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Closed-loop supply chain coordination strategy for the remanufacture of patented products under competitive demand
Accepted Manuscript
Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands Cheng-Tang Zhang , Ming-Lun Ren PII: DOI: Reference:
S0307-904X(16)30070-1 10.1016/j.apm.2016.02.006 APM 11032
To appear in:
Applied Mathematical Modelling
Received date: Revised date: Accepted date:
13 July 2013 15 January 2016 3 February 2016
Please cite this article as: Cheng-Tang Zhang , Ming-Lun Ren , Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands, Applied Mathematical Modelling (2016), doi: 10.1016/j.apm.2016.02.006
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Highlights
Compare of the prices, performances of supply chain systems, etc. under two models.
Investigate the combined coordinated pricing mechanism of a revenue-and-expense sharing contract and
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two-part tariffs.
Provide a reasonable range for the sharing coefficient and agency fees.
Perfect coordinate the closed-loop supply chain of patented products
Study the impact that substitute ratio, salvage value, coordination parameters, etc. have on supply chain
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decisions and performance.
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Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands Cheng-Tang Zhang a,b,*, Ming-Lun Ren b a
Institute of Science, Anhui Agricultural University, Hefei 230036,P.R.China
b
School of Management, Hefei University of Technology, Hefeii 230009,P.R.China
*Corresponding author. Tel: +86 55165786164 E-mail address: [email protected] (C.-T. Zhang)
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Abstract: The paper studies a closed-loop supply chain (CLSC) system that consist of an original manufacturer, a third-party remanufacturer and a retailer. In the system, the remanufacturer can only recycle and remanufacture the patented products with the patent licensing from the original manufacturer; new manufactured and remanufactured products are sold together in the same market at different prices; the demand for the two types of products is sensitive to the retail prices. Firstly, we establish a leader-follower game model and a joint decision-making model, and make comparison of the CLSC members’ performance, e.g., collection price, selling prices and profits. Secondly, we investigate
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contract coordination issues among the three parties in the decentralized case, and develop a coordinated pricing mechanism that incorporates revenue-and-sharing contract and two-part tariffs can perfectly coordinate the CLSC. Accordingly, a reasonable range for the sharing coefficient and agency fees for qualifications can be identified. Finally, through some numerical examples, we analyze the impact that the salvage value, substitute ratio, coordination parameters and so on have on the optimal supply chain performance.
Key words: closed-loop supply chain; patented products; pricing; coordination
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1. Introduction
Due to the increasing concerns on environment and awareness of natural resource limitation in recent years , many
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countries have intensified their legislative efforts with regard to the environment and resources protection (e.g., [1]), giving rise to widespread concern in the industry for the collection and remanufacture of used items (e.g.,
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[2-4]). Many enterprises, such as Hewlett-Packard and Kodak, have sensed that the collection of used products will enable substantial savings in manufacturing costs as well as elevation of their social prestige and economic
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benefits, creating a closed-loop responsive supply chain in a “resources-production-consumption-renewable resources” looping sequence (e.g., [5]). This process reduces the resources initially acquired along with the garbage eventually produced, and contributes to the realization of coordinated development of economy and
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environment for the manufacturer. It is, therefore, of positive significance to the sustainable development of the society. For reasons of cost or brand, the original manufacturer may not engage in the collection and remanufacture of used items, thus leaving the work to third-party manufacturers. And this inevitably brings certain competitive threat to the new manufactured item by the original manufacturer (e.g., [6]). Accordingly, the original manufacturer may ease such threat of third-party manufacturers by charging patent licensing fees. In addition, the remanufacture of patented products involves the licensing issues of patented technologies, so patent license is not only a factor to be considered in the decision-making of enterprises regarding remanufacture, but also an issue to be taken seriously in remanufacture supply chain studies. Pricing decisions with regard to product sales and recovery are critical in closed-loop supply chain
ACCEPTED MANUSCRIPT management, as they directly affect the supply and demand of products as well as the operational efficiency of CLSC. Therefore, the pricing of CLSC has become an important issue that attracts much academic attention in recent years. Savaskan et al. [7] studied the pricing strategy and channel efficiency of different collection structures in CLSC. However, by assuming the quantities of returned items is proportionate to the market demand for products, their study did not take into account the impact that collection price has on the quantities of returned items and the collection price was considered as an exogenous variable, which is inconsistent with the reality. El Saadany and Jaber [8] suggested that the quantity of returned items is controlled by price and quality, and
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presented for multiple remanufacturing and production cycles. As sales price of used items follows a geometric Brownian motion, Liang et al. [9] proposed a centralized model to evaluate the acquisition price of used items. Wei and Zhao [10] investigated the optimal wholesale and retail prices of CLSC under the competition of retailers using the game theory and fuzzy theory. Shi et al. [11] assumed that the selling prices of new manufactured and remanufactured items are the same while demand correlates with price, and examined the two types of products
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with regard to their production quantity, selling price and collection price of used items. However, the market price of remanufactured items is in fact always different from that of manufactured items. The demands for the two types of products are not the same either.
There are relatively few studies focusing on the coordinated pricing of CLSC. Based on game theory, Yi and Yuan [12] studied the CLSC system under hybrid collection mode, and analyzed the impact that hybrid collection
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mode has on pricing and profits. Then they adopted a two-part tariff to improve the performance of the whole CLSC. However, as a leader of the channel, the manufacturer will obtain all of the excess profits generated after
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cooperation, while the retailer only gets the profits under decentralized decision-making. Shen and Xiong [13] based their study on the assumption that the manufactured and remanufactured items are homogeneous and the market demand is a linear function of price. They discussed that the coordination of CLSC can be realized through
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the collection and remanufacture of patented products, analyzed the pricing decision-making CLSC members, and proposed a revenue-and-expense sharing contract to control the sharing ratio through negotiations. However, the
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literature did not discuss the situation where new manufactured and remanufactured items compete in the same market. In addition, CLSC was studied with regard to the pricing strategy and system performance in different
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collection channels, modes (e.g., [14, 15]) and collection efficiencies (e.g., [16, 17]). Despite the fact that many studies investigated pricing and coordination in CLSCs, there are some research
issues that have not been addressed yet, such as:
Competition amongst products.
Remanufactured and manufactured items are of different prices, with the first being of a lower price.
Remanufactured items with salvage value or stockout penalty cost should be considered.
Revenue-and-expense sharing contract has not been reported in literature; perfect coordination cannot be achieved with a two-part tariff alone. In view of the above, pricing and coordination model of CLSC system under patent licensing will be
established. The paper focuses on the following issues:
ACCEPTED MANUSCRIPT Examine the difference in sales between manufactured and remanufactured items, and study how competition
between them in a market affect supply chain performance. Compare of the selling and collection prices of products by each supply chain member, and determine the
performance of the supply chain system, etc., under a leader-follower game and joint decision-making model. Explain why a decentralized CLSC cannot be perfectly coordinated by a revenue-and-expense sharing
contract. Investigate the combined coordinated pricing mechanism of a revenue-and-expense sharing contract and
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two-part tariffs. Study the impact that substitute ratio, salvage value, market base and coordination parameters have on supply
chain decisions and performance.
2. Problem description
This paper considers a CLSC with an original manufacturer, a third-party remanufacturer and a retailer. The
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original manufacturer (hereinafter referred to as the “Manufacturer”) that owns patent rights to the new manufactured item, takes advantage of its proprietary rights to authorize the work to the third-party remanufacturer and provide technical support, staff training, etc.. However, it does not engage in the collection and remanufacture of used items. There are many similar cases in the manufacturing industry, such as engine remanufacturing and hydraulic pump remanufacturing. The third-party remanufacturer is a manufacturer apart
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from the Manufacturer that engages in product collection and remanufacture(the “Remanufacturer”). The Remanufacturer conduct product collection and remanufacture of used items as well as sales of remanufactured
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items with license from the Manufacturer and payment for patent licensing fees. It would be sued for both a tort liability and a breach of contract if the Remanufacturer involves in remanufacture of patented products without
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payment for patent licensing fee. For example, “Cotton-Tie Co. v. Simmons, 1882” and “Sandvik Aktiebolag v. E.J. Co., 1997” are good cases in point.
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Customers’ demands can be satisfied by two alternative ways: purchase of new products manufactured by the Manufacturer with original raw materials, or purchase of remanufactured items by the Remanufacturer with collected used items. Both of the two types of the products with same function are sold by the Retailer together in
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the same market, while the differences between of them lie in price and recognition. 2.1.
Notations and assumptions
The following notations defined in Table 1 are used in the model for the production and pricing problem:
ACCEPTED MANUSCRIPT Table 1 Notations Definition
cn
Manufacturing cost of a manufactured item
cs
Manufacturing cost of a remanufactured item
wn
Wholesale price of a manufactured item charged by the Manufacturer
ws
Wholesale price of a remanufactured item charged by the Remanufacturer
pn
Price of a manufactured item charged by the Retailer
ps
Price of a remanufactured item charged by the Retailer
b
Price of collecting a used items charged by the Remanufacturer
f
Unit patent licensing fee for authorization of the Remanufacture charged by the Manufacturer ( i 1, 2 )
Market base
v
Unit salvage value or unit stockout penalty cost
(b)
Return quantity of used items
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i
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Parameter
Hereinto, wn and f are the decision variables of the Manufacturer, ws and b are the decision variables
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of the Remanufacturer (the Remanufacturer determines on the collection price and collects used items directly from the customers), p n and p s are the decision variables of the Retailer. Moreover, the remanufacturing cost,
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c s , does not include the cost of buying back used items or the patent licensing fees for authorization of the
management costs.
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Remanufacture, but includes the costs of dismantling, quality assurance, components, remanufacturing and other
The following assumptions are made to develop the subsequent model
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Assumption 1. The CLSC decisions are considered in a single-period setting. We assume some products sold in the previous periods can be recycled. The Remanufacturer buys back the used items from the customers at the unit
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collection price b . Suppose that all used items purchased are to be remanufactured, so the remanufacturing rate would be 1. There is substitution relationship between new manufactured and remanufactured items. The similar forms of this assumption have been used in the sample (e.g., [18, 19]). Assumption 2. We assume that new manufactured and remanufactured items make a competitive market. The new manufactured items demand Dn ( pn , p s ) is a function of retail prices Dn ( pn , p s ) 1 pn p s , with
1 , and being non-negative parameters and 1 cs cn ;The remanufactured items demand Ds ( pn , p s ) is expressed as
Ds ( pn , ps ) 2 ps pn ,with being positive parameter and
ACCEPTED MANUSCRIPT 2 cn cs . Hereinto,
1 and 2 are market base ( 1 2 ), which denote respectively the primary demand of
manufactured and remanufactured items, items is relatively lower than that of
2 1 indicates that customers’ recognition of the remanufactured
the new manufactured items; denotes the measure of the responsiveness
of retailer’s market demand to his own retail price, and the value of
rely on many factors, including social
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factors, economic factors and psychological factors, is the substitute ratio of two types of product (when 0 , the market demands for manufactured and remanufactured items are only related to their own retail price), whereas indicates that one type of product’s own price effect is greater than the cross-price effect (e.g., [20],[21]).
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Assumption 3. The demand of manufactured items may be different from that of remanufactured items, so with reference to Jaber & El Saadany [18] we assume that there is no surplus manufactured item, and the demand of remanufactured items depends on retail price and customers’ recognition of the remanufactured items. On the one hand, customers’ low recognition of the remanufactured items gives rise to the relatively low market demand for of remanufactured items. Therefore, we can assume that remanufactured items are in excessive supply. For the items”, the Remanufacturer will obtain certain unit salvage value v , and
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“unsold remanufactured
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v cs b f to ensure that the Remanufacturer is motivated to collect and remanufacture returned items. In addition, let v ws p s , so that the Remanufacturer sells the remanufactured items aggressively.
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On the other hand, if the remanufactured items are in exceed supply, the parameter v will be correspondingly regarded as a unit stockout penalty cost.
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Assumption 4. The return quantity of used items depends on the price of collecting a used items charged by the Remanufacturer,
the
relationship
between
return
quantity
and
price
is
known
as
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(b) 0 1b ( 0 0 , 1 0 ). The parameter 0 is the quantity of volunteer to return used items from customers (a fraction of the produced quantity), and another level as a measure of environmental awareness (e.g., [22]);
1 is the price sensitivity of customers for collection price offered by the Remanufacturer.
Assumption 5. Other rational assumptions: cn c s , wn ws , pn p s , b cn c s . 2.2.
Pricing decision-making model In this subsection, we will present two pricing models: Model TLG (i.e., three-level leader-follower game
model) and Model JD (i.e., joint decision-making model), and analyze the optimal strategies of the two models., In our leader-follower non-cooperative game, the Manufacturer will act as the leader to decide how much the
ACCEPTED MANUSCRIPT wholesale price of manufactured item and the patent licensing fees would be optimal. The Remanufacturer and the Retailer all act as the followers and will make the best response according to the Manufacturer’s decision. Note, the Remanufacturer and the Retailer are in the different flows (the former is in the forward chain and the latter is in the closed-loop chain), so they act as Stackelberg game. Subsequently we develop the joint decision-making model described below as a benchmark case for purposes of comparison. 2.2.1. Model TLG If the Remanufacturer is granted the patent license to conduct product collection and remanufacture, then
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under competitive demand of manufactured and remanufactured items, the Manufacturer, the Remanufacturer and the Retailer all act in their own best interests and seek the way to maximize their respective profits. In the three-level leader-follower game, the sequence of moves is given as follows: Firstly the leader (the Manufacturer) will make best decision and announce a wholesale price of new manufactured item wn and a patent licensing
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fees f to maximize his own profit; then in response to the Manufacturer’s decision wn and f ,the follower (the Remanufacturer) will determine the wholesale price of remanufactured item ws and the collection price of used items b ; finally, according to the above decision wn and ws , the other follower (the Retailer) will make best
wn
Manufacturer
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response and determine the retail prices p n and p s . The pricing decision-making model is depicted in Fig.1. pn , ps
Customers
Retailer
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ws
f
Remanufacturer
Reverse Logistics
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Forward Logistics
b
Fig. 1. Framework of CLSC for remanufacture with patent license.
T and R denote the profits of the Manufacturer, the Remanufacturer and the Retailer respectively,
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Let M ,
we get the Manufacturer’s profit function as follows
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M (wn , f ) (wn cn ) Dn f (b) (wn cn )(1 pn ps ) ( 0 1b) f
(1)
The Remanufacturer’s profit is
T (ws , b) (ws cs ) Ds b(b) v[(b) Ds ] f (b) (ws cs )( 2 ps pn ) v[ 0 1b 2 ps pn ] (b f )( 0 1b)
(2)
and the Retailer’s profit is
R ( pn , p s ) ( p n wn ) Dn ( p s ws ) Ds ( p n wn )( 1 p n p s ) ( p s ws )( 2 p s p n )
(3)
ACCEPTED MANUSCRIPT According to the above description about Model TLG, this can be expressed as
( L) : max ( w , f ) M n wn , f T ( ws , b ) s.t.( F1) : max ws ,b s.t.( F 2) : max R ( p n , p s ) pn , p s The above game model is solved using backward induction.
conditions of the maximization problem of the Retailer
R pn 0 , R p s 0 .
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First of all, with respect to Eq. (3), we can solve the following simultaneous equations from the first-order
Therefore, the best response function of the Retailer can be given as follows
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1 2 wn ~ 1 2 ws ~ pn , ps . 2 2 2( ) 2 2( 2 2 ) 2
(4)
Then, substituting Eq. (4) into Eq. (2), similar to the above, the Remanufacturer’s best response can be obtained from the Eq. (2)
0 1 v f） ~ 2 wn v c s ， b~ （ . w s 21 2 2
(5)
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Given the Retailer and the Remanufacturer’s response Eqs. (4) and (5), the Manufacturer solves
~ max M (wn , f ) max[(wn cn )(1 ~ pn ~ p s ) ( 0 1b ) f ] wn , f
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wn , f
to determine the optimal pricing *
(v c s ) (21 2 ) cn 1v ，f* 0 . 2 2 2 21 2(2 )
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wn
(6)
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Therefore, the optimal pricing of the Remanufacturer and the Retailer can be derived from simultaneous Eqs. (4), (5) and (6).The optimal wholesale price and collection price offered by the Remanufacturer are
v 3 0 （ 2 v c s )(4 2 2 ) 2 1 cn * ws , b 1 2 2 41 4 4 (2 )
(7)
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*
and the optimal retail price of manufactured and remanufactured items are
pn
1 2 cn (v c s ) (21 2 ) . 2( 2 2 ) 4 4(2 2 2 )
(8)
ps
1 2 cn （ 2 v c s )(4 2 2 ) 2 1 . 2( 2 2 ) 8 8 ( 2 2 2 )
(9)
*
*
* Thus, the sum of CLSC members’ profit in Model TLG, denoted as , can be presented
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*
*
Based on the equilibrium results of Model TLG, we can obtain some propositions as shown below. Proposition 1. When the level of environmental awareness of the customers, 0 , changes in Model TLG, we find (i) The collection price b * negatively correlates with 0 ; (ii) The patent licensing fees f , the Manufacturer’s profit M and the Remanufacturer’s profit T *
*
*
positively correlate with 0 , while the Retailer’s profit R remains unchanged. Proof. Since b * 0
is decreasing in
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*
3 1 0 and f * 0 0 , this simply implies that the collection price b * 41 21
0 and yet the patent licensing fees f * is increasing in 0 . As is known from the equilibrium
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results of Model TLG, the wholesale price and retail price of the product is constant for 0 . Correspondingly, the Retailer’s profit remains the same. Moreover, M
*
0
0 1v 1v * 0 and T 0 0 0. 41 81
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Hence it can be concluded that the profits of the Manufacturer and the Remanufacturer increase as 0 increases.□ The conclusions of Proposition 1 indicate that the enhancement of customers’ environmental awareness helps
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to save collection costs of the enterprises, increases the profits of the Manufacturer and the Remanufacturer, and enhances the initiative of the enterprises to conduct collection and remanufacture, thus advancing CLSC members to acquire positive social externalities. The profit of the Retailer is not affected by the quantity of used items that
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customers voluntarily return. Accordingly, the government may intensify their efforts in promotion of environmental protection and relevant legislation in order to elevate the level of the environmental awareness of
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the customers, increase the social responsibilities of the enterprises, and advance the sound development and stable operation of CLSC.
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2.2.2. Model JD
As a benchmark to evaluate the channel decision under different decision models, we examine a joint
decision case, in which one entity made up of the three parties to optimize the whole system performance. This means the cooperation of all members in a centralized system with a central planner/decision-maker, which is common in traditional supply chain. So in our research, we consider the joint decision system as the “centralized” system (Fig.2).
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Manufacturer
pn , ps Customers
Remanufacturer
b Retailer
Forward Logistics
Reverse Logistics
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Fig. 2. Framework of CLSC under joint decision-making model.
The Manufacturer’s wholesale price wn , patent licensing fees f and the Remanufacturer’s wholesale price
ws are seen as inner transfer prices, which influence the profits of each participant, but they do not affect the whole system’s strategies and profit. Thus, from Eqs. (1)-(3), we can easily get the total system profit equation.
J ( pn , ps , b) M T R ( pn cn ) Dn ( ps cs ) Ds b(b) v[(b) Ds ]
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(10)
We know that the objective of the joint decision case is to maximize the system profit J ( pn , p s , b) , which can be denoted as follow
max J ( p n , p s , b) max [( p n cn ) Dn ( p n , p s ) ( p s c s ) Ds ( p n , p s )
p n , p s ,b
p n , p s ,b
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b(b) v((b) Ds ( p n , p s ))]
From the first-order conditions, the optimal retail prices and the optimal collection price are given as follows
v 0 1 2 cn 2 v c s , ps 1 2 , b 1 . 2 2 2 2 21 2( ) 2 2( )
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pn
(11)
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Accordingly, the optimal profit of the CLSC system in Model JD can be expressed by
Where, Dn
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J ( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ] .
1 pn p s
and Ds
2 p s pn , and (b ) 0 1b
(12)
0 1v 2
.
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Proposition 2. Compare the results in Model TLG and Model JD. It is obvious that b * b , p n p n , *
p s p s , and * . *
Proof. By the comparison of the optimal results under the two models, we can easily obtain Proposition 2.□ From Proposition 2, we have some obvious but important observations. The CLSC system has the advantage of resources integration in Model JD, which will enable the central decision-maker to obtain more used items with higher collection price, and sell more products in the market with lower retail price. Therefore, the system profit will reach the highest level in the Model JD with relevant equilibrium results strictly better than those in Model TLG. It is clear that CLSC system is better off through all members’ cooperation.
ACCEPTED MANUSCRIPT In this joint decision-making model, the central decision-maker focuses on improving coordination and integration of distinct activities, such as technical collaboration, patent-licensing arrangement, product-process (manufacturing, remanufacturing, distribution, transportation, etc.) integration and information sharing, within a framework of collaborative inter-enterprise. As an example, it is possible to reduce the transportation costs of returned items when the new manufactured items are delivered to the same client in the area. Thus, the chain members will obtain real benefits resulting from the double-edged impact of increased market share on a lower asset base. In the next section, we will discuss how to distribute the system profit remained and obtain the best
3. Combined coordinated pricing mechanism
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feasible Pareto efficiency.
When the benefits of the three members’ cooperation are shared among them, some mechanism is needed to balance the benefits among the membership so that the coalition remains intact and the benefits of their cooperation are obtained. Accordingly, a pricing mechanism incorporating revenue-and-expense sharing contract
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and two-part tariffs are conceived, which can achieve the system coordination and the individual perfect coordination. It is obviously a motivate mechanism. In other words, if the chain members accept this mechanism and report truthfully the cost/revenues, the mechanism must ensure the member’s profit is not lower than the profit level in Model TLG. Correspondingly, the individual’s optimal decision in Model TLG must be consistent with the system’s optimal decision in Model JD.
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3.1. Revenue-and-expense sharing contract
Due to product collection expenses, traditional revenue sharing contract is unable to achieve CLSC
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coordination. It has been upgraded to a revenue-and-expense sharing contract and used to coordinate the CLSC with single collection channel in recent years by several scholars. Revenue-and-expense sharing refers to the
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sharing of profits, losses and external expenses (e.g., collection expenses) among the CLSC members. As an example, on the basis of a revenue-and-expense sharing contract, a high-tech enterprise providing digital products
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can share revenues, advertisement expenses and collection expenses with its retailer. That is to say, the Manufacturer not only shares with the Retailer the revenue from the sales of the products, but also the expenses for collection used items per the same ratio. Therefore, the CLSC for collection and remanufacture with patent
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license will be investigated using the revenue-and-expense sharing contract. Assume that the Manufacturer, the Remanufacturer and the Retailer share salvage value of the
Remanufacturer and sales revenue of the Retailer as well as collection expenses of used items according to respective ratios:
1 , 2 and 1 1 2 . With regard to f (b) , patent licensing fees of the Manufacturer, they
are not counted as to be shared, as they are internal expenses of the entire supply chain, just like the wholesale expenses of product. Therefore, the respective profits of the Manufacturer, the Remanufacturer and the Retailer are
M 1{ pn Dn ps Ds b(b) v[(b) Ds ]} (wn cn ) Dn f (b).
(13)
ACCEPTED MANUSCRIPT T 2 { pn Dn ps Ds b(b) v[(b) Ds ]} (ws cs ) Ds f (b).
(14)
R (1 1 2 ){ pn Dn ps Ds b(b) v[(b) Ds ]} wn Dn ws Ds .
(15)
From the first-order conditions, the Retailer decides the retail prices p n , p s and the collection price b as follows.
wn 2(1 1 2 )
(1 1 2 )v ws 1 2 v 0 1 2 f ， pˆ s ， bˆ 1 . (16) 2 2 2 2 2(1 1 2 ) 21 2 2 2( ) 2( )
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pˆ n
By comparing Eqs. (16) and (11), it can be inferred that if the optimal pricings for the Manufacturer and the Remanufacturer are
wn (1 1 2 )cn , ws (1 1 2 )cs , f 0 .
(17)
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Then p n p n , p s p s , b b , which means the entire CLSC system achieves the optimal prices of joint decision-making model.
As is shown in Eq. (17), the optimal pricing results, upon agreement on a revenue-and-expense sharing contract, the Manufacturer will not charge patent licensing fees from the Remanufacturer. The Manufacturer and
the Remanufacturer will wholesale their products to the Retailer at low prices ( wn and ws ), thus enabling low
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retail price under joint decision-making as well as more market share and competitiveness of the product (either manufactured items or remanufactured ones). The customers will also enjoy more benefits with no doubt. The
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three parties of the supply chain ensure their profits through sharing salvage value of the Remanufacturer and sales income of the Retailer. At this point, the profit of the Manufacturer is
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M 1{ p n Dn p s Ds b (b ) v[(b ) Ds ]} （1 2 )cn Dn 0 (b )
1{( p n cn ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} ( 2 cn Dn 1c s Ds ) 1 1 J [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] . 2
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(18)
The profit of the Remanufacturer is
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T 2 { p n Dn p s Ds b (b ) v[(b ) Ds ]} （1 2 )c s Ds 0 (b )
2 {( p n c n ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} ( 2 c n Dn 1c s Ds ) .(19) 1 2 J [(1 c s 2c n )(v c s ) 2 c n ( 1 c n ) 1c s ( 2 c n )] 2
The profit of the Retailer is
R (1 1 2 ){ p n Dn p s Ds b (b ) v[(b ) Ds ]}
（1 1 2 )c n Dn （1 1 2 )c s Ds
(1 1 2 ){( p n c n ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} (1 1 2 ) J
.
(20)
ACCEPTED MANUSCRIPT The above results show that the sum of profits of the Manufacturer, the Remanufacturer and the Retailer reaches its optimal level under joint decision-making:
M T R J . Therefore, a revenue-and-expense sharing contract enables global coordination of the supply chain system. However, as is shown in the profit function expressions of the Manufacturer and the Remanufacturer, profits earned by the Remanufacturer are higher than the sharing ratio of revenue-and-expense sharing contract. It is indicated that the profits of the Manufacturer is not maximized due to differentiated competition of products and
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lack of patent licensing fees. As leader of the CLSC, the Manufacturer will endeavor to pursue profit maximization. 3.2. Two-part tariffs
A two-part tariff is a pricing mechanism according to which the buyer pays to the seller a fixed fee and a constant charge for each unit purchased (see [23]). The following items could be identified as two-part tariffs:
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loyalty cards or clubs, credit cards which charge an annual fee plus a per-transaction fee, “membership discount retailers” such as shopping clubs that charge an annual fee for admission to the point of sale and also charge for purchases.
In our framework, the per-unit payment can be also viewed as a per-unit patent licensing fee. Further, a two-part tariff can be used as a vehicle for manipulating the incentives given to the buyers, allowing also the
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sellers to capture part of the residual surplus through an appropriately chosen fixed fee. In this subsection and the next, the fixed fee can be viewed as an agency fee for qualification obtained.
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On basis of the above, in the event that revenue-and-expense sharing contract enables global coordination of the supply chain system, the closed-loop supply chain can be perfectly coordinated using two-part tariffs as below:
PT
M 1{ pn Dn ps Ds b (b ) v[(b ) Ds ]} （1 2 )cn Dn 0 (b ) H .(21)
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T 2 { pn Dn ps Ds b (b ) v[(b ) Ds ]} （1 2 )cs Ds 0 (b ) H . (22) Where H is the agency fee for qualifications of the Remanufacturer to conduct product collection and remanufacture during a certain period. According to Eqs. (18) and (19), the Remanufacturer only has to decide the
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agency fee for qualifications as showing below
1 H ** [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] . 2
(23)
Then under the combined coordinated pricing model that combines revenue-and-expense sharing contract
and two-part tariffs (marked as “Model MC”), the respective optimal profits of the Manufacturer, the Remanufacturer and the Retailer are
M ** 1{( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ]} 1 J .
(24)
T ** 2 {( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ]} 2 J .
(25)
ACCEPTED MANUSCRIPT R ** (1 1 2 ){( p n cn ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} (1 1 2 ) J
.
(26)
At this point, the profits of the Manufacturer are increased. The Manufacturer, the Remanufacturer and the Retailer share profits of the entire CLSC according to the respective ratios: 1 , 2 and 1 1 2 . Therefore, the optimal total profit in the Model MC, denoted as ** , can be presented as
**
**
**
**
**
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Provided that supply chain members are subject to individual rationality constraints: M
T ** T * and R ** R * , which means on basis of ensuring
1 J M * , 2 J T * , (1 1 2 ) J R * . Choosing appropriate values for
M T R J . M , *
(27)
1 and 2 will enable global coordination of supply chain system and perfect
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coordination of supply chain members. It can be derived from Eq. (27) that the respective reasonable ranges for 1 ,
2 and 1 1 2 are
1 and 2 depend on the bargaining power of the three parties of the supply chain. M * R* M* T * R* T * 1 1 , , and 1 2 J J J J
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The values of
M
M * R* R* M * T* M* T * R* T * 1 1 ， 2 1 ， 1 1 2 1 . J J J J J J
Proposition 3. Under conditions that
PT
R* M * T* 1 1 , if the respective pricing mechanisms for the Manufacturer, the 1 2 J J
**
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Remanufacturer and the Retailer are ( wn , f , H ) , ( ws , b ) and ( p n , p s ) , the CLSC system is perfectly coordinated with Model MC.
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Where
1 wn (1 1 2 )cn , f 0 , H ** [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] , 2
ws (1 1 2 )cs , b
1v 0 1 2 cn 1 2 v c s p , pn , . s 21 2 2( 2 2 ) 2 2( 2 2 )
Proof. Based on the above-mentioned analysis, we can easily obtain Proposition 3.□ Proposition 3 shows that the wholesale price has to be lower than manufacturing cost, exactly to achieve the maximum channel profit. It uncovers the lure of combined coordinated pricing mechanism in the decentralized case. Thus, the Manufacturer, the Remanufacturer and the Retailer are driven by profit motives to maximize theirs
ACCEPTED MANUSCRIPT own as well as the channel profit. Within the range of individual rationality constraints, the chain members can share the optimal total profits of CLSC system with each other by way of sharing per certain ratios. It also highlights the importance of a reasonable distribution of channel profits in channel management. Proposition 4. By comparing the results in Model TLG and Model MC, the following conclusions can be drawn.
(i) wn wn , ws ws , p n p n , p s p s , b * b ; *
*
*
*
(ii) M M , T * T ** , R R , * ** . *
**
*
**
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As stated in the above proposition, the Manufacturer offers a combined coordinated pricing mechanism for making the retail prices of the products equal to the centralized channel prices level, thereby overcoming inefficiencies because of double marginalization. Therefore, the performances of the whole system and the supply chain members under Model MC are significantly better than those under Model TLG. That is to say, the combined coordinated pricing mechanism enables the multi-win of CLSC members.
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4. Numerical examples
Some numerical examples are presented to illustrate the optimization problem and used to gain some insight into the CLSC system.
Example 1 In this example, we examine the effect of on the equilibrium results of Model TLG and Model JD. The selected parameters values should satisfy the assumptions mentioned in Subsection 2.1, assume that the
1 400 , 2 100 , 0 10 , 1 2 and 1 .
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parameters values for cn 60 , c s 20 , v 80 ,
The optimal solutions for example 1 are b * 16.25 , f
*
42.5 and b 37.5 , then given different values
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of , the outcome is shown in Table 2. Table 2
*
( pn , pn )
*
( ps , ps )
CE
PT
Equilibrium results of Model TLG and Model JD under different substitute ratio of demand
( Dn , Dn )
( Ds , Ds )
( M , T , R )
( * , J )
*
*
*
*
*
(325, 237)
(126, 120)
(87, 175)
(6, 3)
(17222,973,7886)
(26081,34662)
0.3
(364, 266)
(190, 170)
(93, 185)
(19, 9)
(19988,1635,11118)
(32741,42409)
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0.1
0.5
(443, 330)
(286, 250)
(99,195)
(36, 15)
(24379,3479,19641)
(47499,58513)
0.7
(631,490)
(482,422)
(106, 205)
(59,21)
(31669,8036,46503)
(86208,98697)
0.9
(1510,1319)
(1360,1260)
(113, 215)
(99, 27)
(45165,20664,226840)
(292669,305730)
As is shown in Table 2, under competitive demand for manufactured and remanufactured items, the bigger the substitute ratio of demand is, the bigger customer demand’s reaction to price change of competing product is. The demand for the product increases as the price of substitutable product increases (either Model TLG or Model JD). As a result of the interactive effects of competition, the market demands and selling prices of manufactured and remanufactured items also increase accordingly. Therefore, the profits of corresponding members and system profits increase as product substitutability increases. And system profit in Model JD is remarkably higher than that
ACCEPTED MANUSCRIPT in Model TLG. Since the Retailer is in closest proximity to the consumer market, the substitute ratio of demand affects it the most. Let =0.5 in the following numerical examples in order to reflect generality. Example 2 In this example, we examine the effect of v on the optimal results of Model TLG and Model JD. We set 0.5 , and other parameter values the same as those in Example 1. Then given different values of v , the outcomes are depicted in Figs. 3-5. It is obvious that, the collection price of the Remanufacturer as well as the patent licensing fees increase as the salvage value increases. Even though the increase of salvage value has little impact on the selling price of
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manufactured item, the increase of retail price of remanufactured item is sure to give rise to the shrinkage of market demand for remanufactured items, thereby increasing the market demand for manufactured items. The results reveal the most significant rise in the profit of the Manufacturer, certain increase in profit of the Remanufacturer as well as minor decrease in profit of the Retailer. So it can be inferred that the increase of salvage value is the most unfavorable towards the downstream Retailer.
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55 50 45 40 35 30 25 15 80
M
20 85
90
95
f* b b*
100
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Salvage value
Fig. 3. Collection prices or patent licensing fees vs
v.
500
pn
400
pn
PT Price
CE AC
*
450
350
ps
300
ps
250 200 80
85
90
95
100
Salvage value
Fig. 4. Retail prices vs
v
.
*
ACCEPTED MANUSCRIPT 27000
Profit
22000 Manufacturer 17000
Retailer Remanufacturer
12000 7000 2000 80
85
90
95
100
Salvage value
Example 3 In this example, we examine the effects of 0 and Model JD. Given different values of 0
v
(Model TLG).
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Fig. 5. Members’ profits vs
1 , 1 and 2 on the optimal results of Model TLG
1 , 1 and 2 , the outcomes are depicted in Figs. 6-8.
From Fig. 6, we can see that the collection prices (either Model TLG or Model JD) are decreasing in the ratio
1 ), this will motivate the Remanufacturer to collect more used items and then remanufacture. However, the
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(0
Remanufacturer must pay higher patent licensing fees to the Manufacturer for remanufactured items, which indicates that the Manufacturer wants to ease certain competitive threat to his manufactured items by this means.
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Fig. 6 shows that the uncertainty of return affects the pricing policy of used items and the remanufacturing plan.
40 35
f* b b*
PT
30
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45
25
CE
20
AC
15 0.1 0.2 0.3 0.4 0.5
Fig. 6. Collection prices or patent licensing fees vs
As the value of
1
2
3
4
5
T he ratio of 0 to 1
0 1 ( cn 60 , c s 20 , v 80 , 1 400 , 2 100 , 1 and 0.5 ).
2 increases, the selling prices of manufactured and remanufactured items increase (see Fig.
7), and the demands for manufactured and remanufactured items increase except that the demand for manufactured items remains the same in the joint decision case (see Fig. 8). Furthermore, the results reveal the most significant rise in the selling price and market demand for remanufactured items. It is because the market base ( 2 ) has high impact on the remanufacturing plan and the selling pricing policy of remanufactured items,
ACCEPTED MANUSCRIPT while it has little influence on those of the manufactured items. Given the joint decision case, the demand for manufactured items is unaffected, which means that cooperative scenario can avoid ‘bank run’ in the market demand of remanufactured and manufactured items. 550
pn*
500
pn
450
ps*
Price
400
wn*
ps
300 250
ws*
200 150 100
150
200
250
300
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Market base 2
2 ( cn 60 , c s 20 , v 80 , 1 400 , 0 10 , 1 2 , 1 and 0.5 ).
Fig. 7. Prices vs
250
PT
50
Dn* Ds*
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150 100
Dn
M
200
Demand
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350
Ds
0
CE
100
AC
Fig. 8. Demand vs
150
200
250
300
Market base 2
2 ( cn 60 , c s 20 , v 80 , 1 400 , 0 10 , 1 2 , 1 and 0.5 ).
Example 4 In this example, we examine the effects of
1 and 2 on the coordination results of Model
MC.
According to Table 2, if 0.5 and v 80 , then it can be derived that M 24379 , T 3479 , *
*
R * 19641 and J 58513 . In Model MC, the respective ranges of revenue-and-expense sharing coefficients 1 ,
2 and 1 1 2 are
ACCEPTED MANUSCRIPT 0.42 1 0.60 ， 0.06 2 0.25 ， 0.34 1 1 2 0.52 . Given different values of
1 and 2 under the above conditions, the outcome is shown in Table 3.
Table 3 demonstrates that the profit sharing ratio of the Retailer decreases as
1 and 2 increases.
However, the wholesale price provided by the Manufacturer and the Remanufacturer also decreases. So the profit of the Retailer is still higher than that in Model TLG. In the event that
1 stays unchanged, the Remanufacturer
2 increases, but there is certain
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needs to pay more agency fees for qualifications to the Manufacturer as
increase in the final profit it shares. In Model MC, as the leader of the supply chain, the Manufacturer enjoys the highest profits at all times. Since the collection price maintains its level under joint decision-making in Model MC, the Remanufacturer is able to recover more products with relatively high price, thus advancing the sound development of CLSC and enabling the optimal channel benefits under joint decision-making. Within the range of
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individual rationality constraints, the profits of the chain members gained by way of sharing per certain ratios are remarkably higher than those in Model TLG. Therefore, combined coordinated pricing mechanism enables perfect coordination of the CLSC. Table 3
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Coordination results of Model MC under different sharing coefficients
M **
T **
R **
H **
wn
(0.43,0.15,0.42)
25161
8777
24575
1626
25.2
8.4
(0.45,0.15,0.40))
26331
8777
23405
1620
24.0
8.0
(0.47,0.15,0.38)
27501
8777
22235
1614
22.8
7.6
(0.49,0.15,0.36)
28671
8777
21065
1608
21.6
7.2
(0.51,0.13,0.36)
29842
7606
21065
1368
21.6
7.2
(0.51,0.11,0.38)
29842
6436
22235
1134
22.8
7.6
(0.51,0.09,0.40)
29842
5266
23405
900
24.0
8.0
(0.51,0.07,0.42)
29842
4096
24575
666
25.2
8.4
(0.49,0.09,0.42)
28672
5266
24575
906
25.2
8.4
(0.47,0.11,0.42)
27501
6437
24575
1146
25.2
8.4
(0.45,0.13,0.42)
26331
7607
24575
1386
25.2
8.4
(0.43,0.15,0.42)
25161
8777
24575
1626
25.2
8.4
AC
CE
PT
ED
(1 , 2 ,1 1 2 )
ws
5. Conclusion This paper provides an integrated view to analyze the supply chain for remanufacture of patented products by taking into account pricing and coordination. A mathematical model is developed to optimize the decisions on the
ACCEPTED MANUSCRIPT collection price of used items, the selling price of items, and the patent licensing fees. Due to differentiated pricing of manufactured and remanufactured items, competitive demand for the two types of products and issues concerning the patent license or agency for qualifications, the pricing of supply chain herein is very important. The analysis of numerical examples shows that the impact of uncertainties of some important parameters, such as substitute ratio, salvage value, market base and so on. Accordingly the agency fees for qualifications, sharing coefficients and pricing are coordinated together to obtain the maximum profit of the system. Therefore, with certain agency fees for qualifications paid by the Remanufacturer, the coordinated pricing mechanism will
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encourage supply chain members to conduct joint decision-making, substantially improve channel benefits and enable the multi-win of the Manufacturer, the Remanufacturer and the Retailer. In addition, some significant conclusions, drawn through theoretical analysis and investigations of numerical examples with regard to the relationship between performance parameters and pricing, profits and so on, provide certain theoretical reference to the development and decision-making of CLSC. Further studies may consider the issues concerning a
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multi-period model, such as product life cycle patterns, used items with different quality levels and multiple recovery options, which can help better understand the influence of demand, return and pricing on the system. Acknowledgments
This work was supported by National Natural Science Foundation of China (Project Nos. 71531008, 71271073,71201044 and 71571002), Program for New Century Excellent Talents in University (Project
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No.NCET-11-0625) and Key Project of HSSR of Education Department of Anhui Province(Project Nos. SK2016A379 and SK2014A393). The authors express their gratitude to Editor M.Y. Jaber and the anonymous
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referees for their most insightful and valuable comments on the paper, which were instrumental for elevating the
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ACCEPTED MANUSCRIPT [7] R.C. Savaskan, S. Bhattacharya, L.N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science. 50(2) (2004) 239-252. [8] A.M.A. El Saadany, M.Y. Jaber, A production/remanufacturing inventory model with price and quality dependant return rate, Computers & Industrial Engineering. 58(3) (2010) 352-362. [9] Y. Liang, S. Pokharel, G.H. Lim, Pricing used products for remanufacturing, European Journal of Operational Research. 193(2) (2009) 390-395. [10] J. Wei, J. Zhao, Pricing decisions with retail competition in a fuzzy closed-loop supply chain, Expert Systems
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[13] C. Shen, Z. Xiong, Decision and coordination of the closed-loop supply chain under patent protection, Advances in Industrial Engineering, Information and Water Resources. 80 (2013) 155. [14] Y. Yi, Y. Chen, Closed-loop supply chain models under uncertain demand, Computer Integrated Manufacturing Systems.16(7) (2010) 1531-1538 (in Chinese).
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Management. 2(1) (2000) 100-106.
[17] A.A. Tsay, Risk sensitivity in distribution channel partnerships:implications for manufacturer return policies, Journal of Retailing.78(2) (2002) 147-160.
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[18] M.Y. Jaber, A.M.A. El Saadany, The production, remanufacture and waste disposal model with lost sales, International Journal of Production Economics. 120(1) (2009) 115-124.
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[19] P. Hasanov, M.Y. Jaber, S. Zolfaghari, Production, remanufacturing and waste disposal models for the cases of pure and partial backordering, Applied Mathematical Modelling. 36(11) (2012) 5249-5261.
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Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands Cheng-Tang Zhang , Ming-Lun Ren PII: DOI: Reference:
S0307-904X(16)30070-1 10.1016/j.apm.2016.02.006 APM 11032
To appear in:
Applied Mathematical Modelling
Received date: Revised date: Accepted date:
13 July 2013 15 January 2016 3 February 2016
Please cite this article as: Cheng-Tang Zhang , Ming-Lun Ren , Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands, Applied Mathematical Modelling (2016), doi: 10.1016/j.apm.2016.02.006
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Highlights
Compare of the prices, performances of supply chain systems, etc. under two models.
Investigate the combined coordinated pricing mechanism of a revenue-and-expense sharing contract and
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two-part tariffs.
Provide a reasonable range for the sharing coefficient and agency fees.
Perfect coordinate the closed-loop supply chain of patented products
Study the impact that substitute ratio, salvage value, coordination parameters, etc. have on supply chain
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AC
CE
PT
ED
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decisions and performance.
ACCEPTED MANUSCRIPT
Coordination strategy of closed-loop supply chain for remanufacture of patented products under competitive demands Cheng-Tang Zhang a,b,*, Ming-Lun Ren b a
Institute of Science, Anhui Agricultural University, Hefei 230036,P.R.China
b
School of Management, Hefei University of Technology, Hefeii 230009,P.R.China
*Corresponding author. Tel: +86 55165786164 E-mail address: [email protected] (C.-T. Zhang)
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Abstract: The paper studies a closed-loop supply chain (CLSC) system that consist of an original manufacturer, a third-party remanufacturer and a retailer. In the system, the remanufacturer can only recycle and remanufacture the patented products with the patent licensing from the original manufacturer; new manufactured and remanufactured products are sold together in the same market at different prices; the demand for the two types of products is sensitive to the retail prices. Firstly, we establish a leader-follower game model and a joint decision-making model, and make comparison of the CLSC members’ performance, e.g., collection price, selling prices and profits. Secondly, we investigate
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contract coordination issues among the three parties in the decentralized case, and develop a coordinated pricing mechanism that incorporates revenue-and-sharing contract and two-part tariffs can perfectly coordinate the CLSC. Accordingly, a reasonable range for the sharing coefficient and agency fees for qualifications can be identified. Finally, through some numerical examples, we analyze the impact that the salvage value, substitute ratio, coordination parameters and so on have on the optimal supply chain performance.
Key words: closed-loop supply chain; patented products; pricing; coordination
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1. Introduction
Due to the increasing concerns on environment and awareness of natural resource limitation in recent years , many
ED
countries have intensified their legislative efforts with regard to the environment and resources protection (e.g., [1]), giving rise to widespread concern in the industry for the collection and remanufacture of used items (e.g.,
PT
[2-4]). Many enterprises, such as Hewlett-Packard and Kodak, have sensed that the collection of used products will enable substantial savings in manufacturing costs as well as elevation of their social prestige and economic
CE
benefits, creating a closed-loop responsive supply chain in a “resources-production-consumption-renewable resources” looping sequence (e.g., [5]). This process reduces the resources initially acquired along with the garbage eventually produced, and contributes to the realization of coordinated development of economy and
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environment for the manufacturer. It is, therefore, of positive significance to the sustainable development of the society. For reasons of cost or brand, the original manufacturer may not engage in the collection and remanufacture of used items, thus leaving the work to third-party manufacturers. And this inevitably brings certain competitive threat to the new manufactured item by the original manufacturer (e.g., [6]). Accordingly, the original manufacturer may ease such threat of third-party manufacturers by charging patent licensing fees. In addition, the remanufacture of patented products involves the licensing issues of patented technologies, so patent license is not only a factor to be considered in the decision-making of enterprises regarding remanufacture, but also an issue to be taken seriously in remanufacture supply chain studies. Pricing decisions with regard to product sales and recovery are critical in closed-loop supply chain
ACCEPTED MANUSCRIPT management, as they directly affect the supply and demand of products as well as the operational efficiency of CLSC. Therefore, the pricing of CLSC has become an important issue that attracts much academic attention in recent years. Savaskan et al. [7] studied the pricing strategy and channel efficiency of different collection structures in CLSC. However, by assuming the quantities of returned items is proportionate to the market demand for products, their study did not take into account the impact that collection price has on the quantities of returned items and the collection price was considered as an exogenous variable, which is inconsistent with the reality. El Saadany and Jaber [8] suggested that the quantity of returned items is controlled by price and quality, and
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presented for multiple remanufacturing and production cycles. As sales price of used items follows a geometric Brownian motion, Liang et al. [9] proposed a centralized model to evaluate the acquisition price of used items. Wei and Zhao [10] investigated the optimal wholesale and retail prices of CLSC under the competition of retailers using the game theory and fuzzy theory. Shi et al. [11] assumed that the selling prices of new manufactured and remanufactured items are the same while demand correlates with price, and examined the two types of products
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with regard to their production quantity, selling price and collection price of used items. However, the market price of remanufactured items is in fact always different from that of manufactured items. The demands for the two types of products are not the same either.
There are relatively few studies focusing on the coordinated pricing of CLSC. Based on game theory, Yi and Yuan [12] studied the CLSC system under hybrid collection mode, and analyzed the impact that hybrid collection
M
mode has on pricing and profits. Then they adopted a two-part tariff to improve the performance of the whole CLSC. However, as a leader of the channel, the manufacturer will obtain all of the excess profits generated after
ED
cooperation, while the retailer only gets the profits under decentralized decision-making. Shen and Xiong [13] based their study on the assumption that the manufactured and remanufactured items are homogeneous and the market demand is a linear function of price. They discussed that the coordination of CLSC can be realized through
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the collection and remanufacture of patented products, analyzed the pricing decision-making CLSC members, and proposed a revenue-and-expense sharing contract to control the sharing ratio through negotiations. However, the
CE
literature did not discuss the situation where new manufactured and remanufactured items compete in the same market. In addition, CLSC was studied with regard to the pricing strategy and system performance in different
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collection channels, modes (e.g., [14, 15]) and collection efficiencies (e.g., [16, 17]). Despite the fact that many studies investigated pricing and coordination in CLSCs, there are some research
issues that have not been addressed yet, such as:
Competition amongst products.
Remanufactured and manufactured items are of different prices, with the first being of a lower price.
Remanufactured items with salvage value or stockout penalty cost should be considered.
Revenue-and-expense sharing contract has not been reported in literature; perfect coordination cannot be achieved with a two-part tariff alone. In view of the above, pricing and coordination model of CLSC system under patent licensing will be
established. The paper focuses on the following issues:
ACCEPTED MANUSCRIPT Examine the difference in sales between manufactured and remanufactured items, and study how competition
between them in a market affect supply chain performance. Compare of the selling and collection prices of products by each supply chain member, and determine the
performance of the supply chain system, etc., under a leader-follower game and joint decision-making model. Explain why a decentralized CLSC cannot be perfectly coordinated by a revenue-and-expense sharing
contract. Investigate the combined coordinated pricing mechanism of a revenue-and-expense sharing contract and
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two-part tariffs. Study the impact that substitute ratio, salvage value, market base and coordination parameters have on supply
chain decisions and performance.
2. Problem description
This paper considers a CLSC with an original manufacturer, a third-party remanufacturer and a retailer. The
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original manufacturer (hereinafter referred to as the “Manufacturer”) that owns patent rights to the new manufactured item, takes advantage of its proprietary rights to authorize the work to the third-party remanufacturer and provide technical support, staff training, etc.. However, it does not engage in the collection and remanufacture of used items. There are many similar cases in the manufacturing industry, such as engine remanufacturing and hydraulic pump remanufacturing. The third-party remanufacturer is a manufacturer apart
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from the Manufacturer that engages in product collection and remanufacture(the “Remanufacturer”). The Remanufacturer conduct product collection and remanufacture of used items as well as sales of remanufactured
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items with license from the Manufacturer and payment for patent licensing fees. It would be sued for both a tort liability and a breach of contract if the Remanufacturer involves in remanufacture of patented products without
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payment for patent licensing fee. For example, “Cotton-Tie Co. v. Simmons, 1882” and “Sandvik Aktiebolag v. E.J. Co., 1997” are good cases in point.
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Customers’ demands can be satisfied by two alternative ways: purchase of new products manufactured by the Manufacturer with original raw materials, or purchase of remanufactured items by the Remanufacturer with collected used items. Both of the two types of the products with same function are sold by the Retailer together in
AC
the same market, while the differences between of them lie in price and recognition. 2.1.
Notations and assumptions
The following notations defined in Table 1 are used in the model for the production and pricing problem:
ACCEPTED MANUSCRIPT Table 1 Notations Definition
cn
Manufacturing cost of a manufactured item
cs
Manufacturing cost of a remanufactured item
wn
Wholesale price of a manufactured item charged by the Manufacturer
ws
Wholesale price of a remanufactured item charged by the Remanufacturer
pn
Price of a manufactured item charged by the Retailer
ps
Price of a remanufactured item charged by the Retailer
b
Price of collecting a used items charged by the Remanufacturer
f
Unit patent licensing fee for authorization of the Remanufacture charged by the Manufacturer ( i 1, 2 )
Market base
v
Unit salvage value or unit stockout penalty cost
(b)
Return quantity of used items
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i
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Parameter
Hereinto, wn and f are the decision variables of the Manufacturer, ws and b are the decision variables
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of the Remanufacturer (the Remanufacturer determines on the collection price and collects used items directly from the customers), p n and p s are the decision variables of the Retailer. Moreover, the remanufacturing cost,
ED
c s , does not include the cost of buying back used items or the patent licensing fees for authorization of the
management costs.
PT
Remanufacture, but includes the costs of dismantling, quality assurance, components, remanufacturing and other
The following assumptions are made to develop the subsequent model
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Assumption 1. The CLSC decisions are considered in a single-period setting. We assume some products sold in the previous periods can be recycled. The Remanufacturer buys back the used items from the customers at the unit
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collection price b . Suppose that all used items purchased are to be remanufactured, so the remanufacturing rate would be 1. There is substitution relationship between new manufactured and remanufactured items. The similar forms of this assumption have been used in the sample (e.g., [18, 19]). Assumption 2. We assume that new manufactured and remanufactured items make a competitive market. The new manufactured items demand Dn ( pn , p s ) is a function of retail prices Dn ( pn , p s ) 1 pn p s , with
1 , and being non-negative parameters and 1 cs cn ;The remanufactured items demand Ds ( pn , p s ) is expressed as
Ds ( pn , ps ) 2 ps pn ,with being positive parameter and
ACCEPTED MANUSCRIPT 2 cn cs . Hereinto,
1 and 2 are market base ( 1 2 ), which denote respectively the primary demand of
manufactured and remanufactured items, items is relatively lower than that of
2 1 indicates that customers’ recognition of the remanufactured
the new manufactured items; denotes the measure of the responsiveness
of retailer’s market demand to his own retail price, and the value of
rely on many factors, including social
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factors, economic factors and psychological factors, is the substitute ratio of two types of product (when 0 , the market demands for manufactured and remanufactured items are only related to their own retail price), whereas indicates that one type of product’s own price effect is greater than the cross-price effect (e.g., [20],[21]).
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Assumption 3. The demand of manufactured items may be different from that of remanufactured items, so with reference to Jaber & El Saadany [18] we assume that there is no surplus manufactured item, and the demand of remanufactured items depends on retail price and customers’ recognition of the remanufactured items. On the one hand, customers’ low recognition of the remanufactured items gives rise to the relatively low market demand for of remanufactured items. Therefore, we can assume that remanufactured items are in excessive supply. For the items”, the Remanufacturer will obtain certain unit salvage value v , and
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“unsold remanufactured
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v cs b f to ensure that the Remanufacturer is motivated to collect and remanufacture returned items. In addition, let v ws p s , so that the Remanufacturer sells the remanufactured items aggressively.
PT
On the other hand, if the remanufactured items are in exceed supply, the parameter v will be correspondingly regarded as a unit stockout penalty cost.
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Assumption 4. The return quantity of used items depends on the price of collecting a used items charged by the Remanufacturer,
the
relationship
between
return
quantity
and
price
is
known
as
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(b) 0 1b ( 0 0 , 1 0 ). The parameter 0 is the quantity of volunteer to return used items from customers (a fraction of the produced quantity), and another level as a measure of environmental awareness (e.g., [22]);
1 is the price sensitivity of customers for collection price offered by the Remanufacturer.
Assumption 5. Other rational assumptions: cn c s , wn ws , pn p s , b cn c s . 2.2.
Pricing decision-making model In this subsection, we will present two pricing models: Model TLG (i.e., three-level leader-follower game
model) and Model JD (i.e., joint decision-making model), and analyze the optimal strategies of the two models., In our leader-follower non-cooperative game, the Manufacturer will act as the leader to decide how much the
ACCEPTED MANUSCRIPT wholesale price of manufactured item and the patent licensing fees would be optimal. The Remanufacturer and the Retailer all act as the followers and will make the best response according to the Manufacturer’s decision. Note, the Remanufacturer and the Retailer are in the different flows (the former is in the forward chain and the latter is in the closed-loop chain), so they act as Stackelberg game. Subsequently we develop the joint decision-making model described below as a benchmark case for purposes of comparison. 2.2.1. Model TLG If the Remanufacturer is granted the patent license to conduct product collection and remanufacture, then
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under competitive demand of manufactured and remanufactured items, the Manufacturer, the Remanufacturer and the Retailer all act in their own best interests and seek the way to maximize their respective profits. In the three-level leader-follower game, the sequence of moves is given as follows: Firstly the leader (the Manufacturer) will make best decision and announce a wholesale price of new manufactured item wn and a patent licensing
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fees f to maximize his own profit; then in response to the Manufacturer’s decision wn and f ,the follower (the Remanufacturer) will determine the wholesale price of remanufactured item ws and the collection price of used items b ; finally, according to the above decision wn and ws , the other follower (the Retailer) will make best
wn
Manufacturer
M
response and determine the retail prices p n and p s . The pricing decision-making model is depicted in Fig.1. pn , ps
Customers
Retailer
ED
ws
f
Remanufacturer
Reverse Logistics
PT
Forward Logistics
b
Fig. 1. Framework of CLSC for remanufacture with patent license.
T and R denote the profits of the Manufacturer, the Remanufacturer and the Retailer respectively,
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Let M ,
we get the Manufacturer’s profit function as follows
AC
M (wn , f ) (wn cn ) Dn f (b) (wn cn )(1 pn ps ) ( 0 1b) f
(1)
The Remanufacturer’s profit is
T (ws , b) (ws cs ) Ds b(b) v[(b) Ds ] f (b) (ws cs )( 2 ps pn ) v[ 0 1b 2 ps pn ] (b f )( 0 1b)
(2)
and the Retailer’s profit is
R ( pn , p s ) ( p n wn ) Dn ( p s ws ) Ds ( p n wn )( 1 p n p s ) ( p s ws )( 2 p s p n )
(3)
ACCEPTED MANUSCRIPT According to the above description about Model TLG, this can be expressed as
( L) : max ( w , f ) M n wn , f T ( ws , b ) s.t.( F1) : max ws ,b s.t.( F 2) : max R ( p n , p s ) pn , p s The above game model is solved using backward induction.
conditions of the maximization problem of the Retailer
R pn 0 , R p s 0 .
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First of all, with respect to Eq. (3), we can solve the following simultaneous equations from the first-order
Therefore, the best response function of the Retailer can be given as follows
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1 2 wn ~ 1 2 ws ~ pn , ps . 2 2 2( ) 2 2( 2 2 ) 2
(4)
Then, substituting Eq. (4) into Eq. (2), similar to the above, the Remanufacturer’s best response can be obtained from the Eq. (2)
0 1 v f） ~ 2 wn v c s ， b~ （ . w s 21 2 2
(5)
M
Given the Retailer and the Remanufacturer’s response Eqs. (4) and (5), the Manufacturer solves
~ max M (wn , f ) max[(wn cn )(1 ~ pn ~ p s ) ( 0 1b ) f ] wn , f
ED
wn , f
to determine the optimal pricing *
(v c s ) (21 2 ) cn 1v ，f* 0 . 2 2 2 21 2(2 )
PT
wn
(6)
CE
Therefore, the optimal pricing of the Remanufacturer and the Retailer can be derived from simultaneous Eqs. (4), (5) and (6).The optimal wholesale price and collection price offered by the Remanufacturer are
v 3 0 （ 2 v c s )(4 2 2 ) 2 1 cn * ws , b 1 2 2 41 4 4 (2 )
(7)
AC
*
and the optimal retail price of manufactured and remanufactured items are
pn
1 2 cn (v c s ) (21 2 ) . 2( 2 2 ) 4 4(2 2 2 )
(8)
ps
1 2 cn （ 2 v c s )(4 2 2 ) 2 1 . 2( 2 2 ) 8 8 ( 2 2 2 )
(9)
*
*
* Thus, the sum of CLSC members’ profit in Model TLG, denoted as , can be presented
ACCEPTED MANUSCRIPT as * M T R . *
*
*
Based on the equilibrium results of Model TLG, we can obtain some propositions as shown below. Proposition 1. When the level of environmental awareness of the customers, 0 , changes in Model TLG, we find (i) The collection price b * negatively correlates with 0 ; (ii) The patent licensing fees f , the Manufacturer’s profit M and the Remanufacturer’s profit T *
*
*
positively correlate with 0 , while the Retailer’s profit R remains unchanged. Proof. Since b * 0
is decreasing in
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*
3 1 0 and f * 0 0 , this simply implies that the collection price b * 41 21
0 and yet the patent licensing fees f * is increasing in 0 . As is known from the equilibrium
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results of Model TLG, the wholesale price and retail price of the product is constant for 0 . Correspondingly, the Retailer’s profit remains the same. Moreover, M
*
0
0 1v 1v * 0 and T 0 0 0. 41 81
M
Hence it can be concluded that the profits of the Manufacturer and the Remanufacturer increase as 0 increases.□ The conclusions of Proposition 1 indicate that the enhancement of customers’ environmental awareness helps
ED
to save collection costs of the enterprises, increases the profits of the Manufacturer and the Remanufacturer, and enhances the initiative of the enterprises to conduct collection and remanufacture, thus advancing CLSC members to acquire positive social externalities. The profit of the Retailer is not affected by the quantity of used items that
PT
customers voluntarily return. Accordingly, the government may intensify their efforts in promotion of environmental protection and relevant legislation in order to elevate the level of the environmental awareness of
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the customers, increase the social responsibilities of the enterprises, and advance the sound development and stable operation of CLSC.
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2.2.2. Model JD
As a benchmark to evaluate the channel decision under different decision models, we examine a joint
decision case, in which one entity made up of the three parties to optimize the whole system performance. This means the cooperation of all members in a centralized system with a central planner/decision-maker, which is common in traditional supply chain. So in our research, we consider the joint decision system as the “centralized” system (Fig.2).
ACCEPTED MANUSCRIPT
Manufacturer
pn , ps Customers
Remanufacturer
b Retailer
Forward Logistics
Reverse Logistics
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Fig. 2. Framework of CLSC under joint decision-making model.
The Manufacturer’s wholesale price wn , patent licensing fees f and the Remanufacturer’s wholesale price
ws are seen as inner transfer prices, which influence the profits of each participant, but they do not affect the whole system’s strategies and profit. Thus, from Eqs. (1)-(3), we can easily get the total system profit equation.
J ( pn , ps , b) M T R ( pn cn ) Dn ( ps cs ) Ds b(b) v[(b) Ds ]
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(10)
We know that the objective of the joint decision case is to maximize the system profit J ( pn , p s , b) , which can be denoted as follow
max J ( p n , p s , b) max [( p n cn ) Dn ( p n , p s ) ( p s c s ) Ds ( p n , p s )
p n , p s ,b
p n , p s ,b
M
b(b) v((b) Ds ( p n , p s ))]
From the first-order conditions, the optimal retail prices and the optimal collection price are given as follows
v 0 1 2 cn 2 v c s , ps 1 2 , b 1 . 2 2 2 2 21 2( ) 2 2( )
ED
pn
(11)
PT
Accordingly, the optimal profit of the CLSC system in Model JD can be expressed by
Where, Dn
CE
J ( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ] .
1 pn p s
and Ds
2 p s pn , and (b ) 0 1b
(12)
0 1v 2
.
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Proposition 2. Compare the results in Model TLG and Model JD. It is obvious that b * b , p n p n , *
p s p s , and * . *
Proof. By the comparison of the optimal results under the two models, we can easily obtain Proposition 2.□ From Proposition 2, we have some obvious but important observations. The CLSC system has the advantage of resources integration in Model JD, which will enable the central decision-maker to obtain more used items with higher collection price, and sell more products in the market with lower retail price. Therefore, the system profit will reach the highest level in the Model JD with relevant equilibrium results strictly better than those in Model TLG. It is clear that CLSC system is better off through all members’ cooperation.
ACCEPTED MANUSCRIPT In this joint decision-making model, the central decision-maker focuses on improving coordination and integration of distinct activities, such as technical collaboration, patent-licensing arrangement, product-process (manufacturing, remanufacturing, distribution, transportation, etc.) integration and information sharing, within a framework of collaborative inter-enterprise. As an example, it is possible to reduce the transportation costs of returned items when the new manufactured items are delivered to the same client in the area. Thus, the chain members will obtain real benefits resulting from the double-edged impact of increased market share on a lower asset base. In the next section, we will discuss how to distribute the system profit remained and obtain the best
3. Combined coordinated pricing mechanism
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feasible Pareto efficiency.
When the benefits of the three members’ cooperation are shared among them, some mechanism is needed to balance the benefits among the membership so that the coalition remains intact and the benefits of their cooperation are obtained. Accordingly, a pricing mechanism incorporating revenue-and-expense sharing contract
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and two-part tariffs are conceived, which can achieve the system coordination and the individual perfect coordination. It is obviously a motivate mechanism. In other words, if the chain members accept this mechanism and report truthfully the cost/revenues, the mechanism must ensure the member’s profit is not lower than the profit level in Model TLG. Correspondingly, the individual’s optimal decision in Model TLG must be consistent with the system’s optimal decision in Model JD.
M
3.1. Revenue-and-expense sharing contract
Due to product collection expenses, traditional revenue sharing contract is unable to achieve CLSC
ED
coordination. It has been upgraded to a revenue-and-expense sharing contract and used to coordinate the CLSC with single collection channel in recent years by several scholars. Revenue-and-expense sharing refers to the
PT
sharing of profits, losses and external expenses (e.g., collection expenses) among the CLSC members. As an example, on the basis of a revenue-and-expense sharing contract, a high-tech enterprise providing digital products
CE
can share revenues, advertisement expenses and collection expenses with its retailer. That is to say, the Manufacturer not only shares with the Retailer the revenue from the sales of the products, but also the expenses for collection used items per the same ratio. Therefore, the CLSC for collection and remanufacture with patent
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license will be investigated using the revenue-and-expense sharing contract. Assume that the Manufacturer, the Remanufacturer and the Retailer share salvage value of the
Remanufacturer and sales revenue of the Retailer as well as collection expenses of used items according to respective ratios:
1 , 2 and 1 1 2 . With regard to f (b) , patent licensing fees of the Manufacturer, they
are not counted as to be shared, as they are internal expenses of the entire supply chain, just like the wholesale expenses of product. Therefore, the respective profits of the Manufacturer, the Remanufacturer and the Retailer are
M 1{ pn Dn ps Ds b(b) v[(b) Ds ]} (wn cn ) Dn f (b).
(13)
ACCEPTED MANUSCRIPT T 2 { pn Dn ps Ds b(b) v[(b) Ds ]} (ws cs ) Ds f (b).
(14)
R (1 1 2 ){ pn Dn ps Ds b(b) v[(b) Ds ]} wn Dn ws Ds .
(15)
From the first-order conditions, the Retailer decides the retail prices p n , p s and the collection price b as follows.
wn 2(1 1 2 )
(1 1 2 )v ws 1 2 v 0 1 2 f ， pˆ s ， bˆ 1 . (16) 2 2 2 2 2(1 1 2 ) 21 2 2 2( ) 2( )
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pˆ n
By comparing Eqs. (16) and (11), it can be inferred that if the optimal pricings for the Manufacturer and the Remanufacturer are
wn (1 1 2 )cn , ws (1 1 2 )cs , f 0 .
(17)
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Then p n p n , p s p s , b b , which means the entire CLSC system achieves the optimal prices of joint decision-making model.
As is shown in Eq. (17), the optimal pricing results, upon agreement on a revenue-and-expense sharing contract, the Manufacturer will not charge patent licensing fees from the Remanufacturer. The Manufacturer and
the Remanufacturer will wholesale their products to the Retailer at low prices ( wn and ws ), thus enabling low
M
retail price under joint decision-making as well as more market share and competitiveness of the product (either manufactured items or remanufactured ones). The customers will also enjoy more benefits with no doubt. The
ED
three parties of the supply chain ensure their profits through sharing salvage value of the Remanufacturer and sales income of the Retailer. At this point, the profit of the Manufacturer is
PT
M 1{ p n Dn p s Ds b (b ) v[(b ) Ds ]} （1 2 )cn Dn 0 (b )
1{( p n cn ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} ( 2 cn Dn 1c s Ds ) 1 1 J [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] . 2
CE
(18)
The profit of the Remanufacturer is
AC
T 2 { p n Dn p s Ds b (b ) v[(b ) Ds ]} （1 2 )c s Ds 0 (b )
2 {( p n c n ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} ( 2 c n Dn 1c s Ds ) .(19) 1 2 J [(1 c s 2c n )(v c s ) 2 c n ( 1 c n ) 1c s ( 2 c n )] 2
The profit of the Retailer is
R (1 1 2 ){ p n Dn p s Ds b (b ) v[(b ) Ds ]}
（1 1 2 )c n Dn （1 1 2 )c s Ds
(1 1 2 ){( p n c n ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} (1 1 2 ) J
.
(20)
ACCEPTED MANUSCRIPT The above results show that the sum of profits of the Manufacturer, the Remanufacturer and the Retailer reaches its optimal level under joint decision-making:
M T R J . Therefore, a revenue-and-expense sharing contract enables global coordination of the supply chain system. However, as is shown in the profit function expressions of the Manufacturer and the Remanufacturer, profits earned by the Remanufacturer are higher than the sharing ratio of revenue-and-expense sharing contract. It is indicated that the profits of the Manufacturer is not maximized due to differentiated competition of products and
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lack of patent licensing fees. As leader of the CLSC, the Manufacturer will endeavor to pursue profit maximization. 3.2. Two-part tariffs
A two-part tariff is a pricing mechanism according to which the buyer pays to the seller a fixed fee and a constant charge for each unit purchased (see [23]). The following items could be identified as two-part tariffs:
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loyalty cards or clubs, credit cards which charge an annual fee plus a per-transaction fee, “membership discount retailers” such as shopping clubs that charge an annual fee for admission to the point of sale and also charge for purchases.
In our framework, the per-unit payment can be also viewed as a per-unit patent licensing fee. Further, a two-part tariff can be used as a vehicle for manipulating the incentives given to the buyers, allowing also the
M
sellers to capture part of the residual surplus through an appropriately chosen fixed fee. In this subsection and the next, the fixed fee can be viewed as an agency fee for qualification obtained.
ED
On basis of the above, in the event that revenue-and-expense sharing contract enables global coordination of the supply chain system, the closed-loop supply chain can be perfectly coordinated using two-part tariffs as below:
PT
M 1{ pn Dn ps Ds b (b ) v[(b ) Ds ]} （1 2 )cn Dn 0 (b ) H .(21)
CE
T 2 { pn Dn ps Ds b (b ) v[(b ) Ds ]} （1 2 )cs Ds 0 (b ) H . (22) Where H is the agency fee for qualifications of the Remanufacturer to conduct product collection and remanufacture during a certain period. According to Eqs. (18) and (19), the Remanufacturer only has to decide the
AC
agency fee for qualifications as showing below
1 H ** [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] . 2
(23)
Then under the combined coordinated pricing model that combines revenue-and-expense sharing contract
and two-part tariffs (marked as “Model MC”), the respective optimal profits of the Manufacturer, the Remanufacturer and the Retailer are
M ** 1{( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ]} 1 J .
(24)
T ** 2 {( pn cn ) Dn ( ps cs ) Ds b (b ) v[(b ) Ds ]} 2 J .
(25)
ACCEPTED MANUSCRIPT R ** (1 1 2 ){( p n cn ) Dn ( p s c s ) Ds b (b ) v[(b ) Ds ]} (1 1 2 ) J
.
(26)
At this point, the profits of the Manufacturer are increased. The Manufacturer, the Remanufacturer and the Retailer share profits of the entire CLSC according to the respective ratios: 1 , 2 and 1 1 2 . Therefore, the optimal total profit in the Model MC, denoted as ** , can be presented as
**
**
**
**
**
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Provided that supply chain members are subject to individual rationality constraints: M
T ** T * and R ** R * , which means on basis of ensuring
1 J M * , 2 J T * , (1 1 2 ) J R * . Choosing appropriate values for
M T R J . M , *
(27)
1 and 2 will enable global coordination of supply chain system and perfect
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coordination of supply chain members. It can be derived from Eq. (27) that the respective reasonable ranges for 1 ,
2 and 1 1 2 are
1 and 2 depend on the bargaining power of the three parties of the supply chain. M * R* M* T * R* T * 1 1 , , and 1 2 J J J J
ED
The values of
M
M * R* R* M * T* M* T * R* T * 1 1 ， 2 1 ， 1 1 2 1 . J J J J J J
Proposition 3. Under conditions that
PT
R* M * T* 1 1 , if the respective pricing mechanisms for the Manufacturer, the 1 2 J J
**
CE
Remanufacturer and the Retailer are ( wn , f , H ) , ( ws , b ) and ( p n , p s ) , the CLSC system is perfectly coordinated with Model MC.
AC
Where
1 wn (1 1 2 )cn , f 0 , H ** [(1 c s 2cn )(v c s ) 2 cn (1 cn ) 1c s ( 2 cn )] , 2
ws (1 1 2 )cs , b
1v 0 1 2 cn 1 2 v c s p , pn , . s 21 2 2( 2 2 ) 2 2( 2 2 )
Proof. Based on the above-mentioned analysis, we can easily obtain Proposition 3.□ Proposition 3 shows that the wholesale price has to be lower than manufacturing cost, exactly to achieve the maximum channel profit. It uncovers the lure of combined coordinated pricing mechanism in the decentralized case. Thus, the Manufacturer, the Remanufacturer and the Retailer are driven by profit motives to maximize theirs
ACCEPTED MANUSCRIPT own as well as the channel profit. Within the range of individual rationality constraints, the chain members can share the optimal total profits of CLSC system with each other by way of sharing per certain ratios. It also highlights the importance of a reasonable distribution of channel profits in channel management. Proposition 4. By comparing the results in Model TLG and Model MC, the following conclusions can be drawn.
(i) wn wn , ws ws , p n p n , p s p s , b * b ; *
*
*
*
(ii) M M , T * T ** , R R , * ** . *
**
*
**
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As stated in the above proposition, the Manufacturer offers a combined coordinated pricing mechanism for making the retail prices of the products equal to the centralized channel prices level, thereby overcoming inefficiencies because of double marginalization. Therefore, the performances of the whole system and the supply chain members under Model MC are significantly better than those under Model TLG. That is to say, the combined coordinated pricing mechanism enables the multi-win of CLSC members.
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4. Numerical examples
Some numerical examples are presented to illustrate the optimization problem and used to gain some insight into the CLSC system.
Example 1 In this example, we examine the effect of on the equilibrium results of Model TLG and Model JD. The selected parameters values should satisfy the assumptions mentioned in Subsection 2.1, assume that the
1 400 , 2 100 , 0 10 , 1 2 and 1 .
M
parameters values for cn 60 , c s 20 , v 80 ,
The optimal solutions for example 1 are b * 16.25 , f
*
42.5 and b 37.5 , then given different values
ED
of , the outcome is shown in Table 2. Table 2
*
( pn , pn )
*
( ps , ps )
CE
PT
Equilibrium results of Model TLG and Model JD under different substitute ratio of demand
( Dn , Dn )
( Ds , Ds )
( M , T , R )
( * , J )
*
*
*
*
*
(325, 237)
(126, 120)
(87, 175)
(6, 3)
(17222,973,7886)
(26081,34662)
0.3
(364, 266)
(190, 170)
(93, 185)
(19, 9)
(19988,1635,11118)
(32741,42409)
AC
0.1
0.5
(443, 330)
(286, 250)
(99,195)
(36, 15)
(24379,3479,19641)
(47499,58513)
0.7
(631,490)
(482,422)
(106, 205)
(59,21)
(31669,8036,46503)
(86208,98697)
0.9
(1510,1319)
(1360,1260)
(113, 215)
(99, 27)
(45165,20664,226840)
(292669,305730)
As is shown in Table 2, under competitive demand for manufactured and remanufactured items, the bigger the substitute ratio of demand is, the bigger customer demand’s reaction to price change of competing product is. The demand for the product increases as the price of substitutable product increases (either Model TLG or Model JD). As a result of the interactive effects of competition, the market demands and selling prices of manufactured and remanufactured items also increase accordingly. Therefore, the profits of corresponding members and system profits increase as product substitutability increases. And system profit in Model JD is remarkably higher than that
ACCEPTED MANUSCRIPT in Model TLG. Since the Retailer is in closest proximity to the consumer market, the substitute ratio of demand affects it the most. Let =0.5 in the following numerical examples in order to reflect generality. Example 2 In this example, we examine the effect of v on the optimal results of Model TLG and Model JD. We set 0.5 , and other parameter values the same as those in Example 1. Then given different values of v , the outcomes are depicted in Figs. 3-5. It is obvious that, the collection price of the Remanufacturer as well as the patent licensing fees increase as the salvage value increases. Even though the increase of salvage value has little impact on the selling price of
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manufactured item, the increase of retail price of remanufactured item is sure to give rise to the shrinkage of market demand for remanufactured items, thereby increasing the market demand for manufactured items. The results reveal the most significant rise in the profit of the Manufacturer, certain increase in profit of the Remanufacturer as well as minor decrease in profit of the Retailer. So it can be inferred that the increase of salvage value is the most unfavorable towards the downstream Retailer.
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55 50 45 40 35 30 25 15 80
M
20 85
90
95
f* b b*
100
ED
Salvage value
Fig. 3. Collection prices or patent licensing fees vs
v.
500
pn
400
pn
PT Price
CE AC
*
450
350
ps
300
ps
250 200 80
85
90
95
100
Salvage value
Fig. 4. Retail prices vs
v
.
*
ACCEPTED MANUSCRIPT 27000
Profit
22000 Manufacturer 17000
Retailer Remanufacturer
12000 7000 2000 80
85
90
95
100
Salvage value
Example 3 In this example, we examine the effects of 0 and Model JD. Given different values of 0
v
(Model TLG).
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Fig. 5. Members’ profits vs
1 , 1 and 2 on the optimal results of Model TLG
1 , 1 and 2 , the outcomes are depicted in Figs. 6-8.
From Fig. 6, we can see that the collection prices (either Model TLG or Model JD) are decreasing in the ratio
1 ), this will motivate the Remanufacturer to collect more used items and then remanufacture. However, the
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(0
Remanufacturer must pay higher patent licensing fees to the Manufacturer for remanufactured items, which indicates that the Manufacturer wants to ease certain competitive threat to his manufactured items by this means.
M
Fig. 6 shows that the uncertainty of return affects the pricing policy of used items and the remanufacturing plan.
40 35
f* b b*
PT
30
ED
45
25
CE
20
AC
15 0.1 0.2 0.3 0.4 0.5
Fig. 6. Collection prices or patent licensing fees vs
As the value of
1
2
3
4
5
T he ratio of 0 to 1
0 1 ( cn 60 , c s 20 , v 80 , 1 400 , 2 100 , 1 and 0.5 ).
2 increases, the selling prices of manufactured and remanufactured items increase (see Fig.
7), and the demands for manufactured and remanufactured items increase except that the demand for manufactured items remains the same in the joint decision case (see Fig. 8). Furthermore, the results reveal the most significant rise in the selling price and market demand for remanufactured items. It is because the market base ( 2 ) has high impact on the remanufacturing plan and the selling pricing policy of remanufactured items,
ACCEPTED MANUSCRIPT while it has little influence on those of the manufactured items. Given the joint decision case, the demand for manufactured items is unaffected, which means that cooperative scenario can avoid ‘bank run’ in the market demand of remanufactured and manufactured items. 550
pn*
500
pn
450
ps*
Price
400
wn*
ps
300 250
ws*
200 150 100
150
200
250
300
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Market base 2
2 ( cn 60 , c s 20 , v 80 , 1 400 , 0 10 , 1 2 , 1 and 0.5 ).
Fig. 7. Prices vs
250
PT
50
Dn* Ds*
ED
150 100
Dn
M
200
Demand
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350
Ds
0
CE
100
AC
Fig. 8. Demand vs
150
200
250
300
Market base 2
2 ( cn 60 , c s 20 , v 80 , 1 400 , 0 10 , 1 2 , 1 and 0.5 ).
Example 4 In this example, we examine the effects of
1 and 2 on the coordination results of Model
MC.
According to Table 2, if 0.5 and v 80 , then it can be derived that M 24379 , T 3479 , *
*
R * 19641 and J 58513 . In Model MC, the respective ranges of revenue-and-expense sharing coefficients 1 ,
2 and 1 1 2 are
ACCEPTED MANUSCRIPT 0.42 1 0.60 ， 0.06 2 0.25 ， 0.34 1 1 2 0.52 . Given different values of
1 and 2 under the above conditions, the outcome is shown in Table 3.
Table 3 demonstrates that the profit sharing ratio of the Retailer decreases as
1 and 2 increases.
However, the wholesale price provided by the Manufacturer and the Remanufacturer also decreases. So the profit of the Retailer is still higher than that in Model TLG. In the event that
1 stays unchanged, the Remanufacturer
2 increases, but there is certain
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needs to pay more agency fees for qualifications to the Manufacturer as
increase in the final profit it shares. In Model MC, as the leader of the supply chain, the Manufacturer enjoys the highest profits at all times. Since the collection price maintains its level under joint decision-making in Model MC, the Remanufacturer is able to recover more products with relatively high price, thus advancing the sound development of CLSC and enabling the optimal channel benefits under joint decision-making. Within the range of
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individual rationality constraints, the profits of the chain members gained by way of sharing per certain ratios are remarkably higher than those in Model TLG. Therefore, combined coordinated pricing mechanism enables perfect coordination of the CLSC. Table 3
M
Coordination results of Model MC under different sharing coefficients
M **
T **
R **
H **
wn
(0.43,0.15,0.42)
25161
8777
24575
1626
25.2
8.4
(0.45,0.15,0.40))
26331
8777
23405
1620
24.0
8.0
(0.47,0.15,0.38)
27501
8777
22235
1614
22.8
7.6
(0.49,0.15,0.36)
28671
8777
21065
1608
21.6
7.2
(0.51,0.13,0.36)
29842
7606
21065
1368
21.6
7.2
(0.51,0.11,0.38)
29842
6436
22235
1134
22.8
7.6
(0.51,0.09,0.40)
29842
5266
23405
900
24.0
8.0
(0.51,0.07,0.42)
29842
4096
24575
666
25.2
8.4
(0.49,0.09,0.42)
28672
5266
24575
906
25.2
8.4
(0.47,0.11,0.42)
27501
6437
24575
1146
25.2
8.4
(0.45,0.13,0.42)
26331
7607
24575
1386
25.2
8.4
(0.43,0.15,0.42)
25161
8777
24575
1626
25.2
8.4
AC
CE
PT
ED
(1 , 2 ,1 1 2 )
ws
5. Conclusion This paper provides an integrated view to analyze the supply chain for remanufacture of patented products by taking into account pricing and coordination. A mathematical model is developed to optimize the decisions on the
ACCEPTED MANUSCRIPT collection price of used items, the selling price of items, and the patent licensing fees. Due to differentiated pricing of manufactured and remanufactured items, competitive demand for the two types of products and issues concerning the patent license or agency for qualifications, the pricing of supply chain herein is very important. The analysis of numerical examples shows that the impact of uncertainties of some important parameters, such as substitute ratio, salvage value, market base and so on. Accordingly the agency fees for qualifications, sharing coefficients and pricing are coordinated together to obtain the maximum profit of the system. Therefore, with certain agency fees for qualifications paid by the Remanufacturer, the coordinated pricing mechanism will
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encourage supply chain members to conduct joint decision-making, substantially improve channel benefits and enable the multi-win of the Manufacturer, the Remanufacturer and the Retailer. In addition, some significant conclusions, drawn through theoretical analysis and investigations of numerical examples with regard to the relationship between performance parameters and pricing, profits and so on, provide certain theoretical reference to the development and decision-making of CLSC. Further studies may consider the issues concerning a
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multi-period model, such as product life cycle patterns, used items with different quality levels and multiple recovery options, which can help better understand the influence of demand, return and pricing on the system. Acknowledgments
This work was supported by National Natural Science Foundation of China (Project Nos. 71531008, 71271073,71201044 and 71571002), Program for New Century Excellent Talents in University (Project
M
No.NCET-11-0625) and Key Project of HSSR of Education Department of Anhui Province(Project Nos. SK2016A379 and SK2014A393). The authors express their gratitude to Editor M.Y. Jaber and the anonymous
ED
referees for their most insightful and valuable comments on the paper, which were instrumental for elevating the
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