SUPPLY CHAIN STRUCTURES ON THE INTERNET and the role of marketing-operations interaction 1

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1 Chapte 19 SUPPLY CHAIN STRUCTURES ON THE INTERNET and the ole of maketing-opeations inteaction 1 Seguei Netessine Univesity of Pennsylvania Philadelphia, PA [email protected] Nils Rudi Univesity of Rocheste Rocheste, NY [email protected] Abstact The idespead adoption of the Intenet has esulted in the possibility of sepaation of infomation flo and physical goods flo: a company selling a poduct no longe has to on/delive it to the custome. As a esult, supply chain stuctues aise in hich the etaile is pimaily concened ith custome acquisition, and the holesale takes inventoy isk and pefoms fulfillment. This fom of doing business on the Intenet is identical to the pactice of dop-shipping that some catalog companies employ. A ecent suvey indicates that moe than 30% of online-only etailes use dop-shipping as the pimay ay to fulfill odes. Since maketing and opeations functions unde such aangement ae pefomed by sepaate companies, ne inefficiencies aise that esult in suboptimal system pefomance. In this chapte, e analyze the inteaction beteen a holesale and a single etaile fo dop-shipping supply chains in a multi-peiod envionment. Thee distinct dop-shipping models ae consideed: ith a poeful holesale, ith a poeful etaile and ith a holesale and a etaile having equal poe. Futhe, e conduct a compaative analysis beteen the dop-shipping supply chains, a vetically integated supply chain, and the taditional stuctue in hich the etaile both takes inventoy isk and acquies customes. Optimal solutions ae obi

2 Supply chain stuctues on the Intenet 1 tained fo both the taditional and dop-shipping models, and e sho that both solutions ae system sub-optimal. We demonstate ho decision poe in the chain affects decision vaiables and pofits. It is found that both channel membes pefe the dop-shipping ageement ove the taditional ageement fo a ide ange of poblem paametes. One of ou esults is that none of the mechanisms descibed in the liteatue on channel coodination (except fo those that allo side payments) ae able to induce an optimal system behavio in the pesence of custome acquisition expenses. We theefoe popose a ne coodination scheme hee, in addition to using a compensation plan that is linea in caied-ove inventoy, the holesale subsidizes a pat of the etaile s maketing expenses. Extensive comments ae povided on the compaative benefits of taditional and dop-shipping supply chains. A link to an inteactive eb site fo numeical expeiments is made available at.nilsudi.com. Keyods: Intenet, supply chain, competition, Nash, Stackelbeg, maketing, advetising

3 2 1. Intoduction Spun.com, a small CD/DVD Intenet etaile, has about 200,000 CD titles listed on its eb site. Supisingly, the company does not hold/on any inventoy of CDs. Instead, the company patneed ith the holesale Alliance Entetainment Cop. (AEC), hich stocks CDs and ships them diectly to Spun.com s customes ith Spun.com labels on the packages. In this ay, the etaile avoided an estimated inventoy investment of $8M Fobes (2000), since it only paid the distibuto fo sold poducts. AEC calls this distibution system Consume Diect Fulfillment. Accoding to the company s eb site,... using AEC as afulfillment patne gives you moe time and esouces to focus on attacting moe consumes to you stoe.... The list of etailes pacticing such foms of Intenet business includes Zappos.com (Inbound Logistics 2000), Cybeian Outpost (Compute Reselle Nes 1999) and many othes. Dop-shipping is defined in maketing liteatue as a maketing function hee physical possession of goods sold bypasses a middleman, hile title flos though all those concened. The function of dop-shipping involves both the middleman ho initiates the dop ship ode and the stocking entity that povides dop-shipping sevices by filling the ode fo the middleman (Scheel 1990). Clealy, the above example of Spun.com fits this desciption. Dop-shipping is diffeent fom many of the supply chain stuctues peviously descibed in the liteatue in hich the holesale is involved in the etaile s inventoy management. It diffes fom the taditional consignment ageements in hich the etaile holds (but does not on) inventoy and decides hat the stocking policy should be unde dop-shipping the stocking policy is entiely contolled by the holesale. Dop-shipping is close to but diffeent fom Vendo Managed Inventoy (VMI), since the etaile does not deal ith inventoies and hence does not incu any inventoy-elated costs. At the same time, the holesale does not have diect access to the etaile s stoe hee she could ent space and oganize it in a ay that influences demand accoding to the holesale s pefeences (as is often the case unde VMI). Dop-shipping also diffes fom outsoucing of inventoy management, since unde outsoucing the etaile usually still influences stocking quantities fo each poduct. Pio to the Intenet, the pactice of dop-shipping as mainly esticted to to settings. Fo lage tansactions of industial goods, the holesale might have the manufactue make the shipment diectly to

4 Supply chain stuctues on the Intenet 3 the etaile (and in some cases diectly to the end custome). This is typically beneficial fo shipments that in themselves achieve sufficient economies of scale, making the holesale act pimaily as a maketmake. The second use of dop-shipping, hich is moe elevant to ou setting, occus hen a catalog company has the holesale dop-ship the poduct diectly to the end custome. This pactice, hoeve, has had vey limited success, mainly due to poblems in the integation and timeliness of infomation beteen the business patnes, as ell as high tansaction costs. As a esult, even the catalog companies using dopshipping only use it fo bulky and high cost items (see Catalog Age 1997). Hence, many maketing books see dop-shipping as having limited potential (see liteatue evie in Scheel 1990 page 7). With the Intenet, hoeve, eal time data-integation is eadily available at a lo cost. The combination of the physical concept of dop-shipping ith the infomation integation made possible by the Intenet esolves the poblems that peviously limited the adoption of dop-shipping. A suvey of Intenet etailes (Eetailing Wold 2000) indicates that 30.6% of Intenet-only etailes use dop-shipping as the pimay ay to fulfill odes, hile only 5.1% of multi-channel etailes pimaily ely on dop-shipping. In a ecent suvey of Supply Chain Management in e-commece applications Johnson and Whang (2002) cite seveal cases itten about companies utilizing dop-shipping (o vitual supply chains). One of the majo diffeences beteen selling goods on the Intenet and though the conventional bick-and-mota etaile is the sepaation of physical goods flo and infomation flo. In a physical stoe, a custome selects a poduct and pays fo it at the same time and place that she physically eceives the poduct. On the Intenet this is not the case. A custome on the Intenet cannot obseve fom hee the poduct is dispatched. Futhe, Intenet customes (simila to mail-ode catalog customes) do not expect an immediate delivey of the poduct. Togethe, this allos the etaile and the holesale to adopt the dopshipping ageement efficiently at a lo cost. Ageements of this type benefit the etaile by eliminating inventoy holding costs and oveall up-font capital equied to stat the company. The holesale inceases he involvement in the supply chain and hence can potentially demand a highe holesale pice, thus captuing moe pofits (as evidenced by empiical data in Scheel 1990 page 42). Futhe, supply chain benefits occu due to isk pooling if the holesale pefoms dop-shipping fo multiple etailes. Finally, each paty can concentate its esouces: the etaile on custome acquisition and the holesale on fulfillment.

5 4 Despite seveal clealy attactive featues, dop-shipping intoduces ne inefficiencies into the supply chain. Unde dop-shipping, the holesale keeps the decision ights elated to stocking policies, hile the etaile s main task in the supply chain is custome acquisition. This sepaation of maketing and opeations functions esults in inefficiencies, some of hich have been the subject of discussion in the liteatue on maketing-opeations coodination. Many questions aise in such a situation: ill the supply chain pefomance unde the dop-shipping stuctue be bette than unde a taditional stuctue in hich the etaile holds inventoy? Futhe, is it pefeable fo both the etaile and the holesale to engage in this sot of ageement? Can dop-shipping ageements lead to system-optimal pefomance, and if not, hat fom of contact can coodinate the supply chain? To the best of ou knoledge, this chapte epesents the fist fomal model of a dop-shipping supply chain, the pactice hee the etaile acquies customes hile the holesale is esponsible fo fulfillment and takes inventoy isk. We compae taditional supply chain stuctues in hich the etaile both takes inventoy isk and acquies customes ith supply chain stuctues employing dop-shipping ageements. Ou focus is on the supply chains in hich both the etaile and the holesale ae pesent. We concentate on to cost aspects of the distibution channel: maketing (custome acquisition) and opeational (inventoy). In the case of Intenet etailes, thee exists vast evidence that these to cost components constitute a dominant potion of the company s budget. Since e-tailes do not have a physical pesence that ould attact customes by physical location o stong band name, custome acquisition becomes a majo issue. Online-only etailes spend about tice as much of thei budget on custome acquisition as do multi-channel etailes Compute Wold (2000). At the ealy stages of Intenet development, the typical maketing budget of an Intenet-only etaile as 40.5% of sales, hile the maketing budget fo a multi-channel etaile as 21.4% Eetailing Wold (2000). A suvey of online etailes conducted in 2000 shos that the catalog-based companies spend on aveage $11 to acquie a custome, compaed to the $32 spent by a physical stoe and $82 by an e-taile Compute Wold (2000). Although afte the Intenet bubble advetising spendings have gone don, Intenet etailes still spend much moe on advetising than taditional etailes (see Latcovich and Smith (2001). Futhemoe, empiical studies have shon that advetising is used by the Intenet etailes to signal quality and since Intenet shoppes espond much moe to advetising than to lo pices (Latcovich and Smith 2001). These findings suppot ou use of advetising as a

6 Supply chain stuctues on the Intenet 5 key aspect of the Intenet etailing. On the othe hand, to be able to compete ith taditional etailes, Intenet companies typically offe extensive poduct vaiety and a high sevice level that in tun equies a lage inventoy investment. In addition, at the pesent time Intenet etailing is in its ealy stages of development, and the demand fo poducts is highly uncetain; hence, lage inventoies must be caied to maintain high sevice levels. To bette undestand the holesale-etaile inteaction and inventoy isk allocation in dop-shipping supply chains, e focus on a simple model ith a holesale and a single etaile. Note that fo cases hee the etaile buys diectly fom the manufactue the holesale in ou model is simply eplaced by the manufactue ithout any effect on othe esults. Thee main models ae analyzed and compaed in this chapte: a taditional vetically integated channel (Model I fo Integated ), a taditional vetically disintegated channel (Model T fo Taditional ) and a dop-shipping channel (Model D fo Dop-shipping ). The solution fo the dop-shipping channel futhe depends on the channel poe (hee poe is modeled as being the fist move in a Stackelbeg game). Hence, ithin the dop-shipping model e futhe conside thee submodels, in hich eithe the holesale o the etaile is a Stackelbeg leade o hee each paty has an equal decision poe (i.e. moves simultaneously) and the solution is a Nash equilibium. Fist, e demonstate that a unique competitive equilibium exists in each model, and e find optimal inventoy and custome acquisition spending fo each channel in analytical fom. We find that, fo the dop-shipping channel, maketingopeations misalignment esults fom the fact that these functions ae managed by to diffeent fims. In addition, double maginalization is pesent in both the taditional and dop-shipping stuctues. Unde identical poblem paametes, e analytically compae the models in tems of decision vaiables and pofits and sho that the dop-shipping models, as ell as the taditional model, alays lead to undespending on custome acquisition in addition to undestocking. We chaacteize the situations hee dop-shipping supply chains outpefom taditional supply chains and ou analysis indicates the impotance of the effects of channel poe on supply chain pefomance. We then sho that a pice-only contact, a evenue shaing contact, o a etuns/puchase commitment contact cannot coodinate the supply chain hen custome acquisition costs ae pesent. Fo the taditional and dop-shipping supply chains e popose a contact that combines a compensation plan that is linea in caied ove inventoy ith subsidized advetising, and

7 6 sho that this contact induces coodination. Ou main inteest in this chapte is to get a bette undestanding of inventoy isk allocation issues in dop-shipping supply chains as ell as the impact of poe distibution beteen the channel entities. To keep focus and to not diffuse economic insights, e do not explicitly eflect othe issues encounteed in e-commece fulfillment, since many ae had to include in a fomal model. Among these issues ae: possible diffeences in tanspotation costs and esponsiveness, coodination issues aising hen multiple holesales ae needed to fulfill a single ode, and the ationing of inventoy hen a holesale seves multiple etailes. These and othe issues ae teated qualitatively in Randall et al. (2002). The est of the chapte is oganized as follos. In the next section, e povide a suvey of the elevant liteatue. Section 3 outlines the notation and modeling assumptions. In Section 4, all thee models ae pesented and in Section 5, e sho that none of the channel coodination mechanisms descibed in the liteatue can achieve a fist-best solution. Optimal coodinating contacts ae also poposed in this section. Section 6 contains numeical expeiments, and in Section 7 e apup the chapte ith a discussion of manageial insights and conclusions. 2. Liteatue suvey The pactice of dop-shipping has been descibed qualitatively in the maketing liteatue (see Scheel 1990 and efeences theein, page 7), but, to the best of ou knoledge, its distinct featues, i.e., the holesale taking inventoy isk hile the etaile, a sepaate fim, acquiing customes, have neve been fomally modeled and analyzed peviously 2. In a majoity of maketing textbooks, the qualitative analysis of dopshipping is limited to one paagaph. Futhe, the liteatue on dopshipping does not aise the issue of maketing-opeations misalignment and poe in the supply chain. With the exception of Scheel (1990), all the souces e cite eithe ignoe inventoy o assume that inventoy is held by the etaile. Opeations management has a ealth of liteatue that deals ith the inventoy aspects of the supply chain, but ignoes maketing expenses like custome acquisition costs (see, fo example, Tayu et al. 1998). At the same time, the maketing liteatue tends to deal ith custome acquisition costs in the fom of advetising and sales suppot (see, fo

8 Supply chain stuctues on the Intenet 7 example, Lilien et al. 1992), but ignoes opeational issues. Fo example, Chu and Desai (1995) model a supply chain ith a etaile and a holesale, both investing into impovement of custome satisfaction hich stimulates demand. Hoeve, they do not explicitly conside inventoy isk. This ok belongs to the ecent steam of eseach dealing ith the alignment of maketing and opeations incentives (see Shapio 1977 and Montgomey and Hausman 1986 fo discussions of some of the poblems that aise fom maketing-opeations misalignment). Ou model diffes fom the pevious liteatue in seveal ays. Fist, in ou dop-shipping model opeations and maketing functions ae pefomed by to independently oned and opeated companies that make thei decisions competitively. Since maketing and opeational functions ae pefomed by sepaate companies and e do not conside infomation asymmety, the poblem e conside is diffeent fom sales agent compensation. Second, inventoy isk in the dop-shipping model is ith the holesale, esulting in channel dynamics that diffe fom the existing liteatue. Finally, the maketing function is custome acquisition that affects demand fo the poduct, hile the sales pice is exogenous. The majoity of papes in this aea assume that the maketing function is to set the sales pice o pomotion level and manufactuing makes poduction decisions ithin one company (see, fo example, Sagomonian and Tang 1993 and efeences theein). De Goote (1989) consides poduct line choice as a maketing function. Eliashbeg and Steinbeg (1987) give an excellent summay of a numbe of papes modeling opeations/maketing intefaces, but none of the papes they cite model uncetain demand. Poteus and Wang (1991) model a company hee the pincipal specifies compensation plans fo one manufactuing and multiple maketing manages ithin the same company. Each poduct is exclusively assigned to a maketing manage, ho stimulates the poduct s demand by effot. The manufactuing manage can affect capacity available to poduce all these poducts. Although this pape is somehat simila to ou chapte in tems of stuctue of the poblem and the issues consideed, the pincipal-agent fameok used by Poteus and Wang makes diffeences in motivation, stuctue and modeling. Poteus and Wang (1991) also cite a numbe of elevant papes, but none of these papes model custome acquisition spending o advetising as a maketing decision vaiable. Balce (1980) models coodination of advetising and inventoy decisions ithin one company and focuses on a dynamic nonstationay model in hich demand is influenced by the level of goodill.

9 8 Balce (1983) futhe extends this model by assuming that the advetising effect lasts fo moe than one peiod. Gechak and Pala (1987) look at a single-peiod model in hich demand is a specific function of the maketing effot. None of the latte thee papes conside supply chain issues, i.e., the inteaction beteen seveal fims. Fo taditional supply chains only, some papes model situations that in cetain aspects ae elated to ous. Cachon and Laiviee (2000), among othes, model a situation hee the etaile both takes inventoy isk and influences demand by exeting effot. They assume that the effot cannot be contacted upon, and hence they do not find a contact that coodinates the supply chain. While this assumption is easonable in the poblem setting they use, on the Intenet it is possible to contact upon at least some foms of custome acquisition spending. Fo example, if the etaile pays fo advetising based on the volume of click-though and puchase by the customes, then this type of custome acquisition can easily be independently veified and contacted upon. In the last section, e ill comment moe specifically on the viability of this type of contact and on pactical ays to implement such contacts. Naayanan and Raman (1998) look at a poblem that in some ays is the opposite of dop-shipping, i.e., hee the etaile cannot affect demand distibution but the manufactue can. In thei pape, the manufactue s effot is incopoated analogously to the ay e use custome acquisition spending by the etaile. Most of thei analysis, hoeve, is done ith some quite estictive assumptions about the functional foms of the poblem paametes and decision poe in the channel. They demonstate that vetical disintegation of the channel leads to suboptimal pefomance but do not deive an optimal coodination contact that ould mitigate this poblem ithout side-payments. Cachon (2003) studies a model that is closely elated to ous: eithe the etaile, the holesale, o both may on inventoy. He focuses on Paeto-impoving holesale pice contacts hile e take holesale pices as exogenous. Fo the majoity of the analysis, advetising effot is not consideed and channel poe is not an issue in his ok. Relevant ok on supply chain coodination in taditional supply chains includes penalty contacts (Laiviee 1999) and etuns contacts (Pastenak 1985 and Kandel 1996). See also Cachon (2002) fo a suvey of contacting liteatue in Supply Chain Management. Jeuland and Shugan (1983) model maketing effot fo the poblem of distibution channel coodination unde deteministic demand, but ignoe inventoy issues. The maketing liteatue has idely addessed a phenomena

10 Supply chain stuctues on the Intenet 9 of subsidized advetising in the context of fanchising ageements (see Michael 1999 and efeences theein). The only ok e ae aae of that addesses subsidized custome acquisition o advetising beteen to fims that ae not bound by a fanchising ageement is Bege (1983), Bege (1972) and Bege and Magliozzi (1992), ith inventoy issues ignoed. Cobett and DeCoix (2000) conside a shaed savings contact, a poblem that is diffeent fom ous but is simila in mathematical stuctue: in ou poblem, custome acquisition expenses affect the demand; in thei poblem, use-eduction effot affects the consumption of indiect mateials. In thei poblem, hoeve, thee is no inventoy involved, and both the upsteam supplie and the donsteam buye exet effot of the same natue. Hence, issues elated to maketing-opeations inteaction do not aise. Thee is a ealth of maketing and economics liteatue addessing Intenet-elated issues, though, to the best of ou knoledge, the pactice of dop-shipping has neve been mentioned. The most elevant ok is Hoffman and Novak (2000), ho descibe custome acquisition models on the Intenet. Finally, the only elevant opeations management pape addessing supply chain stuctues on the Intenet of hich e ae aae is Van Mieghem and Chopa (2000), in hich the authos qualitatively addess the choice of e-business fo a given supply chain (ithout consideing dop-shipping). 3. Notation and modeling assumptions We model a supply chain ith to echelons: holesale and etaile. Only a single poduct and a single fim in each echelon is consideed. Demand fo the poduct in each time peiod is uncetain and mean demand depends on the amount of custome acquisition spending by the etaile in this peiod (by custome acquisition e imply the total cost a company spends on advetising and maketing pomotions). This is an extension of the standad maketing models that usually assume deteministic demand. Since ou focus is the holesale-etaile inteaction, e assume that the unit pice is exogenously given, hich is a depatue fom the taditional liteatue on the maketing-opeations inteface in hich the pice is a pimay maketing decision vaiable. This assumption might be easonable fo Intenet etail since advetising seem to influence Intenet shoppes moe than lo pices (see Latcovich and Smith 2001 fo discussion and many examples). Futhe, all the poblem paametes ae identical fo the etaile and the holesale and knon to eveyone (thee is no infomation asymmety). We use a multi-peiod fameok ith

11 10 lost sale epesenting a penalty fo undestocking though lost magin. Left-ove inventoy is caied ove to the next peiod incuing holding cost. The folloing notation is used thoughout the chapte (supescipt t indicates elevant time peiod, vectos ae undelined): x t beginning inventoy befoe placing the ode in peiod t, Q t ode-up-to quantity in peiod t, Q t x t, unit evenue, unit holesale pice, c unit cost, β discounting facto, β [0, 1), h unit holding cost pe peiod, A t custome acquisition spending (includes all types of elated maketing activities), D t (A t ) demand (andom vaiable), paameteized by the custome acquisition spending, f D ( ) pobability density function of the demand, Π, Π, Π discounted infinite-hoizon expected pofit function of etaile, holesale, and total supply chain, coespondingly. Supescipts I, T and D ill denote vetically integated, vetically disintegated (taditional), and dop-shipping supply chains, coespondingly. Futhe, e ill conside thee dop-shipping models. In Model DW the holesale has channel poe, in Model DR the etaile has channel poe, and in Model DN the playes have equal poe. We also assume the folloing quite geneal fom of the demand distibution: Assumption 1. Demand distibution has the folloing fom: D t (A t )= θ(a t )+ε t,heeθ(a t ) is a eal-valued function and ε t ae i.i.d. andom vaiables such that D t (0) 0. Assumption 2. Expected demand is inceasing in custome acquisition spending and it is alays pofitable to spend a non-zeo amount on custome acquisition: ded t (A t ) t ded t (A t ) 0, lim A t 0 t =.

12 Supply chain stuctues on the Intenet 11 Assumption 3. Expected demand is diminishingly concave (i.e., it is flattening out as A appoaches infinity) in custome acquisition spending: d 2 ED t (A t ) d (A t ) 2 0, d3 ED t (A t ) d (A t ) 3 0. The fom of the demand function specified in Assumption 1 is used extensively in the opeations and economics liteatue (see Petuzzi and Dada 1999 and efeences theein). Unde this assumption, only the mean demand depends on A t, and the uncetainty is captued by an eo tem ε t. The fist pat of Assumption 2 is standad in maketing models (see page 265 in Lilien et al. 1992). We add the conditions that guaantee the existence of the non-degeneate (inteio) solution, hich is needed fo the compaisons of the models. Assumption 3 is suppoted by empiical evidence fom the maketing liteatue (see, fo example, Simon and Andt 1980 and Aake and Caman 1982). 4. Supply chain models ithout coodination In this section e ill assume that the etaile and the holesale ae employing a contactual ageement ith a fixed tansfe pice. This might be a esult of outside competition o othe aangements existing in the industy. The objective is to maximize infinite-hoizon discounted expected pofit. If a poduct is out of stock, the sale is lost. Unsold inventoy is caied ove to the next peiod incuing holding cost. The lost sale assumption leads to the folloing inventoy balance equation in all models: ³ ³ x t+1 = Q t D t A t Model I - vetically integated supply chain The holesale and the etaile ae vetically integated. At the beginning of each peiod, the poduct is puchased at a fixed unit cost c and sold to the customes at a fixed unit pice. The integated etaile-holesale is the sole decision make ho chooses both the stocking quantity and the custome acquisition spending. Using a standad setup (see Heyman and Sobel 1984), the integated fim ill seek to maximize the folloing objective function: ³ 1 X Π I A,Q,x = β t 1 E min ³D t t (A t ),Q h ³Q ³ t D t A t + c ³Q t t t x A. t=1 The pofit contibution in each peiod consists of the folloing fou tems: evenue geneated by the units sold (limited by demand and sup-

13 12 ply), holding cost fo the units caied ove (positive diffeence of supply and demand), puchasing cost of inventoy (diffeence beteen odeup-to level and stating inventoy), and custome acquisition spending. By standad manipulation, e can e-ite the optimization poblem as follos: ³ 1 " X ³ t # max Q t x t,a t t ΠI A,Q,x = max cx 1 + β t 1 I,t Q t,a t,x, Q t x t,a t t hee I,t is the expectation of the single-peiod objective function defined as follos: ³ t h I,t Q t,a t,x = E ( + h cβ)min ³D t t (A t ),Q (h + c (1 β)) Q t A ti. Poposition 1. Thee exists a unique pai ³Q I I,A optimizing the single-peiod objective function ithout stating inventoy (i.e., unconstained) I = I,t Q t,a t, 0, chaacteized by the folloing system of equations: ³ P D ³A I I c <Q = + h βc, (19.1) ded(a) 1 = AI c. (19.2) Then, fo any x 1 Q I,thesolution ³Q I I,A is a unique stationay solution to the infinite-hoizon poblem. Poof: Conside the single-peiod unconstained objective function I. To demonstate uniqueness of the solution e ill sho concavity of the objective function, o equivalently e ill veify that the diagonal elements of the Hessian matix of the objective function ae negative and that the deteminant of the Hessian is positive. The fist deivatives ae I Q I A The second deivatives ae t=1 = ( + h βc)p(d(a) >Q) (h + c (1 β)), (19.3) = ( + h βc)p(d(a) <Q)dED(A) 2 I Q 2 = ( + h βc) f D(A) (Q) < 0, 2 I µ ded(a) A 2 = ( + h βc) f D(A) (Q) 1. (19.4) 2

14 Supply chain stuctues on the Intenet 13 +( + h βc)p(d(a) <Q) d2 ED(A) 2 < 0, 2 I Q A = ( + h βc) f D(A)(Q) ded(a) > 0. The diagonal elements ae clealy negative by Assumptions 2 and 3. Positivity of the deteminant is equivalent to the folloing condition: 2 I 2 I Q 2 A 2 > 2 I 2 I Q A A Q. Thiscanbeexpandedasfollos: " µ ded(a) 2 # f D(A) (Q) f D(A) (Q) +P(D(A) <Q) d2 ED(A) 2 > Afte collecting simila tems e obtain f D(A) (Q)P(D(A) <Q) d2 ED(A) 2 > 0. This is tue by Assumption 3, hich completes the poof of uniqueness. To obtain the system of optimality conditions, it is convenient to substitute the fist optimality condition into the second. Finally, folloing Section 3.1 in Heyman and Sobel (1982), the solution to the poblem is myopic in natue. Futhemoe, if initial inventoy is sufficiently lo fo ou poblem, i.e. x 1 Q I, the solution is stationay (i.e. the unconstained solution is feasible). This completes the poof. 4.2 Model T - taditional supply chain The holesale buys the poduct at a fixed unit cost c and sells it to the etaile at a fixed unit holesale pice. The etaile holds inventoy and sells it to the customes at a fixed unit pice. The etaile hee is the sole decision make ho decides on both the stocking quantity and the custome acquisition spending. Simila to model I, max Q t x t,a t t ΠT ³A,Q,x 1 = max Q t x t,a t t " x 1 + X t=1 ³ t # β t 1 T,t Q t,a t,x, hee T,t is the expectation of the etaile s single-peiod objective function defined as follos: ³Q t h t,a t,x = E ( + h β)min T,t f D(A) (Q) ded(a) ³D t (A t ),Q t (h + (1 β)) Q t A ti. (19.5) 2.

15 14 The holesale s expected pofitis Π T ³A,Q,x 1 X = ( c) x 1 + β t 1 T T,t t=1 ³Q t,a t,x t, hee T,t is the expectation of the holesale s single-peiod expected pofit: ³Q t h t,a t,x =( c) E (1 β) Q t + β min ³D ³ t t i t A,Q. (19.6) Poposition 2. Thee exists a unique pai ³Q T,A T optimizing the etaile s single-peiod objective function ithout stating inventoy (i.e., unconstained) T = T,t Q t,a t, 0, chaacteized by the folloing system of equations: ³ P D ³A T <Q T = + h β, (19.7) ded(a) 1 = AT. (19.8) Then, fo any x 1 Q T, the solution ³Q T,A T is a unique stationay solution to the infinite-hoizon poblem (i.e. the unconstained solution is feasible). Poof: Simila to Poposition 1. Note that although in this model the etaile is the sole decision make and theefoe seems to possess some poe in the chain, he also beas all the inventoy-elated isk. In addition, custome acquisition spending incued by the etaile not only benefits him but also benefits the holesale. As e ill demonstate late, this leads to the suboptimal pefomance of the channel. 4.3 Model D dop-shipping The holesale buys the poduct at unit cost c, holds inventoy, and ships the poduct diectly to the custome upon the etaile s equest. The etaile acquies customes and makes sales. He pays unit holesale pice pe closed sale to the holesale, eceives fixed unit evenue fom the custome, and does not hold inventoy. Note at this point that unde dop-shipping, contacts beteen the holesale and the etaile ae not limited to the tansfe picing ageements. Since the poduct is neve physically tansfeed to the etaile, it is often natual to conside a contact hee the evenue is split beteen the etaile and the

16 Supply chain stuctues on the Intenet 15 holesale in popotions λ and 1 λ, and thee is no need to establish a holesale pice. Fo example, Scheel (1990), page 17, indicates that in the dop-shipping business the dominant pactice is fo the holesale to give the etaile a discount ove the suggested etail pice. We do not conside such ageements since the analysis is identical to the tansfe pice contacts ith =(1 λ). Unde a dop-shipping aangement, the channel membes ill make thei decisions stategically and hence a game-theoetic situation aises. Simila to Cachon and Zipkin (1990), e conside games hee each playe chooses a stationay policy: the etaile s stategy is A and the holesale s stategy is ode-up-to quantity Q. Thee situations aise: eithe the holesale o the etaile might have negotiation poe in the supply chain and act as Stackelbeg leades, o it is possible that the playes have equal poe and theefoe the solution is in the fom of a Nash equilibium. We ill conside all thee situations. Denote the best esponse function of the etaile by R (Q) andthe best esponse function of the holesale by R (A), both defined fo zeo initial inventoy. At this point e have not demonstated uniqueness o even existence of the equilibium. It helps, hoeve, to visualize the poblem fist. We begin by pesenting the game gaphically (see Figue 19.1, paametes ae taken fom the example in Section 6 ith =8). Thepoint(A DN,Q DN ) is a Nash equilibium that is located on Q R(Q) Q DW Q DR R(A) Q DN A DN A DW A DR A Figue Stackelbeg and Nash equilibia. the intesection of the best-esponse cuves. A Stackelbeg equilibium ith the holesale as a leade (A DW,Q DW ) is located on the etaile s

17 16 best-esponse cuve, and a Stackelbeg equilibium ith the etaile as aleade(a DR,Q DR ) is located on the holesale s esponse cuve. We begin by chaacteizing the best esponse cuves analytically. Fo a given Q, the etaile s optimization poblem is " X # max A ΠD (A, Q) =max A β t 1 D (Q, A) t=1 hee D is the expectation of the etaile s single-peiod objective function defined as follos: D (A, Q) =E [( )min(d(a),q) A]. (19.9) Note that the objective function is concave, and hence the etaile s fistode condition chaacteizes the unique best esponse. Fo stationay policies, it is sufficient to conside the best esponse functions in the single-peiod game. The slope of the etaile s best-esponse function is found by implicit diffeentiation as follos: dr (Q) dq = 2 D A Q = 2 D A 2 f D (Q) ³ ded(a) f D (Q) ded(a) 2 > 0, P(D(A) <Q) d 2 ED(A) 2 (19.10) hee the second tem of the denominato is positive by Assumption 3. Positivity of the slope means that the etaile s custome acquisition spending is inceasing in the quantity that the holesale stocks. Hoeve, due to the complexity of the expession fo the slope, e ae unable to veify eithe concavity o convexity of the best esponse function. Fotunately, this is not essential fo any of the late esults. Note that Figue 19.1 shos the etaile s best-esponse as a convex function, hich is the case fo the specific poblem paametes used. We ill no chaacteize the holesale s best esponse. Fo a given A, the holesale s optimization poblem is, max Q x ΠD 1 ³A,Q,x 1 =max Q x 1 " cx 1 + # X β t 1 D (Q, A), hee D is the expectation of the etaile s single-peiod objective function defined as follos: D (A, Q) =E [( + h cβ)min(d(a),q) (h + c (1 β)) Q]. (19.11) Again the objective function is concave, and the holesale s fist-ode condition chaacteizes the unique best esponse. The slope of the hole- t=1,

18 Supply chain stuctues on the Intenet 17 sale s best esponse function is found by implicit diffeentiation as follos: dr (A) 2 D = = de(d) > 0. (19.12) Q A 2 D Q 2 We see that the stocking quantity of the holesale is inceasing in the custome acquisition spending by the etaile. This time e can also establish the sign of the second deivative d 2 R (A) 2 = d2 E(D) 2 < 0, and it follos that the holesale s best esponse function is concave. We ae then eady to demonstate that, hen the etaile and the holesale have equal poe in the channel, thee ill be a unique Nash equilibium. Poposition 3. Thee exists a unique Nash equilibium pai (Q DN,A DN ) in the single-peiod dop-shipping game ithout stating inventoy that is chaacteized by the folloing system of equations: ³ P D ³A DN DN c <Q = + h βc, (19.13) ded(a) ADN = 1 + h βc. (19.14) c Then, fo any x 1 Q DN, the solution (Q DN,A DN ) is a unique Nash equilibium of the multi-peiod game. Poof: Existence of the equilibium follos fom the concavity of the etaile s and the holesale s objective functions (see Moulin 1986 page 114). To sho uniqueness it is sufficient to notice that the optimality conditions can be solved sequentially, i.e., condition (19.14) can be solved uniquely fo A DN and then condition (19.13) can be solved uniquely fo Q DN. We no conside the poblem in hich the holesale acts as a Stackelbeg leade and offes the etaile a take-it-o-leave-it contact that specifies a quantity of mechandise that the holesale is illing to stock. Poposition 4. Define: " + h βc ξ(a DW,Q DW )=min, 1 ded(a) c R (Q) Q ADW,Q DW Fo ε having an Inceasing Failue Rate (IFR) distibution, thee exists a unique Stackelbeg equilibium solution pai (Q DW,A DW ) in the single- #.

19 18 peiod game ith a poeful holesale and ithout stating inventoy that is chaacteized by the folloing system of equations: P(D(A DW ) <Q DW ) = ded(a) ADW = c ξ (A DW,Q DW )( + h βc), (19.15) 1 ξ ³A DW,Q DW ( + h βc) (19.16). c Then, fo any x 1 Q DW, the solution (Q DW,A DW ) istheuniquestackelbeg equilibium of the multi-peiod game. Poof: The etaile acts second by solving (19.9). The holesale takes the etaile s best esponse function into account and solves the folloing poblem: max Q D (Q) =max E [( + h βc)min(d(r (Q)),Q) (h + c (1 β)) Q]. Q Since the etaile s best esponse function is single-valued, the Stackelbeg equilibium exists. Futhe, e ill sho that the second deivative of the holesale s objective function is negative (i.e., the objective function is concave), and so the Stackelbeg equilibium is unique. The fist deivative of the holesale s objective function is d D dq = D Q + D dr (Q) A dq = ( + h βc)p(d(r (Q)) >Q) +( + h βc)p(d(r (Q)) <Q) ded(a) (h + c (1 β)) µ = ( c) ( + h βc)p(d(r (Q)) <Q) dr (Q) dq 1 ded(a) The second deivative is: d 2 D dq 2 = ( + h βc) d P(D(R µ (Q)) <Q) 1 ded(a) dr (Q) dq dq ³ +( + h βc)p(d(r (Q)) <Q) d ded(a) dr (Q) dq. dq Note fist that ³ ded(a) 2 dr (Q). dq 1 ded(a) dr (Q) dq =1 f D (Q) ³ f D (Q) ded(a) 2 > 0. P(D(A) <Q) d 2 ED(A) 2

20 Supply chain stuctues on the Intenet 19 Fom the second deivative, conside the tem: d P(D(R (Q)) <Q) dq Next, conside the tem: = ³ d dq d ded(a) P(D(A)<Q) f D (Q) R(Q) Q dq = d 2 ED(A) 2 ³ = f D (Q) µ 1 ded d 1 1 P(D(A)<Q) d2 ED(A) f D (Q) 2 dq. ded(a) 1 P(D(A)<Q) f D (Q) 2+ P(D(A)<Q) f D (Q) d2 ED(A) 2 d dq. ded(a) dr (Q) > 0. dq ³. ded(a) hee d P(D(A) <Q) = d P(ε <Q θ(a)) > 0, dq f D (Q) dq f ε (Q θ(a)) since ε has an IFR distibution, and finally d dq à d 2, µded(a) ED(A) 2! 2 = by Assumptions 2 and 3 so that d esult follos. d 3 ED(A) 3 ³ ded(a) 2. d 2 ED(A) ded(a) , ³ ded(a) ³ 2 ded(a) ³ d 2 ED(A). R (Q) Q dq < 0andthe We ould like to point out that the IFR assumption on ε is vey nonestictive since the IFR family includes just about any commonly used demand distibution. Suppose no that the etaile acts as a Stackelbeg leade and offes the holesale a take-it-o-leave-it contact that specifies an amount of money the etaile is illing to spend on custome acquisition. Poposition 5. Thee is a unique Stackelbeg equilibium solution pai (Q DR,A DR ) in the single-peiod game ith a poeful etaile and ithout stating inventoy that is chaacteized by the folloing system of equations: P(D(A DR ) <Q DR ) = ded(a) = ADR c + h βc, (19.17) 1. (19.18) 2 ded(a) dr (Q) dq < 0,

21 20 Then, fo any x 1 Q DR, the solution (Q DR,A DR ) is a unique Stackelbeg equilibium of the multi-peiod game. Poof: The holesale acts second by solving (19.11). The etaile takes into account the holesale s best esponse function and solves the folloing poblem: max A D (A) =max E [( )min(d(a),r (A)) A]. A Since the holesale s best esponse function is single-valued, the Stackelbeg equilibium exists. The fist deivative is d D = D A + D Q dr (A) = ( )P(D<Q) de(d) +( )P(D>Q) dr (A) 1=( )de(d) 1, and the second deivative is 2 D A 2 =( E(D) )d2 2 < 0. The etaile s objective function is clealy concave, and the uniqueness of the Stackelbeg equilibium follos. Finally, the optimality conditions ae found by equating the fist deivatives to zeo. Note that in Model D, as opposed to Model T, the holesale beas all the inventoy-elated isk. The etaile still incus all the custome acquisition costs that ill benefit not only him, but also the holesale. Hence, none of the playes has an incentive to behave system-optimally, as e ill sho late. 4.4 Compaative analysis of the stationay policies The intepetation of the fist optimality condition (fo Q) in each model is a standad one fo the nesvendo-type models: equating the maginal cost of stocking an exta unit of the poduct ith the maginal benefit. The second optimality condition (fo A) has a simila intepetation in the maketing liteatue. Obsevation 1. Denote by η(a) the elasticity of expected demand..t custome acquisition spending. Fomally: η(a) = ded(a) Á ED(A). A

22 Supply chain stuctues on the Intenet 21 Then the optimality condition that defines custome acquisition fo all Modelscanbee-ittenasfollos: η(a I ) c η(a T ) η(a DW c ) ξ ( + h βc) η(a DR ) η(a DN c ) + h βc = = = = = A I ED(A I ), A T ED(A T ), A DW ED(A DW ), A DR ED(A DR ), A DN ED(A DN ). Each optimality condition is intepeted as follos: the atio of the total custome acquisition spending to the total expected evenue (ight-hand side) is equal to the demand elasticity times the etaile s elative maginal pofit (left-hand side hich is evenue minus maginal cost divided by the evenue). The esult of Obsevation 1 paallels a esult fequently encounteed in the maketing liteatue (see, fo example, page 571 in Lilien et al. 1992). Obsevation 2. In all models, custome acquisition spending and stocking quantity ae stategic complements. Poof: Asufficient condition fo stategic complementaity is positivity of the coss-patial deivative (see Moothy 1993) of the objective function, hich can be easily veified. Fo identical paametes and no initial inventoy e can pefom analytical compaisons of the models. Since all the solutions ae stationay, it is sufficient to compae single-peiod pofits. The folloing table summaizes the optimality conditions of the five models: Model I P D A I <Q I = c +h βc Model T P D A T <Q T = Poeful holesale P D A DW <Q DW = +h β c ξ(+h βc) Model D Poeful etaile P D A DR <Q DR = c +h βc Nash equilibium P D A DN <Q DN = c +h βc ded(a) = 1 c ded(a) = 1 ded(a) = 1 ded(a) = 1 ded(a) = 1 ξ(+h βc) c +h βc c

23 22 The next Poposition summaizes the compaative behavio of the models unde the same holesale pice. Poposition 6. Suppose that in all five models the etail pice, the holesale pice, the unit poduct cost, and the demand distibution ae identical. Then the folloing chaacteizations hold: a) Custome acquisition: A I A T = A DR A DW A DN, the custome acquisition spendings ae highest in Model I and loest in Model D. b) Stocking p quantities: Q I Q T and Q I Q DR Q DN.If( + h βc) (h + c (1 β)) ( + h βc) then Q T Q DR >Q DN, otheise Q DR > Q T and Q DR > Q DN. Futhe, among the thee dopshipping models, Model DN alays has the loest stocking quantity, Q DW Q DN and Q DR Q DN. c) Retaile s pofits: DR DN, DW DN,theetailemakes the loest pofits unde the Nash equilibium. d) Wholesale s pofits: DR DW DN. e) System pofits: Fo ( + h βc) p (h + c (1 β)) ( + h βc), I T DR, otheise I DR T. Futhe, it is alays tue that DW DN and DR DN. Poof: Results a), b), and c) ae obtained by a pai-ise compaison of the fist-ode conditions and employing the fact that ded(a)/ is deceasing in A. Results DR DN and DW DN, i.e. the Stackelbeg leade makes moe pofits than in a Nash equilibium, ae standad fo Stackelbeg games (see Simaan and Cuz 1976). The othe esults in c) andd) ae obtained as follos: DN = D (A DN,Q DN ) D (A DN,Q DW ) D (A DW,Q DW )= DW, hee the fist inequality follos fom the obsevation that in Model D the etaile s pofit isinceasinginq fo a fixed A, and the second inequality holds since A DW is an optimal esponse to Q DW. Similaly DN and also DW = D (A DN,Q DN ) D (A DW,Q DN ) D (A DW,Q DW )= DW, = D (A DW,Q DW ) D (A DR,Q DW ) D (A DR,Q DR )= DR. Finally, e) follos fom the fact that the system pofit isjointlyconcave in A and Q, combined ith the esults in c) andd).

24 Supply chain stuctues on the Intenet 23 Fom pat a) of Poposition 6, e see that vetical disintegation leads to undespending on custome acquisition by the etaile, and in dopshipping models the etaile undespends moe than in the taditional model due to the misalignment of maketing and opeations functions. It is inteesting to note that the dop-shipping model pefoms the ost hen playes have equal poe. The custome acquisition spending is closest to the system optimum hen the etaile has channel poe. The fist pat of this finding, A I A T, that vetical disintegation leads to undespending on maketing effot, is simila to the esult obtained by Jeuland and Shugan (1983). They, hoeve, ignoe inventoy issues and conside deteministic pice-dependent demand. The intuition behind pat b) of the poposition is that not only does vetical disintegation lead to putting too little effot into custome acquisition in Models T and D, but also it leads to undestocking. This is an effect caused by the double maginalization that as descibed in the economics, maketing, and opeations liteatues. We also see that, fo modeate to high holesale pice, the dop-shipping model ith a poeful etaile alays leads to odeing moe than in the taditional model. The model ith poeful holesale is not paticulaly tanspaent to the analysis, due to the pesence of ξ, hich depends on poblem paametes in a non-tivial ay. Note, hoeve, that by studying Figue 19.1 e can see that Q DW can be above o belo Q DR, depending on the cuvatue of the best esponse functions. The Nash equilibium again esults in the loest (i.e. the ost) stocking quantity. Pats c)andd) state that in Model DN both playes ae ose off than in the othe to dop-shipping models. The intuition behind this esult is as follos: note that both best esponse functions ae monotonically inceasing, and that the integated solution consequently has highe optimal decision values than in the Nash equilibium. It is ell knon that a Stackelbeg leade is bette off than unde the Nash equilibium. Hence, the Stackelbeg solution ill be ithin the ectangula aea fomed by the Nash equilibium and the integated solution (see Figue 1). Finally, since the folloe s pofit is inceasing in the leade s decision vaiable, the esult follos. Also, the holesale pefes the model ith a poeful etaile ove the othe to. This makes Model DR a potential candidate fo the best of the thee dop-shipping aangements. Finally, pat e) summaizes the most impotant compaative findings. We see that fo a elatively small thee is no hope that eithe Model DR o DN ill outpefom the taditional model. Hoeve, fo modeate

25 24 to high holesale pices, Model DR alays outpefoms the taditional model. Moeove, thee is hope that even Model DN outpefoms the taditional model fo high holesale pices. Note also that in the condition ( + h βc) > p (h + c (1 β)) ( + h βc), the theshold value p (h + c (1 β)) ( + h βc) isclosetoh+c (1 β) thanto +h βc, and hence this condition accounts fo moe than 50% of the possible values of + h βc. 5. Supply chain coodination In the pevious section, e demonstated that the solutions of Models T and D ae geneally diffeent fom the system-optimal solution. In addition to the double maginalization effect, dop-shipping is also plagued by maketing-opeations misalignment. Can e come up ith a mechanism that ill induce coodination? As the next obsevation shos, a pice-only contact is not sufficient. Obsevation 3. In Model T, the sole pice-only contact that induces coodination has T = c in hich the etaile captues all pofits, and in ModelDtheeisnosuchcontact. Not only ae the pice-only contacts inefficient, but also none of the othe cuently knon contacts can coodinate the supply chain hen custome acquisition expenses ae consideed. Obsevation 4. None of the folloing contacts etuns, quantityflexibility, penalty (all as descibed by Laiviee 1999), evenue shaing (as descibed by Cachon and Laiviee 2000), o quantity discount (as descibed by Jeuland and Shugan 1983) can coodinate the supply chains in Models T o D. To ou knoledge, the only knon contacts that ok hee ae quantity focing and fanchising (Laiviee 1999). These contacts, hoeve, might be difficult to implement in pactice, as as noted in the liteatue. Clealy, in ode to coodinate the supply chains consideed hee, e need a ne fom of contact. In Model T, e need a mechanism that ill allocate a pat of inventoy isk to the holesale and also make the holesale bea some pat of the maketing expenses. Pastenak (1985) and Kandel (1996) sho that a etuns contact in hich the holesale offes patial cedit fo etuned mechandise achieves supply chain coodination in the absence of maketing aspects. In ou model this mechanism coesponds to the holesale offeing the etaile

26 Supply chain stuctues on the Intenet 25 a compensation popotional to the inventoy caied ove in each peiod (somehat simila to holding cost subsidy in Cachon and Zipkin 1999). To achieve coodination, e add the notion of subsidized advetising simila to Chu and Desai (1995) ho use the tem custome satisfaction assistance. Poposition 7. The folloing contact achieves supply chain coodination in Model T: the holesale sponsos a potion of the etaile s custome acquisition expenses a =( c)/( c), and at the same time offes the etaile a compensation b = a ( (1 β)+h) fo each unit of inventoy caied ove in each peiod. Unde this contact, the etaile and the holesale split the total pofit in popotions 1 a and a, espectively. Poof: Unde the coodinating contact, the holesale s objective function is T = E (1 β)( c) Q + β ( c)min(d, Q) b(q D) + aa. By substituting the poposed coodinating paametes and using the fact that (Q D) + = Q min(q, D), e get T = ae [(1 β)( c) Q + β ( c)min(d, Q) ( (1 β)+h)(q min(q, D)) A] = ae [( + h βc)min(d, Q) (h + c (1 β)) Q A]. Clealy, the objective function in the backets is the integated supply chain s pofit. Similaly, the etaile s objective function is T = E [( + h β)min(d(a),q) (h + (1 β)) Q A]. Using the same technique e get T = (1 a) E [( + h cβ)min(d(a),q) (h + c (1 β)) Q A]. Hence, the etaile ill choose the system optimal decisions. This completes the poof. Inteestingly, the popotion of pofit captued by the holesale is equal to the popotion of the custome acquisition costs she sponsos. If the holesale can influence the holesale pice, she should choose it in combination ith a accoding to the coodinating contact, so that a is as high as possible. This finding has an inteesting implication fo business pactices on the Intenet. Cuently, many e-tailes ae plagued by huge maketing expenditues, hile ou finding demonstates that holesales should conside subsidizing a significant popotion of these

27 26 expenditues to thei on benefit. Of couse, the highe the subsidized advetising, the highe the holesale pice. In pactice this ould mean that a etaile ithout sufficient funds fo custome acquisition should seek a contact ith a holesale ho ould be illing to subsidize a lage potion of advetising in exchange fo a highe holesale pice. A diffeent but somehat simila contact oks fo Model D. We need a contact that ould allocate some inventoy-elated isk to the etaile, hile at the same time allocating some maketing expenses to the holesale. One such contact ould be fo the etaile to compensate the holesale fo each unit of the inventoy caied ove hile the holesale subsidizes a potion of custome acquisition expenses. Poposition 8. The folloing contact achieves supply chain coodination in Model D: the holesale sponsos a popotion of the etaile s custome acquisition expenses a =( c)/( c), and at the same time the etaile patially compensates the holesale fo all unsold mechandise in the amount p =(h + c (1 β)) (1 a) pe unit. Unde this contact, the etaile and the holesale split total pofit in popotions 1 a and a, espectively. Poof: Simila to Poposition 7. The insights hee ae simila: the holesale gets a popotion of pofits that is equal to the popotion of the custome acquisition expenses she sponsos. It follos that the holesale should stive to sponso a elatively lage potion of the etaile s custome acquisition expenses in combination ith chaging a highe holesale pice and eceiving loe inventoy compensation accoding to the coodinating contact. Note that both optimal contacts do not depend on the demand distibution, as as noted by Pastenak (1985) fo pue etuns contacts. This leads us to anothe obsevation: Obsevation 5. Popositions 7 and 8 hold fo any demand distibutions, including the ones that do not satisfy Assumptions 1-3. The last obsevation shos that the contacts e popose ae obust, as has been epeatedly shon fo etuns contacts. We can do some compaison of the optimal contacts fo Models T and D. Fist, note that in both cases the holesale sponsos the same popotion of the etaile s maketing costs (povided that the holesale pice is the same). This is a convenient popety since, in this ay, if the holesale oks ith both the taditional and the dop-shipping etailes, she does not

28 Supply chain stuctues on the Intenet 27 need to disciminate among them. Discimination in tems of subsidized custome acquisition costs might invoke some undesiable consequences due to legal limitations, since such discimination might be consideed as pefeential teatment fo some etailes. It is, hoeve, possible that the holesale pices in Models T and D ill be diffeent. Since the holesale in Model D has moe involvement in channel functions and takes inventoy isk, she is likely to demand a highe holesale pice. Scheel (1990), page 42, povides empiical data that indicates 10-20% highe holesale pices fo dop-shipping vs. conventional distibution established by the holesales to cove thei exta costs. Obsevation 6. Suppose T < D. Then in coodinated supply chains, a T <a D and T < D, the holesale sponsos moe of the custome acquisition costs and has highe expected pofit in the dopshipping model. Dop-shipping equies a cetain investment fom the holesale, since she should be able to handle small shipments diectly to the custome. In addition, thee ae costs associated ith taking inventoy isk. This ould lead the holesale to demand an incease in the holesale pice, esulting in, as the last obsevation shos, captuing moe pofits, hich is beneficial in the long un. 6. Numeical expeiments To illustate the models and gain additional insights into the diffeences among the altenative supply chain stuctues, e ill no conside a specific fom of the demand distibution and a specific fom of its dependence on custome acquisition expenses 3. Let the andom tem of the demand follo a unifom distibution, U[0, ]. Futhe, let θ(a) = A. Fo numeical expeiments, e ill assume that c =5, h =1,β =0.95, and =1. Thevaiableofinteestis,ofcouse,the holesale pice. This also allos insight into cases hee the holesale pice of the dop-shipping supply chains is diffeent fom the holesale pice of the taditional supply chain. In hat follos, e assume that the pice-only contact is used. We analyze to scenaios: = 8and 12, to illustate the situations ith lo and high magins. Note that the optimal pofits and decision vaiables can be obtained and compaed in closed-fom. Fist, e look at the optimal custome acquisition expense (Figue 19.2) and stocking quantity (Figue 19.3). Note the stange fom of A DW that is a esult of highly non-linea tem ξ ³A DW,Q DW in the optimality condition. As e can see fom both

29 A 28 =8 A = A I A T A DW A DR A DN 10 A I A T A DW A DR A DN Figue Optimal custome acquisition spending. Q 2.5 Q =8 = Q I Q T Q DW Q DR Q DN Q I Q T Q DW Q DR Q DN Figue Optimal stocking quantity. figues, in Model DN the etaile seveely undespends on the custome acquisition and undestocks. When magins ae high, dop-shipping models ith a Stackelbeg leade closely esemble the taditional model. We ill see this phenomenon again late. Finally, Model DW ith the poeful holesale appeas to pefom somehee in beteen the othe to dop-shipping models, appoaching Model DN fo lo magins and Model DR fo high magins. We ill no conside the etaile s pofits

30 Supply chain stuctues on the Intenet 29 =8 = T DW DR DN T DW DR DN Figue Retaile s pofit. =8 = T DW DR DN 9 8 T DW DR DN Figue Wholesale s pofit. (Figue 19.4). In tems of the etaile s pofit, the dop-shipping models outpefom the taditional vetically disintegated model fo a ide ange of paametes. The etaile (not supisingly) is geneally bette off in Model DR hee he has negotiation poe. But even hen the negotiation poe is ith the holesale (Model DW), the etaile s pofit ishighe than hen the solution is a Nash equilibium (Model DN), as e have demonstated analytically. Any dop-shipping model dominates the ta-

31 30 ditional model fo modeate to high holesale pices. We conside the holesale s pofit next (Figue 19.5). Negotiation poe does not do the holesale much good: she is geneally bette off hen the etaile acts as a leade. The holesale s expected pofit is vitually the same in the taditional channel stuctue T as in the dop-shipping stuctue ith poeful etaile DR. When the holesale pice is elatively high, then both playes pefe Model DR ove Model T this gives indications fo hen (i.e. in tems of holesale pice) this model is pefeable. The Nash equilibium is again the least attactive to anyone. Model DW pefoms somehee in beteen Models DR and DN. We then look at the system pofits (Figue 19.6). =8 = I T DW DR DN I T DW DR DN Figue System pofit. The dop-shipping model ith the poeful etaile poves to be supeio unde modeate to high holesale pices, as e demonstated ealie. Unde a vey high holesale pice, any dop-shipping model outpefoms the taditional model. Among the thee dop-shipping models, Model DN is consistently the ost, and Model DR is consistently the best. Finally, e ill illustate the coodinating contacts. Assume that c = 5, =8, and =1. We denote pofits fo the etaile and the holesale esulting fom the coodinating contact by C and, C coespondingly. As e noted befoe, a etuns contact fo the taditional supply chain and a penalty contact fo the dop-shipping models splits pofits in the

32 Supply chain stuctues on the Intenet 31 same popotions. Figue 19.7 pesents etaile s and holesale s pofits ith and ithout coodination fo all models C T DW DR DN C T DW DR DN Figue Retaile s and holesale s pofits ith and ithout coodination. Obseve that, in ou example, unde the coodinating contact, the etaile alays makes moe pofit than ithout the coodinating contact. This is not tue in geneal: unde the lo unit-evenue and high vaiability the etaile may be bette off ithout the contact fo high holesale pices. The holesale, hoeve, might be bette off ithout coodination fo lo holesale pices. Thus, Paeto optimality of the coodinating contact depends on the poblem paametes. 7. Conclusions and discussion Dop-shipping is a novel ay of doing business on the Intenet that has been inheited fom catalog businesses and has aleady gained temendous populaity. Since unde dop-shipping the holesale takes inventoy isk and pefoms fulfillment, the etailes can focus on custome acquisition. Cuently, lage etailes ae able to captue a majo pat of the supply chain pofit. Adopting dop-shipping ill give holesales an oppotunity to change this unbalance by inceasing thei involvement into the supply chain opeations. Simultaneously, small etailes ill benefit since baies to enty in the fom of lage up-font inventoy investment ill diminish. We find that dop-shipping intoduces a conflict beteen maketing and opeations functions that esults in inefficiencies in the fom of simul-

33 32 taneous undestocking and spending too little on custome acquisition. As a esult, both the etaile and the holesale should choose dopshipping ove the taditional contact only hen the holesale pice is modeate to high. Fo example, if supply chain membes decide to move fom a taditional ay of doing business to dop-shipping, one should conside a simultaneous holesale pice incease. This finding is consistent ith the fact that unde dop-shipping the holesale caies inventoy-elated isk and theefoe should be able to incease the holesale pice; it is also consistent ith the existing pactice in catalog dop-shipping. Dop-shipping is moe attactive hen the etaile has the channel s poe and can execise it ove the holesale. When channel poe is equal, the etaile and the holesale aive at a unique competitive equilibium solution that significantly degades system pefomance and usually does not benefit anyone. We find simple contacts that achieve coodination in both the taditional supply chain and the supply chain ith dop-shipping. Accoding to these contacts, in the taditional channel the holesale subsidizes a potion of custome acquisition expenses as ell as compensates the etaile fo inventoy caied ove. In the case of dop-shipping inventoy compensation goes fom the etaile to the holesale. If the holesale can choose the holesale pice, the popotion of the custome acquisition expenses to subsidize, and the inventoy compensation, an abitay split of pofits can be achieved. In any case, the popotion of pofits that the holesale captues coincides ith the popotion of custome acquisition costs she subsidizes. Theefoe, the highe the subsidy, the highe the holesale pice and the highe the holesale s pofits. One may onde if a contact that specifies a popotion of subsidized custome acquisition expenses is enfoceable. We have obseved that some foms of subsidized maketing expenses ae aleady in use by holesales. Alliance Entetainment Cop., a holesale that has implemented dop-shipping ageements, is one example. AEC publishes electonically an All Media Guide that is available to etailes oking ith AEC. Accoding to AEC, the pupose of this database is to... guide the consume to make an intelligent puchasing decision and lean moe about music and video. In ode to publish this catalog, AEC employs about 600 pofessional and fee-lance ites ho ceate the content. Why ould the holesale get involved into this completely diffeent fom of business? The All Media Guide is a fom of subsidized custome acquisition expense. Spun.com, a etaile oking ith AEC accoding to the dop-shipping ageement, pays a basic eekly pice of

34 Supply chain stuctues on the Intenet 33 $1500 fo access to the database, heeas it ould cost Spun.com about $20M to ceate its on contents Fobes (2000). Othe methods of sponsoing custome acquisition costs ae possible. Many companies no povide tools that egiste ho many visitos sa the advetisement, ho many inteacted ith it, and ho many clicked though and made the puchase. Companies poviding this kind of sevice include AdKnoledge, DoubleClick, MatchLogic, and othes. By using these tools, both the etaile and the holesale can obseve the impact of custome acquisition expenditues and contact upon it. As Scheel (1990), page 89, descibes, in the pactice of catalog dop-shipping it is conventional fo the holesale to povide... fee photos, gaphics, catalog sheets, colo sepaations o othe advetising aids o alloances. This pactice seem to indicate that some sot of subsidized custome acquisition exists in dop-shipping. Ou model is an effot to intoduce and undestand the supply chain issues that aise unde a dop-shipping supply chain stuctue ith emphasis on the inventoy isk allocation, supply chain inteaction, and issues of channel poe. Many extensions to ou model ae possible. The isk pooling effect hen one holesale supplies seveal etailes ill make dop-shipping even moe appealing than ith a single etaile as descibed in this chapte (see Netessine and Rudi 2002 fo the analysis of this issue). It is, hoeve, vey encouaging to see that even ithout the isk pooling effect, dop-shipping in many cases outpefoms the taditional supply chain stuctue. With multiple etailes, it is even possible that the system pofit unde dop-shipping can exceed the pofit of a vetically integated supply chain since the integated channel does not enjoy the benefits of pooling. Finally, as Scheel (1990) suggests, etailes can cay the most popula poducts in inventoy and dop-ship the est diectly fom the holesale. This dual-soucing poblem aises many inteesting questions fo futhe eseach: hich poducts should be stocked vs dop-shipped etc.

35 34 Notes 1. This is an invited chapte fo the book Supply Chain Analysis in the ebusiness Ea edited by David Simchi-Levi, S. David Wu and Zuo-Jun (Max) Shen, to be published by Klue. The authos ae gateful to Gead Cachon, Peyas Desai, Paul Kleindofe and Matin Laiviee fo helpful suggestions that significantly impoved the chapte. The chapte also benefited fom semina discussions at the folloing univesities: Univesity of Rocheste, Datmouth College, Emoy Univesity, INSEAD, Geogia Institute of Technology, Conell Univesity, Nothesten Univesity, Univesity of Chicago, Ne Yok Univesity, Columbia Univesity, Canegie Mellon Univesity, Washington Univesity at St. Louis, Duke Univesity, Univesity of Pennsylvania and Univesity of Utah. 2. The exceptions ae follo-up papes by Netessine and Rudi 2002 hee multiple etailes ae modeled and by Randall et al that focuses on the empiical analysis of Intenet companies. These papes build upon the analysis in this chapte and do not analyze maketing aspects 3. A link to an inteactive eb site fo numeical expeiments is povided at.nilsudi.com.

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