Research on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment

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1 Vol. 7, No. 6 (04), pp hp://dx.doi.org/0.457/ijhi Research on Invenory Sharing and Pricing Sraegy of Mulichannel Reailer wih Channel Preference in Inerne Environmen Hanzong Li College of Environmenal Science and Engineering, Peking Universiy lhz98@6.com Absrac Wih he developmen of he compuer echnology, many reailers sale he producs no only in he eniy shop, bu also in he online shop. The nework channel brings a lo of convenience. However, i also produces he channel conflic. In he dual channel supply chain, he reailers are in a passive posiion. Therefore, hey begin o use he opimal dynamical pricing sraegy o deermine he price of he producs. A he same ime, he reailers obain he greaer benefis according o reduce he invenory cos. Thereby, in his paper, considering he online channel preference, we sudy he invenory sraegy and he pricing sraegy of he producs in he dual channel. And hen we propose a shared invenory and a dynamical pricing sraegy. In addiion, we sudy he influence of he relaed parameers on he profi of he reailers. A las, he numerical analysis shows ha he shared invenory and he dynamical pricing sraegy can bring more profis for he reailers. Keywords: Dual-channel, shared invenory, channel preference. Inroducion Due o he developmen of he Inerne, many merchans begin o increase he produc sales by he sraegy of he eniy shop and he online shop. In addiion, his kind of channel sraegy has brough he increasing sales and he exensive marke share for he merchans. However, here is a problem which canno be ignored. Tha is he channel conflic. Merchans can sell producs no only by radiional channel bu also hrough he esablishmen of nework channel. Many companies, such as Compaq, HP, IBM, Samsung and Sony, have wo channels and muliple sales channels. The conflic of dual channel has araced he aenion of many scholars. Mukhopadhyay e al. argued ha reailers were able o differeniae heir producs hrough he nework channels by adding value o on-he-shelf goods []. Yue sudied he reailers pricing problem in dual channel supply chain []. Hua e al. examined a dual-channel supply chain and considered he facor of delivery lead ime in he pricing decisions [3]. Xie found ha he simple conracs, such as he wholesale price, buyback, revenue-sharing and Vendor Managed Invenory (VMI) conracs, canno coordinae he dual-supply chain wih invenory decisions [4]. Cai e al. showed ha he price discoun conracs perform well in a dual-channel supply chain [5]. Yao and Liu discussed Berrand and Sackelberg equilibrium pricing policies and compared he profi gains under hese wo ypes of compeiion in a dual channel [6]. Cai invesigaed he influence of he channel srucures and he channel coordinaion on he supplier, he reailer, and he enire supply chain in a dual-channel supply chain [7]. Karray and Zaccour discussed he producs reailers, he sales of privae brand producs and he manufacurers [8]. From he wo channels, Xie analyzed he cos and he price of he marke demand which were influenced by he adverising hough opimal decision level. And he poined ou ha he cooperaive game can improve he sysem [9]. Szmerekovsky and Zhangon hough ha he ISSN: IJHIT Copyrigh c 04 SERSC

2 Vol. 7, No. 6 (04) adverising coss will affeced he decision problems of manufacurers and reailers. In above sudy, he sudy abou he adverising decision-making and he sraegy of cooperaive adverising ino he research in dual channel supply chain are less [0]. The research shows ha he price of he producs in elecronic reailers wih zero-invenory was lower han he price of reailers own is own invenory. Bu he differen price would decrease wih ime in he rapid expansion marke []. Chaing W, Monahan G E hough ha cusomers would ransfer o anoher channel o buy goods in a cerain percenage []. Boycai sudied he disribuion sysem of he dual channel condiions. He also discussed he impac on channel efficiency of channel order quaniy decision problem and he raio of subsiuion [3]. Geng and Mallik discussed he invenory compeiion and he double channel assignmen problem. They also proposed he game equilibrium of he condiions ha he manufacurer capaciy was no limied. The sudy found ha even in capaciy limied circumsances, he manufacurers may also refuse o he reailer orders [4]. Yongbo Xiao discussed wo subjecs and each subjec had four differen cusomer group siuaions on he basis of he model of Frank [5]. Frank sudied wo subjecs on he basis of his model. And each subjec had wo differen cusomer group siuaions [6]. Zhang and Cooper researched he special problems of parallel fligh in muli -produc and muli-resource dynamic pricing problem. They srucured his problem as a Markov decision process [7]. Chen F Y, Chen Jian, Xiao Yongbo researched he Dynamic invenory raion conrol sraegy [8, 9] This paper aemps o esablish a model which can conac he dynamic pricing and revenue managemen wih considering he channel preference. We ry o research invenory sraegy and dynamic pricing problem in dual channel supply chain. And we examine he profis of reailers under differen invenory sraegies. In addiion, we sudy he effecs of he parameric variable and he channel preference on he profis of he reailers. The consrucion of his paper is as follows. The firs par is he inroducion. The second par is he esablishmen of he model. The hird par is he numerical analysis and he las par is he conclusion.. Esablishmen of he Model.. Descripion and Assumpion The online shop and he eniy shop sale he same produc. The pricing of he eniy shop is p. The price in he eniy shop is sable during a specific period. We assume ha he price in he sales cycle is fixed. Firsly, we consider ha he sales cycle is shor. Secondly, changing he produc price needs cos and i is no convenien. Therefore, i is reasonable o assume ha he price is fixed in a period. Finally, we assume he pricing of he online shop is p. And i can be changed. The price of he online shop no only influences reversely he demand of he online producs for he cusomers bu also effecs he demand of he eniy shop posiively. Similarly, he price of he eniy shop can influence he demand of he online shop posiively. The higher he price of he online shop, he demand of he online shop decreases and he demand of he eniy shop increases. The lower he price of he online shop, he demand of he online shop increases and he demand of he eniy shop decreases. We use ( p ) o represen he arrival rae of he online shop. And we use ( p ) o express he arrival rae of he eniy shop. We suppose ha a cusomer only buy one produc and he arrival of he wo cusomers is independen. Therefore, we can use he following funcions o express he relaion beween he arrival rae and he pricing. ( p ) A B p, A 0, B Copyrigh c 04 SERSC

3 Vol. 7, No. 6 (04) ( p ) ( ) A B p, A 0, B 0 We make he following assumpions. The hypohesis : B B ha is, for is demand, he influence of he online price is bigger han he eniy shop. This is obvious because he online shop can rea as he subsiues o he eniy shop. The hypohesis : A B p. When he price of he online shop is he same o he eniy shop, he online shop has cerain requiremen. When he price is bigger han A B, he demand of he online shop is zero. Figure. The Share Invenory In addiion, we divide he sell period ino several equal inervals. Every is a sage and is very small. Therefore, he probabiliy of appearing wo or more han wo cusomer arrivals is zero in a inervals. The whole sales cycle is [ 0, T ] and,,,, T. Because he cusomer arrival obeys he Poisson disribuion, he rae of cusomer arrival is equal o he excepion arrival number in. ( p ) T is equal o he number of he excepion cusomer arrival number in nework shop in. The excepion cusomer arrival numbers in nework channel are as follows. ( p ) T P () P () 3 P (3) As he probabiliy of he wo or more cusomer arrivals can be ignored, ( p ) T p ().We se ( p ) T, namely he probabiliy of one cusomer arrives in nework channel is equal o he excepion value of Poisson disribuion. The probabiliy of Copyrigh c 04 SERSC 367

4 Vol. 7, No. 6 (04) one cusomer arrives in eniy shop is equal o ( p ) T in. We se i as.the probabiliy of none cusomer arrives is.we can ge 0 and: A B p T T ( p ) a b p, a 0, b 0 () A B p T T ( p ) ( ) a b p, a 0, b 0 ().. The Opimal Pricing Sraegy We use a hree dimensional vecor (, n, n ) o describe he sae of he whole sales sysem. Among hem, is he curren sae which belongs o he secion [0, T ]. n is he invenory level of he online sore and n is he invenory level of he eniy shop. The firs siuaion is o use a wo dimensional vecor (, n ) o describe he sae of he sysem. From he sar of he sage o he end of he sales, when he invenory of he eniy shop is n, he oal maximum expeced fuure income in he sales period is R ( n ). Then we can wrie he dynamic recursive equaions. The second siuaion is o use hree dimensional vecor (, n, n ) o describe he sae of sysem. From he sar of he sage o he end of he sales, when he invenory level of he online sore is n and he invenory level of he eniy shop is n, he oal maximum expeced fuure income in he sales period [, T ] is R ( n, n ). Then we can wrie he dynamic recursive equaions. In addiion, because he invenory of he eniy shop is no specifically provided for he demand of he online shop, i only provides he emporary supplemen when he nework channel is no he invenory in he second siuaion. Therefore, we need o esablish a specific cos o perform he nework orders and we hypohesis i as d. A las, in order o analyze he opimal iniial invenory of he wo siuaions, he nework channel and he eniy channel belong o he same seller, we assume he purchasing cos of he wo channels is he same. We denoe i as c. The revenue funcion is a increasing funcion abou he remaining invenory n. In addiion, i is a decreasing funcion abou he ime. Theorem : The revenue funcion R ( n ) has he following characerisics. () R ( n ) increases wih he increasing of n and i decreases wih he increasing of. () R ( n ) R ( n ) decreases wih he increasing of n and i decreases wih he increasing of. Theorem The revenue funcion R ( n, n ) has he following characerisics. () R ( n, n ) increases wih he increasing of n and n. And i decreases wih he increasing of. () R n n R n n (3) R n n R n n (4) R n n R n n decreases wih he increasing of n and (, ) (, ) decreases wih he increasing of n and decreases wih he increasing of n. And i increases wih he (, ) (, ) (, ) (, ) n. increasing of (5) R ( n, n ) R ( n, n ) decreases wih he increasing of n and n. And i decreases wih he increasing of. n. n. 368 Copyrigh c 04 SERSC

5 Vol. 7, No. 6 (04)... The Firs Siuaion (he eniy shop and he online shop share he invenory of he eniy shop): In he sage of, he maximum fuure expecaion income for he reailer is as follows. R ( n ) m ax{ [ p R ( n )] [ p R ( n )] ( ) R ( n )} (3) p R (0 ) 0, R ( n ) 0 T Among hem,. Puing he formula () and () ino he formula (3), we can obain he following conclusion. R ( n ) m a x{ ( a b p )[ p R ( n )] (( ) a b p )[ p R ( n )] p [ a ( ) a ( b b ) p ] R ( n )} [ a b R ( n )] b p b [ p R ( n )] ( b b ) R ( n ) 0 b 0 p ( n a b p b b R n R n ) ( )[ ( ) ( )] b (4) According o he analysis of he srucure characerisics for he revenue funcion, from he opimal dynamic pricing (4), we can launch he relaed conclusions of he firs siuaion. These conclusions are as follows. The conclusion : When is a consan value, he opimal dynamic pricing p ( n ) is a series of price series. And i decreases wih he increasing of he remaining invenory n. In addiion, i decreases wih he increasing of. The conclusion : When is a consan value, he relaion beween he opimal dynamic pricing p ( n ) and he coefficiens is ha i increases wih he increasing of a and b. The conclusion 3: When is a consan value, he opimal dynamic pricing is larger han he opimal saic pricing. The saic process is as follows. p is fixed. Therefore, he whole process is given and i needs no o use he dynamic recursive process. So we can direcly obain he maximum benefis p. Tha is, m a x{ R ( Q )} p p ( A B p ) p (( ) A B p ) p p A B p a b p p B b # The saic process is as follows. Each sae (, n ) corresponds o an opimal pricing. Moreover, he range of he opimal pricing has he following relaion. Due o he range of R ( n ) R ( n ) is [0, p ], we inference he following conclusion. a b p b p ( n ) a b p ( b b )[ R ( n ) R ( n )] a b p b b Copyrigh c 04 SERSC 369

6 Vol. 7, No. 6 (04) Therefore, he opimal dynamic pricing is larger han he opimal saic pricing. Because of he range of p, and in order o ensure o have he opimal soluion, we need he following consrains. Then we can ge a b p b p. a b p a b (5) p... The Second Siuaion (he eniy shop and he online shop have heir own invenories): The eniy shop and he online shop respecively have one invenory. If he online shop has no he invenory, we allow he eniy shop o perform he nework order. However, if he eniy shop has no he invenory, we will lose he cusomers. This is accorded wih he realiy. The oal maximum fuure expeced revenue for he reailers is discussed as follows. p R ( n, n ) 0, ( n 0, n 0 ) m a x{ [ p R ( n, 0 )] ( ) R p ( n, 0 )}, ( n 0, n 0 ) m a x{ [ p d R (0, n )] [ p p R (0, n )] ( ) R (0. n )}, ( n 0, n 0 ) m a x{ [ p R ( n, n )] [ p p R ( n, n )] ( ) R ( n, n )}, ( n 0, n 0 ) Among hem, R (0, 0 ) 0, R ( n, n ) 0 T. We pu he formula () and () ino he formula (6). () When n 0, n 0 R ( n ) m a x { ( a b p )[ p R ( n )] [ a b p ] R ( n )} [ a b R ( n )] b p b R ( n ) 0 b 0 p a b [ R ( n ) R ( n )] ( n ) b Due o b 0, he opimal pricing an R ( n ) have a posiive relaionship. From he heorem, we can know he opimal dynamic pricing p ( n ) is a series of price series. And i decreases wih he increasing of n. I decreases wih he increasing of. () When n 0, n Copyrigh c 04 SERSC

7 Vol. 7, No. 6 (04) R ( n ) m a x { ( a b p )[ p d R ( n )] (( ) a b p )[ p R ( n )] [ a ( ) a ( b b ) p ] R ( n )} [ a b R ( n )] b d b p b R ( n ) ( b b ) R ( n ) 0 b 0 p ( n ) a b p b d b b R n R n ( )[ ( ) ( )] Due o b b, he opimal pricing an R ( n ) have a posiive relaionship. From he heorem, we can know he opimal dynamic pricing p ( n ) is a series of price series. And i decreases wih he increasing of n. I decreases wih he increasing of. (3)When n n 0, 0 b R ( n, n ) m a x{ ( a b p )[ p R ( n, n )] p (( ) a b p )[ p R ( n, n )] [ a ( ) a ( b b ) p ] R ( n, n )} d R ( n, n ) a b R ( n, n )] b p b p b R ( n, n ) ( b b ) R ( n, n ) 0 d R ( n ) b 0 And a b p b [ R ( n, n ) R ( n, n )] p ( n, n ) b b [ R ( n, n ) R ( n, n )] b a b p ( b b ) R ( n, n ) b b R ( n, n ) b R ( n, n ) b a b p ( b b )[ R ( n, n ) R ( n, n )] b b p [ R ( n, n -) R ( n, n )] b From he heorem, we can know ha he opimal dynamic pricing p ( n, n ) is a series of price series. And i decreases wih he increasing of n. I decreases wih he increasing of. Copyrigh c 04 SERSC 37

8 Vol. 7, No. 6 (04) 3. Numerical Analysis We assume ha he arrival rae is consisen beween he online shop and he eniy shop. And he oal invenory of he online shop is he same o he eniy shop. T 00, he oal invenory is 000( n n 000 ), he price of he eniy shop is p 50, he price of he nework shop is p and i is dynamic adjusmen. a 8 0 T, a 30 T, b 4 T, b T d T. The online shop adjuss he price dynamically o effec he demand of he eniy shop and he online shop according o he remaining invenory of he eniy shop and he ime sae. Then we can make he income maximum for he reailer. This is he revenue managemen according o adjus he price dynamically. Figure. The Profis of Two Invenory Sraegies Due o n n 000, wih he increasing of n, n decreases. Bu from he Figure, we can find ha wih he increasing of n, he revenue of he reailers increases firsly,hen he revenue begin o decrease. However, no maer how n changes, he profi of he reailers in he shared invenory sraegy is higher han ha in he separae invenory sraegy. Figure 3. The Influence of b on he Profi 37 Copyrigh c 04 SERSC

9 Vol. 7, No. 6 (04) From he Figure 3, we can see he relaion beween he profi of he reailer and he coefficien b. Wih he increasing of b, he revenue increases. A he same ime, we find ha he larger values of he b, he growh rae of he reailer s profi is smaller. Conversely, when he value b becomes small, he profi of he reailer is bigger. Figure 4. The Influence of on he Profi From Figure 4, we can find ha wih he increasing of he online channel preference rae, he profi of he reailer increases. However, he profi of he reailer begins o decrease when increases coninuously. Because he increase of he online channel preference rae, he invenory of he eniy invenory decreases. And he price increases. A he same ime, he reailers need o conduc he marke research o obain he marke informaion. And hen hey also need o pay a high cos. 4. Conclusion In he dual channel supply chain environmen, he channel conflic is an urgen problem o be solved. In he radiional dual channel supply chain, he online shop and he eniy shop have heir own invenory respecively. I makes he invenory increase, hen he invenory cos increases. Therefore, he profis of he reailers decrease. In order o solve he above problem, we combine he online invenory and he eniy shop. Tha is, he online shop and he eniy shop use he same invenory. According o share one invenory, i can reduce he invenory cos. I can make he profis of he reailers maximum. In addiion, for one produc, he pricing of he eniy shop is higher han he online shop. For one produc, he demand rae in he eniy shop and he demand rae in he online demand are inversely proporional. If he price of he online shop is higher, he demand rae is lower. Then he demand rae in he eniy shop increases. In he pas lieraure, i adops he saic pricing sraegy o price producs. In his paper, we use he dynamical pricing sraegy o adjus he price in he online shop and he eniy shop. Then we can ge an opimal pricing sraegy. I makes he oal profis of he reailers maximum. Therefore, he innovaion of his paper is as follows. () According o merge he invenories of he online shop and he eniy shop, we ge a new shared invenory model. This shared invenory model can reduces he invenory cos and make he profis of he reailers increase. () We sudy he pricing problem in he online shop and he eniy shop. We use he Copyrigh c 04 SERSC 373

10 Vol. 7, No. 6 (04) dynamical pricing sraegy o sudy he relaion beween he online shop and he eniy shop. Then we ge an opimal dynamical pricing. I makes he profis of he reailer maximum. References [] S. K. Mukhopadhyay, D. Q. Yao and X. H. Yue, In-formaion sharing of value-adding reailer in a mixed channel hi-ech supply chain [J], Journal of Business Re-search, vol. 6, (008), pp [] X. H. Yue and J. Liu, Demand forecas sharing in a du-al-channel supply chain [J], European Journal of Operaional Research, vol. 74, (006), pp [3] G. Hua, S. Wang and T. C. E. Cheng, Price and lead ime decisions in a dual-channel supply chain, European Journal of Operaional Research, vol. 05, (00), pp [4] J. X. Xie and J. C. Wei, Coordinaing adverising and pricing in a manufacurer-reailer channel [J], European Journal of Operaional Research, vol. 97, (009), pp [5] G. Cai, Z. G. Zhang and M. Zhang, Game heoreical perspecives on dual-channel supply chain compeiion wih price discoun and pricing schemes, Inernaional Journal of Producion Economics, vol. 7, (009), pp [6] D. Yao and J. Liu, Compeiive pricing of mixed reail and e-ail disribuion channels, Omega, vol. 33, (005), pp [7] G. Cai, Channel selecion and coordinaion in dual-channel supply chains, Journal of Reailing, vol. 86, (00), pp. 36. [8] S. Karray and G. Zaccour, Could co-op adverising be a manufacurer s counersraegy o sore brands?, [J ]Journal of Business Research, vol. 59, no. 9, (006), pp [9] J. X. Xie and J. C. Wei, Coordinaing adverising and pricing in a manufacurer-reailer channel [J], European Journal of Operaional Research, vol. 97, (009), pp [0] J. G. Szmerekovsky and J. Zhang, Pricing and wo-ier adverising wih one manufacurer and one reailer [J], European Journal of Operaional Research, vol. 9, (009), pp [] H. Zhao and Y. Cao, The role of e-ailer invenory policy on e-ailer pricing and profiabiliy [J], Journal of Reailing, vol. 80, no. 3, (004), pp [] W. Chaing and G. E. Monahan, Managing invenories in a wo-echolon dual-channel supply chain [J], European Journal of Operaion Research, vol. 6, no. 3, (005), pp [3] T. Boyaci, Compeiive socking and coordinaion in a muli-ple-channel disribuion sysem [J], IIE ransacions, vol. 37, no. 3, (005), pp [4] Q. Geng and S. Mallik, Invenory compeiion and allocaion in a muli-channel disribuion sysem [J], European Journal of Operaion Research, vol. 8, no. 3, (007), pp [5] Y. Xiao, F. Y. Chen and J. Chen, Opimal invenory and dynamic admission policies for a reailer of seasonal producs wih affiliae programs and drop-shipping [J], NRL, vol. 56, no. 4, (009), pp [6] F. Y. Chen, J. Chen, M. Parlar and Y. Xiao, Opimal invenory and admission policies for drop-shipping reailers serving in-sore and online cusomers [J], IIE Transacions, vol. 43, no. 5, (0), pp [7] D. Zhang and W. L. Cooper, Pricing subsiuable fligh in airline revenue managemen [J], European Journal of Operaional Research, vol. 97, no. 3, (009), pp [8] F. Y. Chen, C. Jian and X. Yongbo, Opimal admission policies for a reailer of seasonal producs wih dropshipping [C], IEEE Inernaional Conference on Roboies and Auomaion, Roma, vol. 4, (007), pp [9] X. Yongbo, F. Y. Chen and C. Jian, Opimal invenory and dynamic admission policies for a reailer of seasonal producs wih affiliae programs and drop-shipping [J], Naval Research Logisics, vol. 56, no. 4, (009), pp Auhor Hanzong Li, He is a posdocoral of College of Environmenal Science and Engineering, Peking Universiy. His research direcion is economic sociology and environmenal sociology. 374 Copyrigh c 04 SERSC