b-c)^k+1/(2(k+1)^k+1).

The manufacturer's problem can be stated as

The objective function (7) is concave in . We can obtain ^*CRMRC by the manufacturer's first-order condition. It is easy to obtain p^*CRMRC by substituting with ^*CRMRC into equation (5).

Proposition 3

In Model CTMRC, the optimal value of the wholesale price ^*CTMRC, the retail price p^*CTMRC and the collecting price f^*CTMRC are as follows:

In Model CTMRC, the retailer's problem is

Because the objective function (8) is concave in p, the retailer's first-order condition characterises the unique best response,

The derived demand function of the new products is given by D()=(-)/2.

The third party's problem can be stated as

The objective function (10) is concave in f, the third party's first-order condition characterises the unique best response,

The manufacturer's problem can be stated as

The objective function (12) is concave in . We can obtain ^*CTMRC by the manufacturer's first-order condition. Replacing with ^*CTMRC in equation (9), p^*CTMRC can be obtained.

In terms of the above propositions, the optimal values of the product demand and the profit of each Model are calculated. All the optimal values are listed in Table 1. Based on the optimal results summarised in Table 1, we obtain some propositions as shown below.

Table 1 - The optimal results of the closed-loop supply chain models.

Full table

Proposition 4

In Models CMRC, CRMRC and CTMRC, the collecting prices of the manufacturer, the retailer and the third party are related as follows: f^*CMRC>f^*CRMRC=f^*CTMRC, if b=c_m-c_rm, then f^*CMRC=f^*CRMRC=f^*CTMRC.

The proof of Proposition 4 can be easily obtained from the optimal values of f^* in Table 1.

Proposition 4 indicates that the collecting price of Model CMRC is the highest, and the quantity of the returned used products is the largest because the returned rate of the used products is an increasing function of the collecting price. Considering the unit cost saving of a remanufactured product, Model CMRC can save most manufacturing cost. Moreover, the collecting prices of Models CMRC, CRMRC and CTMRC are equal to each other if the manufacturer transfers all its cost saving to the retailer or the third party.

Proposition 5

In Models CMRC, CRMRC and CTMRC, the wholesale prices of the manufacturer are related as follows: ^*CMRC<^*CTMRC<^*CRMRC.

See Proof of Proposition 5 in the appendix.

As shown in Proposition 5, the wholesale price of the manufacturer in Model CMRC is the lowest. The reason is that the total cost saving of remanufacturing in Model CMRC is the largest among Models CMRC, CRMRC and CTMRC.

Proposition 6

In Models CMRC, CRMRC and CTMRC, the retail prices of the retailer are related as follows: p^*CMRCp^*CRMRC<p^*CTMRC. Consequently, D^*CMRCD^*CRMRC>D^*CTMRC.

See Proof of Proposition 6 in the appendix.

From Proposition 6, we can find that the retail price of the retailer in Model CMRC is the lowest. The reason is that the retail price is based on the wholesale price and the wholesale price of Model CMRC is the lowest. As a result, the product demand is the largest because the product demand is a decreasing function of the retail price.

Proposition 7

In Models CMRC, CRMRC and CTMRC, the profits of the manufacturer are related as follows: _M^*CMRC_M^*CRMRC>_M^*CTMRC, the profits of the retailer are related as follows: _R^*CMRC_R^*CRMRC>_R^*CTMRC and the total profits of the given model are related as follows: ^*CMRC*CRMRC>^*CTMRC.

See Proof of Proposition 7 in the appendix.

Proposition 7 shows us that, among Models CMRC, CRMRC and CTMRC, the profit of the manufacturer in Model CMRC is the highest, the profit of the retailer in Model CMRC is the highest and the total profit of Model CMRC is the highest. Obviously, Model CMRC is the optimal closed-loop supply chain model.

Comparing the closed-loop supply chain models with the collecting price, the wholesale price, the retail price and their profits, we find that it is the manufacturer who is the most effective undertaker of used-product collection activity. From the manufacturer's point of view, retailer for collecting is another choice if the manufacturer has determined to transfer all its cost saving to the retailer.

NUMERICAL EXAMPLE AND ANALYSIS

In this numerical example, let us assume that the potential market capacity of demand is 10,000 (unit: piece), the unit manufacturing cost c_m is 200 (unit: RMB), the unit remanufacturing cost c_rm is 100 (unit: RMB) and the operational cost of collecting c is 5 (unit: RMB). The parameters and are 40 and 0.03.

The impacts of k on the optimal results

The numerical results of the optimal values with variable parameter k are shown in Table 2 and Figure 4; herein, the transfer price b=40 (unit: RMB).

Figure 4.

The change of the optimal results with variable k(b=40)

Full figure and legend (158K)

Table 2 - The numerical results of the optimal values with variable parameter k(b=40).

Full table

From Table 2 and Figure 4, we can obtain the following implications.

1. In Models CMRC, CRMRC and CTMRC, the collecting price will become higher while the collecting price-sensitive coefficient k increases (see Figure 4 (i)). As a result, the quantity of the returned used products will become larger because the return rate of the used products is an increasing function of the collecting price. Considering the unit cost saving of remanufacturing, the total cost saving will increase because of the larger quantity of the returned used products. Moreover, it is in Model CMRC that the collecting price is the highest, the quantity of the returned used products is the largest and the total cost saving is the largest.
2. In Models CMRC, CRMRC and CTMRC, the wholesale price and the retail price will become lower while k increases (see Figure 4 (ii),(iii)). As a result, the new production demand will increase because it is a decreasing function of the retail price. Obviously, it is in Model CMRC that the wholesale price and the retail price are the lowest, and the new production demand is the largest.
3. In Models CMRC, CRMRC and CTMRC, while k increases, the manufacturer's profit will become higher (see Figure 4 (iv)), the retailer's profit will become higher (see Table 2) and the total profit will become higher (see Figure 4 (v)). In Model CTMRC, the third party's profit will become higher while k increases (see Table 2). We can easily find that it is in Model CMRC that the manufacturer's profit, the retail' profit and the total profit are the largest.
4. If one chooses to change Model CRMRC to Model CMRC, the increasing degree of the manufacturer's profit will become larger while k increases (see Figure 4 (vi)). If k is greater than and equal to 0.8, the increasing degree of the manufacturer's profit will be larger than 30 per cent.

The impacts of b on the optimal results

The numerical results of the optimal values with variable parameter b are shown in Table 3 and Figure 5; herein, the sensitive coefficient of the collecting price k=0.8.

Figure 5.

The change of the optimal results with variable b(k=0.8)

Full figure and legend (150K)

Table 3 - The numerical results of the optimal values with variable parameter b(k=0.8).

Full table

From Table 3 and Figure 5, we can obtain the following implications.

1. In Models CRMRC and CTMRC, the collecting price will become higher while the transfer price b increases (see Figure 5 (i)). As a result, the quantity of the returned used products will become larger and the total cost saving will increase. Nevertheless, it is in Model CMRC that the collecting price is the highest, the quantity of the returned used products is the largest and the total cost saving is the largest. Only if b is equal to 100, namely, the manufacturer transfers all his cost saving to the retailer or the third party, the collecting prices of Models CRMRC and CTMRC are equal to the collecting price of Model CMRC.
2. In Models CRMRC and CTMRC, the wholesale price will decrease first, and then increase when b increases (see Figure 5 (ii)). The retail price of Model CRMRC will decrease until it is equal to the retail price of Model CMRC (see Figure 5 (iii)). The retail price of Model CTMRC will decrease first, and then increase with increasing b (see Figure 5 (iii)). Nevertheless, it is in Model CMRC that the wholesale price and the retail price are the lowest, and the new production demand is the largest. Only if b is equal to 100, is the retail price of Model CRMRC equal to the retail price of Model CMRC, and the new product demand of Model CRMRC is equal to the new product demand of Model CMRC.
3. In Model CRMRC, the manufacturer's profit will increase when b increases until it is equal to the manufacturer's profit of Model CMRC (see Figure 5 (iv)), the retailer's profit will increase when b increases (see Table 3) and the total profit will increase when b increases until it is equal to the total profit of Model CMRC (see Figure 5 (v)). In Model CTMRC, while b increases, the manufacturer's profit will increase first and then decrease (see Figure 5 (iv)), the retailer's profit will increase first and then decrease (see Table 3), the third party's profit will increase (see Table 3) and the total profit will increase first and then decrease (see Figure 5 (v)). Nevertheless, it is in Model CMRC that the manufacturer's profit and the total profit are the highest. Only if b is equal to 100, are the manufacturer's profit and the total profit of Model CRMRC equal to the manufacturer's profit and the total profit of Model CMRC.
4. If one chooses to change Model CRMRC to Model CMRC, the increasing degree of the manufacturer's profit will become smaller while b increases (see Figure 5 (vi)). If b is smaller than and equal to 40, the increasing degree of the manufacturer's profit will be larger than 30 per cent.

CONCLUSION

In a closed-loop supply chain, the returned used products have a positive economic value; the manufacturer hopes to take back the used products as much as possible. But the return rate or return quantity is affected by the end-customer's willingness, and the end-customer's willingness needs monetary rewards called collecting price in this paper. At the same time, the wholesale price and the retail price are affected by the collecting price.

In this paper, we give the optimal collecting price of the reverse supply chain, the optimal wholesale price and the optimal retail price of the forward supply chain members based on the closed-loop supply chain models: Model CMRC, Model CRMRC and Model CTMRC. A numerical example is given.

In addition, we compare the optimal prices and the profits of the models. We find that the manufacturer is the best choice for collection, and the retailer is another choice for collection if the manufacturer has decided to transfer all its cost saving to the retailer.

The pricing decisions under incomplete information or information sharing of the closed-loop supply chain may be appropriate subjects for further investigation.

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Appendices

Appendix

Proof of Proposition 5

We divide the proof into two parts:

(i) To prove that ^*CMRC<^*CTMRC

Note that,

^*CTMRC is an increasing function of b when b>[k(c_m-c_rm)+c]/k+1, which is true by ^*CTMRC/b>0, ^*CTMRC is an decreasing function of b when b<k(c_m-c_rm)+c/k+1, which is true by ^*CTMRC/b<0, and ^*CTMRC takes its minimum value (we note that Min^*CTMRC) at the point of b=[k(c_m-c_rm)+c]/(k+1) and Min^*CTMRC=(+c_m)/(2)-[k^k(c_m-c_rm-c)^k+1/(2(k+1)^k+1)] (k/(k+1))^k.

To prove that ^*CMRC<^*CTMRC, we have to show

which holds by 0<k<1. Hence, ^*CMRC<^*CTMRC.

(ii) To prove that ^*CTMRC<^*CRMRC

The proof of ^*CTMRC<^*CRMRC can be easily observed from Table 1.

Proof of Proposition 6

We divide the proof into two parts:

(i) To prove that p^*CMRCp^*CRMRC, we have to show that

We note,

In order to prove k^k(c_m-c_rm-c)^k+1/(4(k+1)^k+1) [(c_m-c_rm-b)/4+(b-c)/(4(k+1))]k^k(b-c)^k/(k+1)^k, we have to show that (b) is an increasing function of b and the max value of (b) is k^k(c_m-c_rm-c)^k+1/(4(k+1)^k+1). The former holds by (b)/b=[k^k(b-c)^k+1/(4(k+1)^k+1)(k+1)(c_m-c_rm-b)>0, and the latter is true by 0<b<(c_m-c_rm) and (c_m-c_rm)=k^k(c_m-c_rm-c)^k+1/4(k+1)^k+1. Hence, p^*CMRCp^*CRMRC.

(ii) To prove that p^*CRMRC<p^*CTMRC

The proof of p^*CRMRC<p^*CTMRC can be easily observed from Table 1.

Because the ordering for the retail price p^* holds, the ordering for the demands of the channels follows trivially.

Proof of Proposition 7

We divide the proof into three parts:

(i) The proof of _M^*CMRC_M^*CRMRC>_M^*CTMRC

From the proof of p^*CMRCp^*CRMRC<p^*CTMRC, we can obtain

Note that >0; we can show

and

Hence, _M^*CMRC_M^*CRMRC>_M^*CTMRC.

(ii) The proof of _R^*CMRC_R^*CRMRC>_R^*CTMRC

In a manner similar to that in the proof of _M^*CMRC_M^*CRMRC>_M^*CTMRC, we can easily prove that _R^*CMRC_R^*CRMRC>_R^*CTMRC.

(iii) The proof of ^*CMRC*CRMRC>^*CTMRC

Obviously, ^*CMRC*CRMRC holds by _M^*CMRC_M^*CRMRC, _R^*CMRC_R^*CRMRC, ^*CMRC=_M^*CMRC+_R^*CMRC, and ^*CRMRC=_M^*CRMRC+_R^*CRMRC.

Easily, ^*CRMRC>_R^*CTMRC is true by

Hence, _M^*CMRC_M^*CRMRC>_M^*CTMRC.

Acknowledgements

The authors would like to thank the referees for the constructive suggestions, which have led the authors to consider more deeply the motivation, modelling and implications of the model. This work was supported by the Ministry of Education Project of Humanities and Social Sciences of China under Grant No. 02JAZ790007 and China Postdoctoral Science Foundation under Grant No. 20060390626.