Research Article Contracting Fashion Products Supply Chains When Demand Is Dependent on Price and Sales Effort

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1 Matheatical Pobles in Engineeing Volue 2015, Aticle ID , 7 pages Reseach Aticle Contacting Fashion Poducts Supply Chains When Deand Is Dependent on Pice and Sales Effot Ying Wei and Liyang Xiong School of Manageent, Depatent of Business Adinistation, Jinan Univesity, Guangzhou , China Coespondence should be addessed to Ying Wei; yingwei@jnu.edu.cn Received 15 May 2014; Revised 2 July 2014; Accepted 11 July 2014 Acadeic Edito: Pui-Sze Chow Copyight 2015 Y. Wei and L. Xiong. This is an open access aticle distibuted unde the Ceative Coons Attibution License, which peits unesticted use, distibution, and epoduction in any ediu, povided the oiginal wok is popely cited. This pape investigates optial decisions in a two-stage fashion poduct supply chain unde two specified contacts: evenueshaing contact and wholesale pice contact, whee deand is dependent on etailing pice and sales effot level. Optial decisions and elated pofits ae analyzed and futhe copaed aong the cases whee the effot investent fee is deteined and undetaken eithe by the etaile o the anufactue. Results eveal that if the etaile deteines the effot investent level, she would be bette off unde the wholesale pice contact and would invest oe effot. Howeve, if the anufactue deteines the effot level, he pefes to the evenue-shaing contact ost likely if both paties agee on consignent. 1. Intoduction Study in fashion poducts supply chains anageent often focuses on inventoy decisions and assues that deand is exogenously deteined [1, 2]. Howeve, in pactice etail stoe anages often cobine aketing decisions such as etailing pice and pootion level, which diectly ipacts consue deands, with opeational decisions like stock levels. Fo exaple, etail outlet anages take exta effot and offe discounting pices to those ovestock ites such as clothes and shoes. Deands ae theefoe egaded as endogenously deteined in such supply chain systes. In paticula, this pape investigates optial decisions in fashion poduct supply chains whee deand is endogenously dependent on both pice and sales effot. Contactsinfashionandtextilesupplychainsexhibits diffeent fos [3, 4]. Although wholesale picing contact hasbeenandstillisadoinantfo,shaingevenuewith patnes has inceasingly gown in ecent yeas [5]. We ae then inteested in how contact types influence picing and sales effot decisions of a fashion poduct supply chain. It is also woth noting though sales effot ost often is offeed by a etaile, it is still quite coon that a anufactue decides and exets effot investent to poote sales. Fo exaple, in Goe, the giant etail outlet in consue electonics in China, those band-nae anufactues tain and hie sales people to poote thei own poducts in Goe s outlets. Does it atte who takes the effot investent? If it does, will it ipacttheeffotlevelaswellasothesupplychaindecisions? In addition, unde diffeent contacting fos will the ipact be diffeent? Unde which scenaio, will the etaile (o the anufactue) be bette off? Thispapeintendstoanswethesequestions.Inpaticula, the pupose of the pape is theefold: fist, to investigate the ipact of pice and sales effot on the deand and supply chain decisions, second, to investigate the contacting fo on the supply chain decisions, and thid, to identify the playes optial choice fo diffeent supply chain settings. To study the degee of effectiveness of pice and sales effot on sales depends on how these factos influence the aggegate deand. The foulation of deand function is theefoevey essential. Huanget al. [6] give a copehensive suvey on deand functions in decision odeling. Hee we assue a powe odel whee both pice and sales effot ae endogenous decision vaiables. The advantage of the powe odel is its ability to chaacteize the nonlinea effects aising in the aket, howeve, with the dawback that the deand elasticity always equals a constant. In addition, when pice o sales effot appoaches zeo, deand appoaches infinity, which is not ealistic.

2 2 Matheatical Pobles in Engineeing Consideing the coplexity of the deand function, this pape confines the discussion to deteinistic deand in a single anufactue-etaile supply chain stuctue. Two types of contacts ae consideed: wholesale pice contact and evenue-shaing contact. With the pupose to axiize thei own pofits, optial decisions of both anufactue and etaile ae investigated and futhe copaed whee the effot investent fee deteined eithe by the anufactue o by the etaile. Ou esults eveal that (1) if the etaile decides the effot investent level, she would be bette off undethewholesalepicecontactandwouldinvestoe effot. (2) Howeve, if the anufactue deteines the effot level, he pefes to the evenue-shaing contact given that the effot ipact facto belongs to cetain specified ange. 2. Related Wok Thee have been a gowing nube of studies investigating the ipact of endogenous deand functions in ecent decades. A vaiety of atheatical fos have been developed to chaacteize deand functions which depend on a fi s opeational and aketing activities, see [6] fo a geneal eview. A siple classification is to divide it into deteinistic deand and stochastic deand foulations. Assuing deand is stochastic and pice-sensitive, a seies of wok study joint picing and inventoy pobles and investigates the optial cobined decisions, with [7]on single-peiod odels and [8 11] on ultiple-peiod odels. Extending the pice-sensitive deand assuption fo onestage poble to supply chain stuctues, Chauhan and Poth [12] study the optial decisions unde a evenue-shaing contact with the pupose to axiize the total chain s net pofit. Chiu et al. [13] show that fo pice-sensitive deand, a policy that cobines the use of wholesale pice, channel ebate, and etuns can coodinate a supply chain channel. Assuing deand is deteinistic and pice-dependent, soe study in joint inventoy and picing poble is based on linea deand odels [14, 15], while othes on powe odels [16]. Conducting a two-stage fashion supply chain with iskavese etaile and pice-dependent deand, Xu et al. [3] discuss evenue shaing contact and two-pat taiff contact and futhe exploes the optial conditions fo coodination. Typical wok assuing deand is dependent on sales effot can be efeed to [17 19]. Taylo [17] studies supply chain coodination consideing the ipact of sales effot on the deand unde channel ebates. Zhang and Chen [18] investigate diffeent fos of contact with effot-dependent deand. Chiu et al. [4] exploe the pefoance of sales ebate contact in fashion supply chains via a ean-vaiance faewok. Futhe noticing the ipact of both pice and sales effot, He et al. [19] study the coodination of supply chains. Soe wok incopoates othe aketing decisions like advetising and display level into opeational odels and study the cobined ipact on deand function. It should be noted that because of the coplexity of the deand function, ostly deand is assued to be deteinistic. Assuing deand is deteinistic and a powe function of picing and advetiseent decisions, Yue et al. [20] study the optial aketing decisions in a anufactue-etaile supply chain, and copaes the esults between a Stackelbeg and a Nash gae setting. Wang and Hu [21] studycapitalallocation s selection effect and investent efficiency poble, assuing deand is a deteinistic powe function depending on pice and investent level. Cao and Zhou [22] findthat quantity discounting contact can coodinate the supply chain given deand is deteinistic and influenced by both pice and stock level. This pape extends the exogenous deand assuption to endogenous deand incopoating pice and sales effot decisions in a supply chain syste, whee deand is assued to be a deteinistic powe function following [20 22]. It contibutes to the liteatue by discussing and copaing optial decisions unde diffeent contacting fo in the supply chain. In addition, it jointly consides supply chain decisions and aketing decisions, whoeve decides and undetakes the sales effot investent level eally depends on supply chain patnes bagain powe in the aket. 3. The Model We fist descibe a base odel unde a wholesale pice contact stuctue. In a two-stage supply chain syste, a isk neutal anufactue supplies a poduct to a single iskneutal etaile. Let w > 0 denote the wholesale pice and let c>0denote the unit poduction cost. The etaile decides the etailing pice p>0and effot investent level e. Hee the effot could be advetising, effot of sales people, and display effot to poote poducts, and so foth. Deand is a continuous vaiable dependent on etailing pice and effot investent level. Moe specifically, let deand D=kp e β, whee k>0is the potential aket size. is the pice ipact facto, with >1iplying that deand is sensitive to the pice, while 0< 1iplying that deand is insensitive to the pice. Following the standad assuption as entioned in [3], hee we assue > 1.Siilaly,β is the ipact facto of effot investent level. In addition, we assue that deandinceaseswiththeeffotinvestentlevel,whileata deceasing ate, that is, 0<β<1[14]. Eploying a wholesale pice contact, the gae s tiing is as follows. The anufactue fist sets a wholesale pice, w. The etaile then decides the etailing pice and effot investent level, odes q 0 units of inventoy and pays the anufactuewq. Noticing that deand is deteinistic, we have q=d=kp e β. Assuing that ode-fulfillent tie is zeo and thee is no poduction capacity constaint, theanufactuetheniediatelysuppliesq units to the etaile to satisfy he custoe. The net pofit of the etaile, π, and the net pofit of the anufactue, π,sepaatelyae π W,R =D(p w) e=k p e β (p w) e, (1) π W,R =Dw c). (2) Hee the fist supescipt W/R denotes fo wholesale pice/evenue-shaing contact, the second supescipt R/M denote fo etaile/anufactue decides the effot investent.

3 Matheatical Pobles in Engineeing 3 Unde a evenue shaing contact, when the etaile decides the effot investent level, the gae s tiing is as follows. The anufactue fist sets a wholesale pice, w, and evenue shaing atio λ. The etaile then decides the etailing pice and effot investent level, odes q 0 units of inventoy and pays the anufactue wq. Siilaly,q=D. The net pofits of both the etaile and the anufactue ae π R,R =D(λ p w) e=(λ p w) k p e β e, (3) π R,R =D [(1 λ) p+w c]. (4) Unde a wholesale pice contact, howeve, if the anufactue deteines and undetakes the effot investent (like P&G, as a anufactue, decides its advetising investent fo Panteen shapoo), the anufactue fist sets a wholesale pice,w, and decides the effot investent level, e. The etaile then decides the etailing pice and odes q 0 units of inventoy and pays the anufactue wq,wheeq= D. The net pofits of both the etaile and the anufactue ae π W,M =D(p w) =k p e β (p w), (5) π W,M =Dw c) e. (6) Unde a evenue-shaing contact, if the anufactue deteines the effot investent level e,weevisetheodel setting as follows. Instead of offeing a wholesale pice w, the anufactue asks the etaile to sell on consignent. The etaile decides the evenue shaing atio λ and the etailing pice p. Thenetpofitsoftheetaileandtheanufactue ae then π R,M =D λ p, (7) π R,M =D[(1 λ) p c] e. (8) In what follows, we will fist discuss the optial supply chain decisions unde the afoeentioned settings, and then copae the fo diffeent scenaios. 4. Optial Decisions If Retaile Deteines the Effot 4.1. Unde a Wholesale Pice Contact. Given a wholesale pice w, the etaile decides optial decisions on the etailing pice p and the effot investent e to axiize (1). Taking fist ode deivative on (1)yields π W,R p = k p 1 e β p w)+k p e β =0, π W,R =β k p e β 1 (p w) 1 = 0. e Solving the above equations, we obtain the optial pice p W,R = w/( 1) and the optial effot e W,R = [((β k)/( 1)) (/( 1)) ] w (1 )/(1 β). The anufactue then decides the optial wholesale pice w W,R to axiize his pofit (see (2)). Poposition 1 suaizes the optial decisions of both the anufactue and the etaile. (9) Poposition 1. (i) w W,R = (( β)/( 1)) c; (ii) p W,R = (/( 1)) (( β)/( 1)) c; (iii) e W,R = [((β k)/( 1)) (/( 1)) ] c (1 )/(1 β) (( β)/( 1)) (1 )/(1 β). Poof. (i) Substituting e W,R = [((β k)/( 1)) (/( 1)) ] w (1 )/(1 β) and D = e/(βp w)) = (e 1))/ (β w) into (2) and taking fist ode optial equation yields π W,R w = c w 2 1 β A w(1 )/(1 β) + 1 β 1 c w ) A 1 1 β w((1 )/(1 β)) 1 =0, (10) whee A = [((β k)/( 1)) (/( 1)) ].Wethen have w W,R = (( β)/( 1)) c, veifying (i). (ii)-(iii) Substituting w W,R back to p W,R and e W,R, (ii) and (iii) can then be easily poved. Based on the esults of Poposition 1, we can then calculate pofits of both the etaile and the anufactue, as suaized in Table Unde a Revenue-Shaing Contact. Given a evenueshaing contact {w, λ}, the etaile decides he optial decisions on p and e to axiize (3), while the anufactue decides his optial decisions on w and λ to axiize (4). Poposition 2 suaizes elated esults. Poposition 2. (i) w R,R =βc;(ii) λ R,R =β (iii) p R,R =c/ ( 1); (iv) e R,R = [((β k)/( 1)) (/( 1)) ] c (1 )/(1 β) β. Poof. The fist ode optial equation of (3) yields p R,R = ( w)/(( 1) λ) and e R,R = [((β k)/( 1)) (/ ( 1)) ] w (1 )/(1 β) λ /(1 β). Substituting the back to (4),andthentakingfistode deivative, we have π R,R λ = λ 2 ( 1) 1 β A w(1 )/(1 β) λ /(1 β) π R,R w +( ( 1) λ 1 1 c w ) 1 β A 1 β w (1 )/(1 β) λ (/(1 β)) 1 =0, = c w 2 1 β A w(1 )/(1 β) λ /(1 β) +( ( 1) λ 1 1 c w ) 1 β A 1 1 β w((1 )/(1 β)) 1 λ /(1 β) =0. (11) Solving the above equations yields w R,R =βcand λ R,R = β. Substituting the back to p R,R and e R,R, (i) (iv) ae then poved.

4 4 Matheatical Pobles in Engineeing Table 1: Pofits unde diffeent settings. a Model setting Pofits unde diffeent settings Pofit of the etaile Pofit of the anufactue (W a, R b ) ( 1 (1 )/(1 β) β 1) β 1 ) [ β k 1 (R, R) ( 1 β 1) β [ β k 1 1 ) ] /(1 β) 1 (W, M) β 1 1 ) [ β k 1 1 ) 1 (R, M) β 1 β 1)β) [ β k 1 1 ) ] W/R : wholesale pice/evenue-shaing contact. b R/M : etaile/anufactue decides the effot investent. 1 ) ] c (1 )/(1 β) ( 1 (1 )/(1 β) β 1) 1 β ) β 1 ) [ β k 1 c (1 )/(1 β) 1 β 1 β 1) β [ β k 1 1 ) ] ] c (1 )/(1 β) ( 1 /(1 β) 1) β 1 ) [ β k 1 1 ) c (1 )/(1 β) ( 1 β 1)β) [ β k 1 1 ) ] ] 1 ) c (1 )/(1 β) c (1 )/(1 β) ] c (1 )/(1 β) c (1 )/(1 β)

5 Matheatical Pobles in Engineeing 5 Siilaly, we can then calculate pofits of both the etaile and the anufactue, suaized in Table Copaison. Copaing the optial decisions and pofits between the above two settings, we have the following esults. Theoe 3. (i) p W,R >p R,R ;(ii) e W,R >e R,R ; (iii) πw,r π R,R. > Poof. (i) Fo Popositions 1 and 2, wehavep W,R /p R,R = ( β)/( 1). Noticing >1and 0<β<1,easilywehave ( β)/( 1) > 1,thus,(i)ispoved. (ii) Notice e W,R /e R,R = [(( 1)/( β)) 1 1/ β)],and1/(1 β) > 1. Toshowe W,R /e R,R > 1,itis equivalently to show ln[(( 1)/( β)) 1 (1/β)] > 0. Let f(, β) = ( 1) [ln( 1) ln( β)] ln β,since f(, β)/ β = ( 1)/( β) 1/β = (β 1))/(β β)) < 0, f(, β) deceases in β.thus,f(, β) > f(, 1) = 0. Siilaly, we have f(, β)/ = [ln( 1) ln( β)] + ( 1) 1/( 1) 1/( β)) = ln(( 1)/( β)) ( 1)/ ( β) + 1. Let x= ( 1)/( β),obviouslyx (0, 1) and x inceases in.letf(x) = ln x x+1,since f(x)/ x = 1/x 1 > 0, then f(x) inceases in x, andf(x) < f(1) = 0. Theefoe f(, β)/ < 0,andf(, β) decease in. As, (( 1)/( β)) 1 = e β 1, f(, β) = ln(e β 1 /β).noticethatf(, β) deceases in β,andf(, β) > f(, 1) = 0, theefoe, f(,β) > f(, β) > 0. Thus, e W,R /e R,R >1holds. (ii) is then poved. (iii) Noticing π W,R /π R,R = [(( 1)/( β)) 1 / β].followingthesaepovepocessasin(ii),thus /π R,R >1. π W,R Reak 4. When the etaile deteines and undetakes the effot investent, the optial wholesale pice and etailing pice ae highe unde wholesale pice. So is the effot investent level. As a payback, the etaile bettes off unde a wholesale pice contact. Theoe 3 also iplies that the etaile has no intension to cay out evenue-shaing contact if she has to undetake the effot investent. 5. Optial Decisions If Manufactue Deteines the Effot 5.1. Unde a Wholesale Pice Contact. Given a wholesale pice w, and the deteined effot investent e, theetaile decides optial etailing pice p to axiize (5). The fist ode optiality of (5) yieldsp W,M = ( w)/( 1). The anufactue then decides the optial w and e to axiize (6). Poposition5 suaizes the optial decisions. Poposition 5. (i) p W,M = (2 /( 1) 2 ) c; (ii) w W,M = (/( 1)) c; (iii) e W,M = [((β k)/( 1)) (/ ( 1)) ] c (1 )/(1 β) (/( 1)) /(1 β). Poof. Substituting p W,M = ( w)/( 1) into (6)obtains π W,M =Dw c) e =k 1 ) w e β (w c) e. Taking its fist ode optiality equation yields π W,M w π W,M e =k 1 ) ( ) w 1 e β (w c) k 1 ) w e β =0, =k 1 ) β w e β 1 (w c) 1=0. (12) (13) Solving the above equations obtains w W,M = (/( 1)) c and e W,M = [((β k)/( 1)) (/( 1)) ] c (1 )/(1 β) (/( 1)) /(1 β). Thus, (ii) and (iii) ae poved. Substituting w W,M into p W,M =( w)/( 1),wecanthen easily pove (i). Pofits of both the etaile and the anufactue ae calculatedandlistedintable Unde a Revenue-Shaing Contact on Consignent. Unde a evenue-shaing contact on consignent, the etaile decides the evenue shaing atio λ and the selling pice p to axiize (7), while the anufactue decides the effot investent e to axiize (8). Poposition 6 suaizes the elated esults. Poposition 6. (i) p R,M = ( c)/( 1);(ii) λ R,M = (1 β)/; (iii) e R,M = [((β k)/( 1)) (/( 1)) ] c (1 )/(1 β) β). Poof. Taking the fist ode deivative on (8) andsetstobe zeo obtains π R,M e =[(1 λ) p c] k p β e β 1 1=0. (14) Solving the equation yields e R,M = [β k] [(1 λ) p c] p /(1 β).substitutingitbackto(7)and taking the fist ode optiality equation yields π R,M p = 1 β 1 β B [(1 λ) p c]β/(1 β) p ((1 β)/(1 β)) 1 +B1 λ) [(1 λ) p c] (β/(1 β)) 1 p (1 β)/(1 β) =0, whee B=λ k [β k] β/(1 β). (15)

6 6 Matheatical Pobles in Engineeing π R,M λ =k [β k] β/(1 β) [(1 λ) p c] β/(1 β) p (1 β)/(1 β) β 1 β p λ k [β k]β/(1 β) [(1 λ) p c] (β/(1 β)) 1 p (1 β)/(1 β) =0. (16) Solving the above equations obtains p R,M = ( c)/( 1) and λ R,M = (1 β)/; thus, (i)-(ii) ae poved. Substituting the back to e R,M and then (iii) is poved. Pofits of both the etaile and the anufactue ae listed in Table Copaison. Copaing the optial decisions and pofits between the above two setting, we have the following theoe. Theoe 7. (i) p W,M >p R,M ;(ii)when1/e 0 β<1,whee e 0 is the iational nube and e , wehavee R,M > e W,M,inaddition,πR,M >πw,m. Poof. (i) Fo above discussions we have p W,M /p R,M = /( 1).Notice>1, thus, (i) holds. (ii) Notice e R,M /e W,M = [β (/( 1)) ].Let f() = (/( 1)) = (1 + 1/( 1)).Noticethatf() is a deceasing function, in addition, as, f() = e 0, whee e 0 is the iational nube and e Thus, if defining f(, β) = β (/( 1)),fo>1, f(, β) > f(, β) = βe 0.If1 > β > 1/e 0,thene R,M /e W,M = [β (/( 1)) ] >1,thus,poved. Siilaly, fo Table 1, π R,M /π W,M = [β/( 1)) ],followingthesaepoofpocess,if1>β>1/e 0, π R,M /π W,M >1holds. Reak 8. When the anufactue deteines and undetakes the effot investent, the optial etailing pice is highe unde wholesale pice. If the effot ipact paaete β is in a cetain ange (1/e 0 β<1), the effot investent level unde the evenue shaing contact is highe, as a payback, the anufactue bettes off as copaed to the wholesale picing contact. Howeve, it is difficult to tell which contact benefits the anufactue if β in the ange of 0<β<1/e Conclusions This pape studies a single anufactue-etaile supply chain unde diffeent contact settings. Optial decisions unde evenue-shaing contact and wholesale pice contact ae analyzed and copaed. If the effot investent level is deteined and undetaken by the etaile, unde wholesale pice contact, she faces a highe wholesale pice, which esults in a highe etailing pice and lage effot investent. As a payback, the etaile is bette off. If the anufactue deteines and undetakes the effot investent, unde the wholesale pice contact, the etailing pice is highe, while the effot investent is lowe if the ipact paaete β satisfies 1/e 0 β < 1. The anufactue would be bette off unde a evenue-shaing contact if both paties agee on consignent. Finally, soe liitations of this pape should be pointed out. Fist, we only conside deteinistic deand function, which liits its application in pactice consideing the ando natue of deand vaiables. Second, we only discuss the optial decisions unde diffeent supply chain contact and sales effot investent settings. Whethe such contacts coodinate the supply chain o not is out of ou discussion, which, howeve, is wothy of exploing in the futue. Conflict of Inteests The authos declae that thee is no conflict of inteests egading the publication of this pape. Acknowledgents The authos would like to thank the suppot by NSFC (Pojects and ). The wok is also suppoted by Scientific Reseach Foundation fo Retuned Scholas, Ministy of Education of China, Jinan Univesity Manageent School Funding Poga, and Institute of Entepise Developent of Jinan Univesity. Refeences [1] G. P. Cachon, Supply chain coodination with contacts, in Handbooks in Opeations Reseach and Manageent Science, Supply Chain Manageent: Design Coodination and Opeation, A.G.deKokandS.C.Gaves,Eds.,vol.11,pp ,Elsevie, Asteda, The Nethelands, [2] Y. Wei and T.-M. Choi, Mean-vaiance analysis of supply chains unde wholesale picing and pofit shaing schees, Euopean Jounal of Opeational Reseach, vol.204,no.2,pp , [3] M. Xu, Q. Wang, and L. Ouyang, Coodinating contacts fo two-stage fashion supply chain with isk-avese etaile and pice-dependent deand, Matheatical Pobles in Engineeing,vol.2013,AticleID259164,12pages,2013. [4] C.-H. Chiu, T.-M. Choi, H.-T. Yeung, and Y. Zhao, Sales ebate contacts in fashion supply chains, Matheatical Pobles in Engineeing,vol.2012,AticleID908408,19pages,2012. [5] Revenue shaing odel in etail industy to gow, 2009, FUO/Revenue-shaing-odel-in-etail-industy-to-gow.htl. [6] J. Huang, M. Leng, and M. Pala, Deand functions in decision odeling: a copehensive suvey and eseach diections, Decision Sciences,vol.44,no.3,pp ,2013. [7] N. C. Petuzzi and M. Dada, Picing and the newsvendo poble: a eview with extensions, Opeations Reseach,vol.47, no. 2, pp , [8] A. Fedeguen and A. Heching, Cobined picing and inventoy contol unde uncetainty, Opeations Reseach, vol. 47, no. 3,pp ,1999. [9] X. Chen and D. Sichi-Levi, Coodinating inventoy contol and picing stategies with ando deand and fixed odeing

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