Coordination of a Supply Chain with Advertising Investment and Allowing the Second Ordering

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1 Technology an Investment, 00,, 9-00 oi:0.436/ti Publishe Online August 00 ( Abstract oorination of a Supply hain with Avertising Investment an Allowing the Secon Orering Tiaojun Xiao, Xinxin Yan, Jiabao Zhao School of anagement Science an Engineering, Nanjing University, Nanjing, hina xiaotj@nju.eu.cn, yostyan@63.com eceive arch 30, 00; revise June 5, 00; accepte June 7, 00 This paper evelops a game theoretic moel of a one-manufacturer an one-retailer supply chain allowing the secon orering to investigate how to coorinate the orer quantity an avertising investment via a markown money-cooperative avertising contract. We focus on the effects of allowing the secon orering on equilibrium outcome an coorination mechanism. We fin: the relationship between the unit wholesale prices an the chargeback rate epens on whether allowing the secon orering; the coorination mechanism is robust to eman uncertainty; the unit wholesale price in perio increases with the unit prouction cost in perio, the unit elaye elivery cost an unit salvage value if an only if the chargeback rate is sufficiently small while that in perio is inepenent of them. In aition, we stuy the Pareto conition of coorination mechanism uner which both manufacturer an retailer are better off using the coorination mechanism an fin that the unit prouction costs in ifferent perios may have contrary effects on the bouns of Pareto range. Keywors: Avertising Investment, Supply hain anagement, arkown oney-ooperative Avertising ontract, eorer, Game Theory.Introuction In business worl, avertising is an important tool of sales promotion for retailer/seller, which raises the supply chain s profitability. However, retailer only reaps a part of the benefit of avertising, which implies that the retailer may invest less in avertising than that of the centralize supply chain. For seasonal proucts, market eman is highly uncertain, which iscourages the purchase behavior of the retailer. To stimulate the retailer s orer, the manufacturer may share the risk of eman uncertainty with the retailer, say, offering returns policy an markown money policy. This paper focuses on how to coorinate the supply chain via a markown moneycooperative avertising contract. The members of supply chain usually cannot accurately make ecisions uner eman uncertainty, especially, orer quantity an investment ecisions. Hence, the retailer often orers a lower quantity to reuce operation risk. In orer to satisfy the market eman, the manufacturer may allow the secon orering. Specifically, at the en of selling season, the retailer is allowe to make the secon orering for unsatisfie eman. They use this policy to reuce the loss incurre by eman uncertainty. The reorer policy becomes very important in business operation management. Lots of companies allow the retailers to reorer. For example, accoring to [], Sport Obemeyer LTD is a company that sells fashion skiwear. If there were unsatisfie eman, Obemeyer woul allow retailers to make the secon orering to replenish for popular items uring the selling season. In fashion inustry, the secon orering is often aopte, say Zara, Lilanz. This also happene in electronics inustry, say, Irico group electronics company limite. In this paper, we evelop a game theoretic moel of a supply chain consisting of one manufacturer an one retailer uner eman uncertainty to investigate how to coorinate the orer quantity an avertising investment ecisions, an explore the effects of allowing the secon orering on the coorination mechanism. The manufacturer offers a markown money-cooperative avertising contract to coorinate the supply chain. We assume that the manufacturer allows the retailer to make the secon orering at the en of selling season. The manufacturer uses a fast prouction moe to satisfy the secon orering, which incurs a higher unit prouction cost. We focus on the effect of some factors relate to the secon orering on the coorination mechanism. We fin that opyright 00 Scies.

2 9 T. J. XIAO ET AL. the relationship between the unit wholesale price an chargeback rate iffers from that without the secon orering. In aition, we stuy Pareto conition of the coorination mechanism. The remainer of this paper is organize as follows. Section reviews relate literature. Section 3 introuces the basic moel. Section 4 investigates the coorination mechanism of the supply chain with general istribution function. Section 5 analyzes Pareto conitions of the coorination mechanism uner uniform istribution. Finally, we summarize this paper an point out some irections for future research in Section 6.. Literature eview This paper is closely relate to cooperative avertising, coorination management an reorer policy. It is well known that avertising can stimulate the market eman while also incurs an avertising cost. Thus, the seller must make a trae-off between the benefit an the cost when it etermines avertising investment. Jørgensen et al. [] pointe out that cooperative avertising is a popular incentive mechanism for avertising investment. Huang an Li [3] introuce a cooperative avertising moel of a supply chain consisting of one manufacturer an one retailer, where the manufacturer invests in national avertising an pays the retailer a subsiy to stimulate the local avertising investment of the retailer. Nagler [4] offere an exploratory empirical investigation of the eterminants of cooperative avertising participation rates an examine the relationship between participation rates an national avertising expenitures by bran. In this paper, we consier a cooperative avertising contract between one manufacturer an one retailer an investigate how to coorinate avertising investment. About supply chain coorination contract, it has been wiely stuie in the literature, such as returns/buyback policy [5], markown money [6,7], revenue-sharing contract [8], an option contract [9]. Donohue [0] investigate how to coorinate supply chain with forecast upating an two prouction moes. Zhang et al. [] examine coorination of an assemble-to-orer system involving a short-life-cycle prouct. Hsieh et al. [] examine coorinate ecisions in a ecentralize supply chain faces ranom eman of a short-life-cycle prouct. eturns policy/buyback contract is a goo coorination mechanism for the retailer to orer more, where the retailer can return some or all unsol items at the en of selling season to the manufacturer an receives a full or partial refun. Kanel [3] investigate the allocation of responsibility for unsol items an conclue that monopolistic manufacturer prefers a buyback contract, while monopolistic retailer prefers a no-buyback policy. He et al. [4] evelope a moel to etermine the optimal returns policy for single-perio proucts in the presence of risk preferences an consiere a markown money contract stimulating orer quantity. In a sense, markown money contract is similar to buyback contract. Their ifference lies in who isposes the leftovers to obtain the salvage value. Nair an loss [5] evaluate the implications of coorinating price markown policy with supply chain policies of inventory replenishment, an transportation expeiting on retail performance of a short lifecycle prouct. Wang an Webster [7] pointe out that markown money is frequently use between manufacturers an retailers selling perishable goos. In this paper, we combine markown money contract with cooperative avertising contract to coorinate the supply chain. There are many publications has iscusse eman uncertainty [6-8]. Uner eman uncertainty, there may be unsatisfie eman at the en of selling season. Some publications assume that the unsatisfie eman is lost [8,9]. However, a few publications assume that the seller reorers to satisfy the unsatisfie eman, say [0]. We consier the case where the retailer reorers to satisfy the unsatisfie eman at the en of selling season. ecause of the elaye elivery, there is penalty cost for all unsatisfie eman. The reorer policy research mainly focuse on two issues: reorer time an the secon orering. ost of the literature about reorer focuse on reorer time. For example, hen [] compare the installation stock policy with the echelon stock policy to analyze the optimal reorer points. Seo et al. [] efine the orer risk policy to ecie reorer time to evelop the optimal reorer policy for a istribution system with one-warehouse an multiple retailers. Dogru et al. [3] use echelon stock newsvenor equations to optimize the reorer policy in an N-echelon stochastic serial inventory system with a given fixe batch size an linear penalty costs. Leng an Parlar [4] evelope a simple profit-sharing contract to achieve supply chain coorination where the retailer manages the inventory system using reorer policy. A few publications only allowe the secon orering at the en of selling season an investigate the effect of allowing the secon orering. For example, Donohue [0] examine the problem of eveloping supply contracts an prouction ecisions of high fashion, seasonal proucts operating in a two-moe prouction environment, an the secon orering was expensive but offere quick turnaroun. Weng [0] evelope a generalize newsvenor moel to analyze the coorinate quantity ecisions between the manufacturer an the buyer where allows the secon orering at the en of the perio if the eman excees stock on han. Seo [5] extene the orer risk policy to general multi-echelon systems, an assume that excessive customer emans at retailers are fully backorere an incur a linear penalty cost. We assume that the retailer makes the secon orering at the opyright 00 Scies.

3 T. J. XIAO ET AL. 93 en of selling season an the secon orer quantity is equal to the quantity of unsatisfie emans, an focus on the effect of allowing the secon orering on the coorination mechanism. The unit prouction cost in the first setup often is lower than that in the secon setup because the former has a longer elivery time. We incorporate this characteristic into moel an investigate its effect on the coorination mechanism. This paper is closely relate to [6] that consiere how to coorinate the orer quantity an avertising investment ecisions in a single perio moel with single prouction moe. However, we assume that the manufacturer has two prouction moes an explore how allowing the secon orering influences the equilibrium outcome an coorination mechanism. In aition, we consier how some factors influence the Pareto conition of coorination mechanism. We try to fin the new results an managerial insights relative to [6]. In fact, we fin some contrary results, for example, the relationship between the unit wholesale prices an chargeback rate epens on whether allowing the secon orering or not. We will point the main ifference between them. This paper complements the literature by investigating coorination of a two-stage supply chain allowing the secon orering to satisfy the unsatisfie eman at the en of selling season via a markown money-cooperative avertising mechanism. Especially, we focus on the effects of allowing the secon orering on the coorination mechanism. In aition, we stuy Pareto conition of coorination mechanism when the ranom eman is uniformly istribute. 3. The asic oel We consier a supply chain consisting of one manufacturer an one retailer. The manufacturer prouces a seasonal prouct an sells it through the retailer who carries out (local) avertising investment to stimulate market eman, where the secon orering is allowe. Owing to the market eman s uncertainty, there may be some unsatisfie emans at the en of selling season. Thus, at the en of selling season, to set up a goo reputation an obtain a higher profit, the retailer must reorer to satisfy all of unsatisfie emans, i.e., this paper allows backorer but shortage will incur a loss of goowill. The unsatisfie customer emans incur a elaye elivery cost. We assume that the manufacturer has enough capacity to satisfy the retailer s orering within a given lea-time an only the secon orering is allowe at the en of selling season ue to a long lea-time. The two players inepenently maximize their own expecte profits. Similar to [9], we assume that the retail price is exogenously given. Owing to the fact that there exists a long elivery lea-time an a short selling season, the manufacturer only allows the retailer to orer two times, one occurring before the selling season, the other occurring at the en of selling season. In response to the retailer s orers, the manufacturer shoul prouce items over two perios. In the first perio, the prouction moe is relatively cheap but nees a long lea-time. An in the secon perio, the manufacturer uses a faster but typically more expensive prouction moe. Similar to [0], we use two ifferent prouction costs to express two ifferent prouction moes. The event sequence of this game is as follows: ) the manufacturer etermines the unit wholesale prices, cooperative avertising subsiy rate an chargeback rate; ) the retailer ecies the avertising investment level an the first orer quantity; 3) if there are unsatisfie emans at the en of selling season, the retailer makes the secon orering to satisfy the market eman. We have following notation: c i the unit prouction cost of the manufacturer in perio i ( i, ), c c; w i the unit wholesale price of the manufacturer in perio i ( i, ), w w; p the unit retail price, p b s; s the salvage value per unit unsol item for the retailer, 0 s c ; Q the first orer quantity of the retailer; c the elaye elivery cost rate for per unit unsatisfie prouct, c 0 ; b the chargeback rate per unit unsol prouct, b 0 ; I the avertising investment per unit expecte eman for the retailer, referring to as avertising level, I p c ; t the fraction of avertising expeniture share by the manufacturer, 0 t ; k scaling constant for eterministic eman part, k 0 ; the avertising elasticity of the eman, 0 ; x the stochastic eman for the retailer. Similar to [6,7], we assume that the retailer faces a ranom eman x D( I) ki, where is istribute over [, ] with a ensity function of f ( ), a cumulative istribution function of F( ) an a mean of, ki 0. Furthermore, the total avertising investment is I E( x) I( D( I) ). Since the market eman is uncertain, it is necessary to ivie the profit function of the retailer into two cases, opyright 00 Scies.

4 94 T. J. XIAO ET AL. x Q an x Q. At the en of selling season, if x Q, the unsol items are ispose in the seconary market by the retailer for a unit salvage value. Further, the retailer s profit function is ( x x Q) px ( b s)( Q x) wq ( t) I( D ) px ( b s) x ( b s w ) Q ( t) I( D ) In the first line, the first term represents the selling revenue; the secon term represents the total revenue of the leftovers from salvage value an chargeback money; the thir term is the purchase cost; an the fourth term represents the avertising investment cost bear by the retailer. If x Q, the retailer makes the secon orering to satisfy all the unsatisfie eman. Similar to [], unsatisfie eman incurs a shortage cost. In this paper, the retailer makes the secon orering to satisfy those unsatisfie emans. The customers at last receive those items a few ays later, which incurs a unit elaye elivery cost c. An the retailer s profit function is ( x x Q) pxwq ( w c)( xq) ( tid ) ( ) px ( w c ) x ( w c w ) Q ( t) I( D ) In the first line, the thir term represents the sum of the reorering purchase cost an the elaye elivery cost. Furthermore, the expecte profit of the retailer is Q D Q D ( x x Q ) f ( ) ( x x Q ) f ( ) pd ( ) ( tid ) ( ) QD [( bsw ) Q( bs)( D )] f( ) QD w c w Q w c D f [( ) ( )( )] ( ) [ p ( ti ) bs]( D) ( bsw) Q ( bsw c ) ( D Q) f( ) QD In (), the term ( D Q ) f ( ) represents QD the expecte shortage quantity. If x Q, the profit function of the manufacturer is ( ) ( ) ( ) ( ) x x Q w c Q ti D b Q x The first term represents the gross profit; the secon term represents the avertising cost bear by the manufacturer; an the last term represents the chargeback cost for the leftovers. If x Q, the manufacturer setups the secon prouction to satisfy the secon orering, an the manufacturer s profit function is ( x xq ) ( w c ) Q ( w c )( xq ) ti ( D ). () The secon term represents the gross profit for the reorer quantity of the retailer. Furthermore, the expecte profit of the manufacturer is Q D Q D QD Q D ( xx Qf ) ( ) ( xx Qf ) ( ) bd ( Q) f( ) ( wc)( D Q) f( ) ( wc) QtI( D) ( w c b) Q( bti)( D) ( w c b) ( D Q) f( ) QD The total expecte profit of supply chain is the sum of the expecte profit functions of the retailer an the manufacturer. Thus, the total expecte profit of supply chain is ( pi s)( D) ( s c ) Q () ( s c c ) ( D Q ) f ( ) (3) QD 4. oorination echanism It is well known that the ecentralize supply chain has a lower profitability than the centralize supply chain at the absence of supply chain competition. That is, coorinating the behavior of the member firms can improve the performance of supply chain. In orer to coorinate the supply chain, the manufacturer offers a markown money-cooperative avertising (A) mechanism ( w, w, b, t ) to inuce the retailer to replicate the optimal avertising level an orer quantity of the centralize supply chain. When the supply chain is coorinate, the supply chain achieves the profit of the centralize system. 4.. Optimal Decisions in the entralize Setting To provie a benchmark, we first consier a centralize system where the central ecision maker etermines all ecisions (avertising level an quantity) to maximize the channel profit. From (3), we erive the following. Proposition. In the centralize setting, the optimal solution of the channel profit satisfies the first-orer conitions GQI (, ) c c c( c c sfq ) ( ki ) 0(for Q ) H I pi c k I ki (for I ). ( ) ( ) 0 Proposition implies that the optimal avertising level is inepenent of the unit salvage value s an the unit prouction cost c while the quantity epens on them. That is, when they change, the central ecision-maker woul like to ajust quantity to react to their effects. Let the optimal quantity an avertising level of the supply opyright 00 Scies.

5 T. J. XIAO ET AL. 95 chain be on Q Q an I an I. The effects of c, an k are similar to those in [6], omitting them. From Proposition, we fin that Q is an increasing function of c, c an s. Specifically, when the unit prouction cost c or the unit elaye elivery cost c increases, the central ecision maker shoul raise the prouction quantity in perio to reuce the cost for the shortage prouct. When the unit salvage value s increases, the central ecision maker raises the prouction quantity in perio ue to a lower loss for the leftovers. 4.. oorination echanism Now, we investigate how to coorinate the ecentralize supply chain in which the manufacturer an the retailer maximize their own profits inepenently. Similar to Proposition, we erive the following. Proposition. The optimal ecisions of the retailer satisfy the first-orer conitions w w c ( w c bs) F( QkI ) 0 (for Q ) (4) ki t k I p w t (for I ) (5) ( )( ) ( ) ( ) 0 Proposition implies that, a higher fraction (t ) of avertising expeniture share by the manufacturer inuces a higher avertising level, which in turn inuces a higher orer quantity in perio. When the supply chain is coorinate, the A mechanism shoul inuce the retailer to orer quantity Q an invest I. Proposition 3 summarizes the A mechanism. Proposition 3. The A mechanism ( w, w, b, t ) with w tp c ( t) an { bc ( c c) cs c( sc) ( c c s)[ tpc( t)]} w c s can coorinate the supply chain. Proposition 3 implies that the A coorination mechanism is robust to eman uncertainty, i.e., inepenent of the istribution of eman uncertainty, which iffers from that in [6]. When the fraction t increases, the manufacturer will raise the unit wholesale prices in two perios to offset a part of the increase avertising cost. It is worthy to note that a higher chargeback rate is along with a lower unit wholesale price in perio an the unit wholesale price in perio is inepenent of the chargeback rate, which iffers from that without the secon orering, see [9,6]. That is, if the manufacturer ecreases the chargeback rate to reuce the excessive orering, it shoul raise the unit wholesale price in perio to stimulate the orer quantity in perio. The unit wholesale price in perio is inepenent of the unit prouction cost c, the unit elaye elivery cost c an the unit salvage value s because they are not relate to perio. The unit wholesale price w increases with the unit prouction cost c if an only if the chargeback rate is sufficiently low ( b c ( t) s pt ); an increases with the unit elaye elivery cost c an the unit salvage value s if an only if the chargeback rate is sufficiently low ( b ( p c ) t ). In aition, although a higher unit prouction cost in perio raises the unit wholesale price in perio, it ecreases the unit wholesale price in perio if the chargeback rate is sufficiently low ( b ( p s) t ), which results in a lower orer quantity in perio. 5. Pareto Analysis of oorination echanism uner Uniform Distribution In Section 4, we iscuss the A coorination mechanism without giving the optimal quantity an avertising level ecisions in the setting with general istribution function. Now, we use a specific form of istribution function to obtain the optimal ecisions an iscuss the Pareto conition of the coorination mechanism. For analytical tractability, we use the uniform istribution function for, efine over a finite range [ A, A], A 0, which implies that the mean is 0. Here, the ensity function is f ( ) /( A), the cumulative istribution function is F( ) ( A)/( A) an A reflects the egree of eman uncertainty. 5.. Equilibrium Outcome in the entralize Setting From Proposition, we erive the following. orollary. Uner uniform istribution, the optimal ecisions of the centralize system are ( p c ) c c c I an Q k( I) AA. ( ) c c s The equilibrium channel profit is ( p c ) [ k( pc)( c c s)( ) Ac ( c c)( cs)( )] ( c c s)( ) In the centralize setting, from orollary an [6], we know that the optimal avertising level is inepen- opyright 00 Scies.

6 96 T. J. XIAO ET AL. ent of whether allowing the secon orering while the optimal quantity epens on it. orollary implies that the channel profit is positive if an only if ( p c ) k( pc)( c c s)( ) ˆ A A ( c c c )( c s)( ) That is, the channel can make a positive profit if an only if the eman uncertainty is not too large ( A Aˆ ). In the following, we assume that the conition A Aˆ is satisfie. It follows from p c that both I an Q increase with. It is surprising that the channel profit is ecreasing with the avertising elasticity if ( pc ). One expects that the avertising elasticity always have a positive effect on the channel profit because this raises the market eman. However, higher avertising elasticity also incurs a higher avertising cost (negative effect). As a consequence, if the unit net profit is sufficiently small ( pc ) or the avertising elasticity is sufficiently small, the channel profit ecreases with the avertising elasticity because the negative effect is larger than the positive effect; otherwise, it increases. orollary implies that, when the retail price increases, the central ecision maker increases the optimal avertising level to stimulate the market eman ue to a higher unit profit. 5.. Equilibrium Outcome in the Decentralize Setting Now, we iscuss the ecentralize system without coorination contract. Here, the manufacturer an the retailer maximize their profits inepenently. The manufacturer first jointly etermines the unit wholesale price in two perios an then the retailer etermines the orer quantity an avertising level. Similar to Section 3, when allowing the secon orering, we get the expecte profit of the retailer is ( pi s) D( sw ) Q ( sw c ) ( D Q)/( A) A QD ( pis) D( sw) Q( ADQ) ( sw c )/(4 A) an the expecte profit of the manufacturer is ( w c ) Q ( w c ) ( D Q )/( A ) A QD ( w c) Q ( w c)( A D Q) /(4 A) (6) (7) Similar to orollary, from (6), it follows that, given the unit wholesale prices ( w, w ), the optimal reactions ( p w ) of the retailer are I( w ) ( ) an A( c s w w) Qw (, w) ki ( ( w)) c w s Inserting I( w ) an Qw (, w ) into (7), we can obtain the expecte profit of the manufacturer ( w, w ). y search the maximum value of ( w, w ) uner the constraint A Q D A, we can obtain the optimal unit wholesale prices ( w, w). Furthermore, we can obtain the equilibrium ecisions of the retailer an the profits of the players. Let the optimal profit of the retailer be an that of the manufacturer in the ecentralize setting Pareto Analysis When the supply chain is coorinate, the supply chain achieves the profit of the centralize system that is higher than that of the ecentralize supply chain. However, the profit allocation of the coorinate supply chain epens on the specific A contract. It is possible that a member of the coorinate supply chain gains a lower profit than that in the ecentralize setting. Thus, it is necessary to stuy when both firms are better off using A coorination mechanism, i.e., Pareto ominant. Proposition 4 summarizes the Pareto conition of coorination mechanism. Proposition 4. The A mechanism is Pareto ominant over the ecentralize setting if b ( bˆ, ˆ L bh), where ˆ ( cc s)[ ki ( t)( pci )] bl c ( t) pts Ac ( c c) an bˆ H c ( t) pt s ( c c s)[ ki ( t)( pci)]. Ac ( c c) Proposition 4 implies that, the retailer is better off accepting the A coorination mechanism only if the chargeback rate is not too low an the manufacturer is better off offering the A mechanism only if the chargeback rate is not too high because a higher chargeback rate ecreases the unit wholesale price in perio (see Proposition 3), which iffers from that in [6]. That is, only when the chargeback rate is appropriate ( b ( bˆ, ˆ L bh )), the two players are better off using the A coorination mechanism. Since it is ifficult to fin the analytic results on the opyright 00 Scies.

7 T. J. XIAO ET AL. 97 bouns of chargeback rate, we investigate how some factors influence the results using a numerical example, where the efault values of parameters are use as: A 5, c 8, c 8, c 4, k 0, p 35, s 6, t 0.7 an 0.5. Figure escribes the effect of the chargeback rate on the profits of the players when the supply chain is coorinate. Figures -5 escribe how the unit elaye cost, the unit prouction cost in perio, the avertising elasticity an the fraction of avertising expeniture influences the bouns of chargeback rate. Since the effects of the unit prouction cost in perio an salvage value on the bouns are similar to those of the unit elaye elivery cost, we omit them. We also omit the effect of scaling constant because it is similar to that of avertising elasticity. From Figure an Proposition 3, we know that a higher chargeback rate is more beneficial to the retailer because the manufacturer charges the retailer a lower unit wholesale price in perio an the retailer obtains a higher chargeback for the unsol quantity in perio, which is ifferent from that in [6]. From Figure, we know that when the unit elaye elivery cost increases, the retailer has a higher incentive to use the A mechanism while the manufacturer has a lower incentive to choose it because the manufacturer bears a part of the Figure 3. ouns of chargeback rate versus unit prouction cost. Figure 4. ouns of chargeback rate versus avertising elasticity Figure. Profits versus chargeback rate. b Figure 5. ouns of chargeback rate versus the fraction. Figure. ouns of chargeback rate versus elaye elivery cost. elaye elivery cost in the coorinate setting. Figure 3 implies that, when the unit prouction cost in perio increases, the retailer has a lower incentive to use the coorination mechanism while the manufacturer has a higher incentive because the manufacturer can better transfer the prouction cost in perio to the retailer via the A mechanism than the ecentralize setting. Furthermore, the unit prouction cost ifference between the two perios plays an important role in the motivation of the players to choose the A mechanism. From Figure 4, we know that, when the avertising elasticity is not too small, higher avertising elasticity implies a opyright 00 Scies.

8 98 T. J. XIAO ET AL. larger range of chargeback rate in which both the manufacturer an the retailer are better off using coorination mechanism because the cooperative avertising can stimulate a higher avertising level an eman rate. From Figure 5, we know that, when the fraction t is sufficiently small, coorination is always beneficial to the retailer but harmful to the manufacturer. Thus, the manufacturer woul like to offer a high fraction to stimulate the avertising investment. In fact, from Proposition 3, we know that the manufacturer offers a higher unit wholesale price to access a higher unit profit, which offsets a part cost of the avertising subsiy as the fraction increases. A higher fraction often is along with a higher chargeback rate because it nees a higher chargeback rate to inuce the retailer to use coorination mechanism. 6. onclusions Seasonal proucts own high eman uncertainty such that there are often leftovers or shortage at the en of selling season. Local avertising plays an important role in promoting the marketing of seasonal proucts. This paper investigates how to coorinate the orer quantity an avertising investment ecisions via a A mechanism when the secon orering is allowe. We allow the retailer to make the secon orering to satisfy the market eman when there exists shortage at the en of selling season an focus on the effects of allowing the secon orering on equilibrium outcome an coorination mechanism. We fin that whether allowing the secon orering influences the coorination mechanism to a large egree an even fully changes the results. For example, it inverts the relationship between the unit wholesale prices an chargeback rate an the motivation of the players to use the A mechanism. In aition, we focus on the effects of the new factors relate to allowing the secon orering (the unit prouction cost c an the unit elaye elivery cost c ) on the results an the characteristics of the unit wholesale price ( w ) in perio. We also illustrate the effects of the changing of economic environment on the Pareto range of coorination mechanism an fin that the unit prouction cost ifference between the two prouction moes remarkably influences the Pareto range, i.e., the unit prouction costs in ifferent perios may have contrary effects on the bouns of Pareto range. This paper assumes that there is a monopoly retailer in the retail market. One may exten it to the case with multiple retailers to consier the effects of competition on equilibrium outcome an coorination mechanism. We assume that the manufacturer oes not carry out (national) avertising investment. Incorporating the national avertising investment into our moel may be interesting. 7. Acknowlegements This research was supporte in part by the National Natural Science Founation of hina uner Grant , , an eferences [] D. Simchi-Levi, P. Kaminsky an E. Simchi-Levi, Designing & anaging Supply hain: oncepts, Strategy & ase Stuies, cgraw-hill, Irwin, 003, pp [] S. Jørgensen, S. P. Sigué an G. Zaccour, Dynamic ooperative Avertising in a hannel, Journal of etailing, New York, Vol. 76, No., 000, pp [3] Z. Huang an S. X. Li, o-op Avertising oels in anufacturer-etailer Supply hains: A Game Theory Approach, European Journal of Operational esearch, Elsevier, Vol. 35, No. 3, December 00, pp [4]. G. Nagler, An Exploratory Analysis of the Determinants of ooperative Avertising Participation ates, arketing Letters, Springer Netherlans, Vol. 7, No., April 006, pp [5] H. S. Lau an A. H. L. Lau, anufacturer s Pricing Strategy an eturn Policy for a Single-Perio ommoity, European Journal of Operation esearch, Elsevier, Vol. 6, No., July 999, pp [6] T. A. Taylor, Supply hain oorination uner hannel ebates with Sales Effort Effects, anagement Science, INFOS, Vol. 48, No. 8, August 00, pp [7]. X. Wang an S. Webster, arkown oney ontracts for Perishable Goos with learance Pricing, European Journal of Operational esearch, Elsevier, Vol. 96, No. 3, August 009, pp. 3-. [8] Z. Yao, S.. H. Leung an K. K. Lai, anufacturer s evenue-sharing ontract an etail ompetition, European Journal of Operational esearch, Elsevier, Vol. 86, No., April 008, pp [9] N. X. Xu an L. Nozick, oeling Supplier Selection an the Use of Option ontracts for Global Supply hain Design, omputers & Operations esearch, Elsevier, Vol. 36, No. 0, October 009, pp [0] K. L. Donohue, Efficient Supply ontracts for Fashion Goos with Forecast Upating an Two Prouction oes, anagement Science, INFOS, Vol. 46, No., November 000, pp [] X. H. Zhang, J. H. Ou an S.. Gilbert, oorination of Stocking Decisions in an Assemble-to-Orer Environment, European Journal of Operational esearch, Elsevier, Vol. 89, No., September 008, pp [].. Hsieh,. H. Wu an Y. J. Huang, Orering an Pricing Decisions in a Two-Echelon Supply hain with Asymmetric Deman Information, European Journal of Operational esearch, Elsevier, Vol. 90, No., October 008, pp [3] E. Kanel, The ight to eturn, Journal of Law an opyright 00 Scies.

9 T. J. XIAO ET AL. 99 Economics, University of hicago, Vol. 39, April 996, pp [4] J. He, K. S. hin, J.. Yang an D. L. Zhu, eturn Policy oel of Supply hain anagement for Single- Perio Proucts, Journal of Optimization Theory an Applications, Springer Netherlans, Vol. 9, No., ay 006, pp [5] A. Nair an D. J. loss, An Examination of the Impact of oorinating Supply hain Policies an Price arkowns on Short Lifecycle Prouct etail Performance, International Journal of Prouction Economics, Elsevier, Vol. 0, No., August 006, pp [6] H. P. arvel an H. Wang, Inventories, eturn Policy, an Equilibrium Price Dispersion uner Deman Uncertainty, hina enter for Economic esearch, eijing University, Working Paper, 00. [7] K. Kogan an A. Herbon, A Supply hain uner Limite-Time Promotion: The Effect of ustomer Sensitivity, European Journal of Operational esearch, Elsevier, Vol. 88, No., July 008, pp [8] Y. J. He an J. Zhang, anom Yiel isk Sharing in a Two-Level Supply hain, International Journal of Prouction Economics, Elsevier, Vol., No., April 008, pp [9]. H. Lee an. D. hee, hannel oorination Using Prouct eturns for a Supply hain with Stochastic Salvage apacity, European Journal of Operational esearch, Elsevier, Vol. 77, No., February 007, pp [0] Z. K. Weng, oorinating Orer Quantities between the anufacturer an the uyer: A Generalize Newsvenor oel, European Journal of Operational esearch, Elsevier, Vol. 56, No., July 004, pp [] F. hen, Echelon eorer Points, Installation eorer Points, an the Value of entralize Deman Information, anagement Science, INFOS, Vol. 44, No., December 998, pp. S-S34. [] Y. Seo, S. Jung an J. Hahm, Optimal eorer Decision Utilizing entralize Stock Information in a Two-Echelon Distribution System, omputers & Operations esearch, Elsevier, Vol. 9, No., February 00, pp [3]. K. Dogru, G. J. Houtum an A. G. Kok, Newsvenor Equations for Optimal eorer Levels of Serial Inventory Systems with Fixe atch Sizes, Operations esearch Letters, Elsevier, Vol. 36, No. 5, September 008, pp [4]. Leng an. Parlar, Lea-Time euction in a Two-Level Supply hain: Non-ooperative Equilibria vs. oorination with a Profit-sharing ontract, International Journal of Prouction Economics, Elsevier, Vol. 8, No., April 009, pp [5] Y. Seo, ontrolling General ulti-echelon Distribution Supply hain with Improve eorer Decision Policy Utilizing eal-time Share Stock Information, omputers & Inustrial Engineering, Elsevier, Vol. 5, No., October 006, pp [6] T. J. Xiao an X. X. Yan, oorinating a Two-Stage Supply hain via a arkown oney an Avertising Subsiy ontract, International Journal of Information an Decision Sciences, Inerscience, 00, in press. [7] F. J. Arcelus, S. Kumar an G. Srinivasan, Evaluating anufacturer s uyback Policies in a Single-Perio Two- Echelon Framework uner Price-Depenent Stochastic Deman, Omega, Elsevier, Vol. 36, No. 5, October 008, pp opyright 00 Scies.

10 00 T. J. XIAO ET AL. Appenix Proof of Proposition. Differentiating with respect to Q, we can obtain the first-orer conition s c( sc c )( F( QkI )) Q c cc ( c c s) F( QkI ) 0 (A.) Note that D is a function of I. Differentiating with respect to I, we obtain the first-orer conition ki ki ( pi s) ki ( s c c )( F( QkI )) I ki ki [( p I cc ) ( cc s) F( QkI )] 0 (A.) From (A.), it follows that the first-orer conition (A.) is equivalent to ( p I c ) k I ki 0 (A.3) From (), p c c s an I p c, it follows that, the secon-orer erivatives are Q ( c c s ) f ( Q ki ) 0 k I ( c c s) f( QkI ) 0 QI k I [ I ( )( p I c ) k I ( c c s ) f ( Q ki )] 0 I ( ) Q I QI ki ( c c s) f( QkI )[ I( )( pic)] 0. Thus, is a jointly concave function of ( QI, ), i.e., the secon-orer conition is satisfie. Thus, the solution of the first-orer conitions is optimal. Proof of Proposition. Given the A mechanism of the manufacturer, the retailer etermines Q an I to maximize given by (). Differentiating with respect to Q an I, we can obtain the first-orer conitions bsw ( bsw c )( F( QkI )) Q w w c ( w c bs) F( QkI ) 0 (A.4) I ( )( ( )) ( t)( ki ) k I [ p ( t) I b s] ki b s w c F Q ki ( ) ( )] 0 ( t)( ki ) k I [ p( t) I w (A.5) c bsw c F QkI From (A.4), it follows that the first-orer conition (A.5) is equivalent to ki ( )( t) ki ( p w ) ( t) 0 (A.6) Similar to Proposition, we can show that is a concave function of ( QI, ), i.e., the secon-orer conition is satisfie. Proof of Proposition 3. y comparing (A.) with (A.4), we know that, if the manufacturer wants to inuce the retailer to replicate the outcome of the centralize system, the optimal unit wholesale price for two perios shoul satisfy bc ( c c) cs c( sc) ( c c sw ) w( w) c s ewriting (A.3) an (A.6), we have ki ( ) ( p c ) ki (A.7) ki ( ) ki ( p w ) / ( t) (A.8) From (A.7) an (A.8), we know that ( p c ) k I ki ( pw )/( t) (A.9) Solving (A.9) for w, we have w p( pc)( t) tpc( t) Proof of orollary. From Proposition an F( ) ( A)/( A), it follows that the first-orer conitions (A.) an (A.3) are equivalent to Ac ( c c) ( AQkI )( c c s) 0 (A.0) ( p c ) k I ki ( ) 0 (A.) Solving (A.0) an (A.) for Q an I, we obtain Q an I, given in orollary. Proof of Proposition 4. Inserting w, w an Q into (), we have ( b) ki ( t)( pc I) A( c c c)[ bsc( t) pt] c c s which is an increasing function of b following from c c s. Solving ( b) for b, we get bˆ L c ( t) pts ( c c s)[ ki ( t)( pci )] Ac ( c c) Thus, the retailer is better off using coorination mechanism if b bˆl. The equilibrium profit of the coorinate manufacturer is () b () b, which is a ecreasing function of b. y solving ( ) b for b, we obtain b ˆH, given in Proposition 4. Furthermore, the manufacturer is better off using coorination mechanism if b b. ˆH opyright 00 Scies.