Pricing decisions for reversesupply chains

Gu QiaolunSchool of Information Technology Engineering,

Tianjin University of Technology and Education, Tianjin, China andAntai College of Economics and Management,Shanghai Jiaotong University, Shanghai, China

Ji JianhuaAntai College of Economics and Management, Shanghai Jiaotong University,

Shanghai, China, and

Gao TiegangCollege of Software, Nankai University, Tianjin, China

Abstract

Purpose – The purpose of this paper is to present the collecting price decisions of used products inreverse supply chains based on the following cases: manufacturer for collecting and processing, thirdparty for collecting and manufacturer for processing, retailer for collecting and manufacture forprocessing, and third party for collecting and processing.

Design/methodology/approach – The paper considers a recycling channel whereby amanufacturer collects and processes the used products or delegates collecting (or processing) to theretailer or a third party; characterizes the steps of processing a returned used product; gives acollection function of used products which is an increasing function of the collecting price, since thequantity of returned used products is affected by the end customer’s willingness and the endcustomer’s willingness is affected by the collecting price. The optimal results were obtained by gametheory.

Findings – By investigating the pricing decisions for different cases, the manufacturer prefers tocollect the used products rather than delegate to others if manufacturer for processing, and a thirdparty joining the reverse supply chains hopes to collaborate more deeply, not only collecting but alsoprocessing the used products.

Research limitations/implications – The main implication is that the reusing ratio of thereturned used products and the remanufacturing ratio of the key parts have impacts on the optimalpricing decisions of reverse supply chains.

Practical implications – The paper describes a very useful method for managers to makecollecting price decisions for reverse supply chains.

Originality/value – The paper provides the optimal results of collecting price decisions. The papercontributes to the reverse supply chains researches and managers who are responsible for the reversesupply chains.

Keywords Cybernetics, Collecting, Recycling, Manufacturing industries, Pricing

Paper type Technical paper

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/0368-492X.htm

This work was supported by the National Nature Science Foundation of China under GrantNo. 70871089.

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KybernetesVol. 40 No. 5/6, 2011

pp. 831-841q Emerald Group Publishing Limited

0368-492XDOI 10.1108/03684921111142377

1. IntroductionCurrently, there are many studies on competition and cooperation in supply chainsincluding forward and reverse supply chains (Choi, 1991; Emmons and Gilbert, 1998;Gu et al., 2005a, b; Huang and Li, 2001; Li et al., 1995, 2003; Luo et al., 2004; Lu et al.,2003; Mu et al., 2006; Pranab and Harry, 2001; Reyniers and Tapiero, 1995; Song et al.,2003; Vorasayan and Ryan, 2006; Wei, 2000; Zhang and Huang, 2006). In reversesupply chains, the used products are returned by or collected from the end customers.This requires decisions on the incentives for the end customers’ willingness ofreturning their used products. Commonly, the collecting price given to the endcustomer is one of the incentives.

In the collecting price decisions of used products literature, Vorasayan and Ryan(2006) study the optimal price and quantity of refurbished products. They model thesale, return, refurbishment, and resale processes in an open-queuing network andformulate a mathematical program to find the optimal price and proportion torefurbish. Gu et al. (2005a, 2005b) study the pricing decisions of returned used productsbased on the reverse supply chains by game theory. They assume that all of thereturned used products can be reused directly by carrying out the necessaryoperations. In fact, a returned used product may not be refurbished or reused directlybecause of its quality uncertainty.

In this paper, we mainly focus on the collecting price decisions for used products inreverses supply chain based on the previous literature. In our study, we will give thestep of processing a returned used product in Section 2. We consider four cases:manufacturer for collecting and processing (MCP), third party for collecting andmanufacturer for processing (TCMP), retailer for collecting and manufacture forprocessing (RCMP), and third party for collecting and processing (TCTP).

This paper is organized as follows. In Section 2, we will give the description andnotation. In Section 3, we will show the optimal price decisions in different cases. InSection 4, we will analyze the optimal results. We summarize our results in Section 5,and also suggest directions for future research.

2. Description and notationWe consider a recycling channel whereby a manufacturer collects and processes the usedproducts by herself or delegates collecting (or processing) to a retailer or a third party.

Collecting. When the manufacturer (or the retailer, the third party) collects the usedproducts from the end customers, they should pay a collecting price for each usedproduct to the end customer.

Processing. We characterize the processing of a returned used product as follows:. reused directly;. if it cannot be reused directly, it will be disassembled so that the key part, the

common parts, the materials, and the remnants can be obtained;. remanufacturing the key part, and if the key part cannot be remanufactured, it

will be disassembled so that the amount of the common parts, the amount of thematerials, and the amount of the remnants will be increased;

. the common parts will be used as spare parts in service logistics and thematerials will be recycled; and

. the remnants will be sent to landfill sites.

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832

The steps of processing are shown in Figure 1.In each period, the manufacturer takes back all of the returned used products from

the retailer or the third party when the manufacturer undertakes the processing of thereturned used products; the manufacturer takes back only the key part that can beremanufactured from the third party when the third party undertakes the processing ofthe returned used products. The manufacturer has decided to remanufacture only a keypart that has the maximized surplus value, for example, the motor of the car. At thesame time, i kinds of common parts and j kinds of materials can be obtained.

We use the following notations throughout the paper:

p reuse The unit income of a used product that can be reused directly.

v reuse The unit marginal cost of cleaning and testing a returned used productwhich can be reused directly.

When the key part can be remanufactured, the notations are as follows:

v retre The unit cost of processing a returned used product that cannot be reuseddirectly, includes disassembling cost, cleaning cost, etc.

p reman The unit income of the key part after remanufacturing.

p spare2 i The unit income of the kind of i common part obtained from a returnedused product.

p recyc2 j The unit income of the kind of j recycled material obtained from areturned used product.

v dis The unit disposal cost of the remnants obtained from a returned usedproduct.

When the key part cannot be remanufactured, the notations are as follows:

v retre1 The unit cost of processing a returned usedproduct that cannot be reused and a key partthat cannot be remanufactured, includesdisassembling cost and cleaning cost, etc.v retre1 $ v retre.

Figure 1.Processing of a returned

used product

A returnedused product

Can be reused directly(Reused directly)

Can’t be reused directly

Disassembly

Cleaning and testingA reusedproduct

The keypart

The commonparts (1 to i)

The materials(1 to j)

The remnants

Can be remanufactured

RemanufacturingA partas new

Can’t be remanufactured

Disassembly

The commonparts (1 to i)

The materials(1 to j)

The remnants

(used as spare part)

(Recycling)

(Disposal)

(Remanufacturing thekey part)

Reverse supplychains

833

p spare12 i The unit income of the kind of i common partobtained from a returned used product. Theunit income will increase after disassemblingthe key part that cannot be remanufacturedp spare12 i $ p spare2 i.

p recyc12 j The unit income of the kind of j recycledmaterial obtained from a returned usedproduct. The unit income will increase afterdisassembling the key part that cannot beremanufactured p recyc12 j $ p recyc2 j.

v dis1 The unit disposal cost of the remnantsobtained from a returned used product, theunit disposal cost will increase afterdisassembling the key part that cannot beremanufactured v dis1 $ v dis.

pMCPm ; pRCMP

m ; pTCMPm , and pTCTPm The unit reclaiming/collecting price for a

returned used product or a key part of themanufacturer in cases MCP, RCMP,TCMP, andTCTP, respectively.

pRCMPr The unit collecting price for a returned used

product of the retailer in case RCMP.

pTCMPt and pTCTPt The unit collecting price for a returned used

product of the third party in cases TCMP andTCTP.

vt The unit marginal operational cost ofcollecting for the third party.

vr The unit marginal operational cost ofcollecting for the retailer.

f( p) The quantity of the returned used products, itis an increasing function of the collecting price,f( p) ¼ (dp k d . 0,0 , k , 1), p denotes thecollecting price of the supply chain memberwho is closer to the customer.

PMCPm ;PRCMP

m ;PTCMPm , and PTCTP

m The profit of the manufacturer in cases MCP,RCMP, TCMP, and TCTP, respectively.

PTCMPt and PTCTP

t The profit of the third party in cases TCMPand TCTP.

PRCMPr The profit of the retailer in case RCMP.

PMCP, PRCMP, PTCMP, and PTCTP The total profit of reverse supply chains incases MCP, RCMP, TCMP, and TCTP,respectively.

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834

l The reusing ratio of the returned usedproducts, 0 # l # 1.

d The remanufacturing ratio of the key parts,0 # d # 1.

3. The optimal price decisionsIn this section, our study is based on the following cases: MCP, TCMP, RCMP, andTCTP.

We assume that the manufacturer has sufficient channel power over the retailer orthe third party to act as a Stackelberg leader in every case. Let p̂ and v̂ denote the totalincome and the total processing cost when the manufacturer or the third partyprocesses a returned used product:

p̂ ¼ lp reuse þ p reman þi

Xp spare2i þ

j

Xp recyc2j

0@

1Adð1 2 lÞ

þi

Xp spare12i þ

j

Xp recyc12j

0@

1Að1 2 dÞð1 2 lÞ ð1Þ

v̂ ¼ lvreuse þ ðvdis þ vretreÞdð1 2 lÞ þ ðvdis1 þ vretre1Þð1 2 dÞð1 2 lÞ ð2Þ

3.1 Case MCP: manufacturer for collecting and processingIn this case, the manufacturer undertakes the used products collecting and processing,and decides the collecting price. Case MCP is shown in Figure 2.

Hence, the manufacturer will optimize:

pMCPm

MaxPMCPm ¼ p̂2 v̂2 pMCP

m

� �d pMCP

m

� �kð3Þ

It is easy to prove that the objective function is concave in pMCPm , the optimal collecting

price is:

pMCP*m ¼

kðp̂2 v̂Þ

kþ 1ð4Þ

The optimal quantity and profits can easily be found by substitution of pMCP*m .

The results are listed in Table I.

Figure 2.Case MCP

Used productsManufacturer

(collecting and processing)End customer

Collecting price

Reverse supplychains

835

Man

ufa

ctu

rer

for

pro

cess

ing

Th

ird

par

tyfo

rp

roce

ssin

gC

ase

MC

PC

ase

RC

MP

Cas

eT

CM

PC

ase

TC

TP

p* m(k

(p̂2

v̂))/

(kþ

1)(k

( p̂2

v̂)þ

v r)/

(kþ

1)(k

(p̂2

v̂)þ

v t)/

(kþ

1)p

reman2

((2k

þ22

k2)(p̂2

v̂2

v t))

/(2

(kþ

1)2d

(12

l))

b* m/

//

(k2(p̂

2v̂2

v t))

/(2(kþ

1)2)

p* r/

k2(p̂

2v̂2

v r)/

(kþ

1)2

//

p* t/

/(k

2(p̂

2v̂2

v t))

/(kþ

1)2

(k2(2kþ

1)(p̂

2v̂2

v t))

/(kþ

1)3

f(p)

*(k

kd

(p̂2

v̂)k)/

(kþ

1)k

(k2kd

(p̂2

v̂2

v r)k

)/(kþ

1)2k

(k2kd

(p̂2

v̂2

v t)k

)/(kþ

1)2k

(k2k(2kþ

1)kd

(p̂2

v̂2

v t)k

)/(kþ

1)3k

P* m

(kkd

(p̂2

v̂)kþ

1)/

(kþ

1)kþ

1(k

2kd

(p̂2

v̂2

v r)kþ

1)/

(kþ

1)2kþ

1(k

2kd

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)2kþ

1((k

2kd

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)2kþ

1)£

(((2kþ

1)k(kþ

12

k2))

/(kþ

1)kþ

1)

P* r

/(k

2kþ

1d

(p̂2

v̂2

v r)kþ

1)/

(kþ

1)2kþ

2/

/

P* t

//

(k2kþ

1d

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)2kþ

2(k

2kþ

1(2kþ

1)kþ

1d

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)3kþ

3

P*

(kkd

(p̂2

v̂)kþ

1)/

(kþ

1)kþ

1(k

2k(2kþ

1)d

(p̂2

v̂2

v r)kþ

1)/

(kþ

1)2kþ

2(k

2k(2kþ

1)d

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)2kþ

2((k

2k(2kþ

1)kd

(p̂2

v̂2

v t)kþ

1)/

(kþ

1)2kþ

2)£

((1þ

3kþ

2k22

k3)/

(kþ

1)kþ

1)

Table I.The optimal results of thereverse supply chains indifferent cases

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836

3.2 Case TCMP: the third party for collecting and manufacturer for processingIn this case, the third party engages in collecting the used products and themanufacturer for processing. To take the products back, the manufacturer must pay areclaiming price for per used product to the third party. The third party will decide thecollecting price and the manufacturer will decide the reclaiming price. Case TCMP isshown in Figure 3.

Because the manufacturer is the Stackelberg leader, we begin by characterizing thebest-response function of the third party. For a given pTCMP

m , the third party’s problem is:

pTCMPt

MaxPTCMPt ¼ pTCMP

m 2 vt 2 pTCMPt

� �d pTCMP

t

� �kð5Þ

Because the objective function is concave in pTCMPt , the third party’s first-order condition

characterizes the unique best response:

pTCMP*t ¼

k pTCMPm 2 vt

� �kþ 1

ð6Þ

The manufacturer’s problem can be stated as:

pTCMPm

MaxPTCMPm ¼ p̂2 v̂2 pTCMP

m

� �d

k pTCMPm 2 vt

� �kþ 1

" #k

ð7Þ

Because the objective function is concave in pTCMPm , and the optimal reclaiming price is:

pTCMP*m ¼

kðp̂2 v̂Þ þ vt

kþ 1ð8Þ

The optimal collecting price, quantity, and profits can easily be found by substitution of

pTCMP*m and pTCMP*

t . The results are listed in Table I.

3.3 Case RCMP: retailer for collecting and manufacturer for processingIn this case, the retailer engages in collecting the used products. To take the productsback, the manufacturer must pay a reclaiming price for per used product to the retailer.The retailer will decide the collecting price and the manufacturer will decide thereclaiming price. Case RCMP is shown in Figure 4.

In the similar means with case TCMP, the optimal results of case RCMP areeasily obtained as shown in Table I. The main difference between cases TCMP and

Figure 3.Case TCMP

Used productsThird party(collecting)

End customerManufacturer(processing)

Used products

Reclaiming price Collecting price

Figure 4.Case RCMP

Used productsRetailer

(collecting)End customer

Manufacturer(processing)

Used products

Collecting priceReclaiming price

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837

RCMP is the operation cost of the third party and the retailer when they collect theused products.

3.4 Case TCTP: the third party for collecting and processingIn this case, the third party engages in collecting and processing of the used productsby contracting to the manufacturer, and the manufacturer undertakes some processingcost. The manufacturer is the Stackelberg leader. In this case, the manufacturer onlytakes back the key part that can be remanufactured. To take the key part that can beremanufactured back, the manufacturer must pay a reclaiming price to the third party.The third party will decide the collecting price and the manufacturer will decide thereclaiming price for the key part. Case TCTP is shown in Figure 5.

Herein, pTCTPm and bTCTPm denote the reclaiming price of the key part and the processingcost undertaken by the manufacturer for processing a used product, respectively.

Because the manufacturer is the Stackelberg leader, we begin by characterizing thebest-response function of the third party. For given pTCTPm , the third party’s problem is:

pTCTPt

MaxPTCTPt ¼ ðp reuse2 vreuse2 pTCTPt Þld pTCTPt

� �k

þ pTCTPm þi

Xp spare2i þ

j

Xp recyc2j2 vdis2 vretre2 pTCTPt

0@

1A

� dð12lÞd pTCTPt

� �kþ

i

Xp spare12i þ

j

Xp recyc12j2 vdis1 2 vretre1 2 pTCTPt

0@

1A

� ð12 dÞð12lÞd pTCTPt

� �k2vtd pTCTPt

� �kþbTCTPm d pTCTPt

� �k¼ p̂2 v̂þ bTCTPm 2 dð12lÞðp reman 2 pTCTPm Þ2 vt 2 pTCTPt

h id pTCTPt

� �kð9Þ

Because the objective function is concave in pTCTPt , the third party’s first-ordercondition characterizes the unique best response:

pTCTP*t ¼

k

kþ 1p̂2 v̂þ bTCTPm 2 dð1 2 lÞðp reman 2 pTCTPm Þ2 vt

h ið10Þ

The manufacturer’s problem can be stated as:

Figure 5.Case TCTP

Used productsThird party(collecting and

processing )End customerManufacturer

Key parts

Collecting priceReclaiming price

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838

pTCTPm ;bTCTPm

MaxPTCTPm ¼ p reman 2 pTCTPm

� �dð1 2 lÞ2 bTCTPm

h i

� dk

kþ 1p̂2 v̂þ bTCTPm 2 dð1 2 lÞ p reman 2 pTCTPm

� �2 vt

h i� �k

ð11Þ

Again, the objective function is concave in pTCTPm , and the optimal results are:

pTCTP*m ¼ p reman 2

p̂2 v̂2 ðkþ 1ÞbTCTP*m 2 vt

ðkþ 1Þdð1 2 lÞð12Þ

and:

bTCTP*m ¼

k 2ðp̂2 v̂2 vtÞ

2ðkþ 1Þ2ð13Þ

The optimal collecting price, quantity, and profits can easily be found by substitution of

pTCTP*m and bTCTP*

m . The results are listed in Table I.

4. Analysis of the optimal resultsHerein, Max (x, y) denotes the larger between x and y, Min(x, y) denotes the smallerbetween x and y. Based on the optimal results summarized in Table I, we obtain somepropositions as shown below:

P1. In cases MCP,TCMP and RCMP, the collecting prices, the quantities of thereturned used products and the profits of the manufacturer, the third partyand the retailer are related as follows:

Max pTCMP*t ; pRCMP*

r

� �, pMCP*

m ;Max�f pTCMP*

t

� �; f pRCMP*

r

� ��, f pMCP*

m

� �;

and Max�PTCMP* ;PRCMP*

�, PMCP* :

P2. In cases TCMP and TCTP, the collection prices, the quantities of the returnedused products, and the profits of the third party are related as follows:

pTCMP*t , pTCTP*

t ; f pTCMP*t

� �, f pTCTP*

t

� �; and PTCMP*

t , PTCTP*t :

The two propositions indicate that the manufacturer prefers to collect the usedproducts rather than delegate others if manufacturer for processing, and if the thirdparty joining the reverse supply chains, he hopes to collaborate more deeply, not onlyto collect but also to process the used products.

5. ConclusionIn this paper, we show the collecting price decisions of the reverse supply chainsconsider a recycling channel whereby a manufacturer collects and processes the usedproducts by herself or delegates collecting (or processing) to a retailer or a third party.Our study is based on four cases: MCP, TCMP, RCMP, and TCTP. By investigating the

Reverse supplychains

839

pricing decisions for different cases, we show that the manufacturer prefer to collectthe used products rather than delegate to others if manufacturer for processing, and ifthe third party joining the reverse supply chains, he hopes to collaborate more deeply,not only to collect but also to process the used products.

In future research, the reclaiming/collecting pricing decisions considering riskmanagement of the reverse supply chains may be appropriate subjects for furtherinvestigation.

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Corresponding authorGu Qiaolun can be contacted at: tjguqiaolun@sohu.com

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