pricing decisions for reverse supply chains
Post on 08-Dec-2016
219 Views
Preview:
TRANSCRIPT
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.
Reverse supplychains
831
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.
K40,5/6
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.
K40,5/6
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
K40,5/6
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
Reverse supplychains
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
K40,5/6
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.
References
Choi, C. (1991), “Price competition in a channel structure with a common retailer”, MarketingScience, Vol. 10 No. 4, pp. 271-96.
Emmons, H. and Gilbert, S.M. (1998), “The role of return policies in pricing and inventorydecisions for catalogue goods”, Management Science, Vol. 44 No. 2, pp. 276-s283.
Gu, Q.L., Gao, T.G. and Shi, L.S. (2005a), “Price decision analysis for reverse supply chains basedon game theory”, Systems Engineering – Theory & Practice, Vol. 25 No. 3, pp. 20-5(in Chinese).
Gu, Q.L., Ji, J.H., Gao, T.G. and Shi, L.S. (2005b), “Research on price decision for reverse supplychains based on fixed lowest quantitative demand”, Computer Integrated ManufacturingSystems, Vol. 11 No. 12, pp. 1751-7 (in Chinese).
Huang, Z.M. and Li, S.X. (2001), “Co-op advertising models in manufacturer-retailer supplychains: a game theory approach”, European Journal of Operational Research, Vol. 135 No. 3,pp. 527-44.
Li, F., Zhao, F.Q. and Li, H.Y. (2003), “Research on the games between factories andwholesalers in a supply chain”, Advances in Systems Science and Applications, Vol. 3 No. 1,pp. 83-6.
Li, S.X., Huang, Z.M. and Ashley, A. (1995), “Seller-buyer system co-cooperation in amonopolistic market”, Journal of Operational Research Society, Vol. 46 No. 1,pp. 1456-70.
Lu, Y.G., Tang, X.W. and Zhou, Z.F. (2003), “An analysis on the chaotic behavior of modelingintegration supply chain system”, Advances in Systems Science and Applications, Vol. 3No. 3, pp. 333-7.
Luo, W., Zang, Z.G. and Ou, Y.M.D. (2004), “Ou Co-op advertising models in simple supply chainbased on a game theory approach”, Systems Engineering – Theory & Practice, Vol. 2 No. 3,pp. 31-6 (in Chinese).
Mu, Y.P., Tang, X.W. and Ni, D.B. (2006), “Analysis of dynamic two-stage transfer pricing formulti-product firm”, Advances in Systems Science and Applications, Vol. 6 No. 1,pp. 134-9.
Pranab, M. and Harry, G. (2001), “Competition in remanufacturing”, Production and OperationsManagement, Vol. 10 No. 2, pp. 125-41.
Reyniers, D.J. and Tapiero, C.S. (1995), “The delivery and control of quality in supplier-producercontracts”, Management Science, Vol. 41 No. 10, pp. 1581-9.
Song, Y.X., Chen, M.Y. and Carl Ma, Y. (2003), “Supply chain partner selection based on fuzzymultiple attribute decision making”, Advances in Systems Science and Applications, Vol. 3No. 3, pp. 315-21.
Vorasayan, J. and Ryan, S. (2006), “Optimal price and quantity of refurbished products”,Production and Operations Management, Vol. 15, pp. 369-83.
K40,5/6
840
Wei, S.L. (2000), “A lemons market? An incentive scheme to induce truth-telling in third partylogistics providers”, European Journal of Operational Research, Vol. 125 No. 3,pp. 519-25.
Zhang, Y. and Huang, W.L. (2006), “Coordination of cooperative pricing for retail and e-tail basedon wholesale price adjustment”, Advances in Systems Science and Applications, Vol. 6 No. 4,pp. 592-8.
Corresponding authorGu Qiaolun can be contacted at: tjguqiaolun@sohu.com
Reverse supplychains
841
To purchase reprints of this article please e-mail: reprints@emeraldinsight.comOr visit our web site for further details: www.emeraldinsight.com/reprints
top related