IntroductionResearch papersConsiderthefollowing situation faced by theA general framework oftoy industry (ohnson, 1999):supply chain contractTwo key features that define many of thechallenges in the toy industry for both large andmodelssmall firms are the seasonal demand and shortproduct life.Toy sales and volumes growexponentially the last few days before Christmas.Charles X. WangNovember and December alone represent nearly45%oftoysales.Shipments frommanufacturersto retailers follow the same lop-sided activity.Fourth quarter shipments have steadily grownover the past ten years with 1997 shipmentsrepresenting 36% of the year's total... Thisstrong seasonal demand is only one componentof thetoymakers'challenge.Whilethousandsoftoys are brought to market every year, only asmall fraction of them succeed.Even fewer haveTheauthorwhatittakestolastlongerthanoneortwovears.Charles X. Wang is a PhD Student, School of Management,Classics, such as Mattel's Barbie and HotWheels are examples of products that have stoodSyracuse University, Syracuse, New York, USAthe test of time.As John Handy,vice president ofproduct design at Mattel Inc., stated: "We'reKeywordsjust onegood idea awayfrom going out ofbusiness."Supply chain, Contracts, Channel managementIn such a volatile market featured byAbstractuncertain demand and a short selling season,the retailer has a great chance to face the riskA supply chain is two or more parties linked by a flow ofofeitherexcessstockorlostsales.Forgoods, information, and funds. When one or more partiesexample,department storemarkdownshaveof the supply chain try to optimize their own profitsgrownfrom8percentofstoresalesin1971tosystem performance may be hurt. Supply chain contract is33 per cent in 1995 (Fisher et al., 2000).Thea coordination mechanism that provides incentives to allapparel, electronics,and semiconductorof its members so that the decentralized supply chainindustries are facing the same problem as thebehaves nearly or exactly the same as the integrated one.toy industry.As time-based competitionWe have seen a vast literature on supply chain contractsintensifies,product lifecyclesbecomeshorterrecently. However, little work has been done on theand shorter so that more and more productsrelationships of those supply chain contract models.Inacquire the attributes of fashion or seasonalthis paper, we provide a general framework thatgoods (Petruzzi and Dada, 1999).In order tosynthesizes existing results for a variety of supply chainavoid significantproduct markdowns,thecontract forms.retailer tends to order less from themanufacturer to maximize his own expectedprofit, which is well-known as"doubleElectronic accessmarginalization"(Spengler, 1950),i.e.theThe research register for this journal is available attotal expected profit of the decentralizedhttp://www.emeraldinsight.com/researchregisterssupplychain is lowerthan the integratedsupply chain.Developing strategies toThe current issue and full text archive of this journal isdecrease the risk faced by the retailer isavailable atbecoming more and more critical in a supplyhttp:/www.emeraldinsight.com/1359-8546.htmchain,especially in theglobal marketplacewhere firm-to-firm competition is beingreplaced by supply-chain-to-supply-chainThe author would like to thank two anonymousreferees and Professor Scott Webster for theirhelpful comments and suggestions.This research isSupply Chain Management An Intemational Journalsupported by Brethen Institute of OperationsVolume 7 -Number 5 -2002-pp. 302-310Management at Syracuse University inMCB UP Limited-ISSN1359-8546EmeraldDOI10.1108/13598540210447746Summer1999.302
A general framework of supply chain contract models Charles X. Wang Introduction Consider the following situation faced by the toy industry (Johnson, 1999): Two key features that define many of the challenges in the toy industry for both large and small firms are the seasonal demand and short product life. Toy sales and volumes grow exponentially the last few days before Christmas. November and December alone represent nearly 45% of toy sales. Shipments from manufacturers to retailers follow the same lop-sided activity. Fourth quarter shipments have steadily grown over the past ten years with 1997 shipments representing 36% of the year’s total This strong seasonal demand is only one component of the toy makers’ challenge. While thousands of toys are brought to market every year, only a small fraction of them succeed. Even fewer have what it takes to last longer than one or two years. Classics, such as Mattel’s Barbie and Hot Wheels are examples of products that have stood the test of time. As John Handy, vice president of product design at Mattel Inc., stated: ‘‘We’re just one good idea away from going out of business.’’ In such a volatile market featured by uncertain demand and a short selling season, the retailer has a great chance to face the risk of either excess stock or lost sales. For example, department store markdowns have grown from 8 per cent of store sales in 1971 to 33 per cent in 1995 (Fisher et al., 2000). The apparel, electronics, and semiconductor industries are facing the same problem as the toy industry. As time-based competition intensifies, product lifecycles become shorter and shorter so that more and more products acquire the attributes of fashion or seasonal goods (Petruzzi and Dada, 1999). In order to avoid significant product markdowns, the retailer tends to order less from the manufacturer to maximize his own expected profit, which is well-known as ‘‘double marginalization’’ (Spengler, 1950), i.e. the total expected profit of the decentralized supply chain is lower than the integrated supply chain. Developing strategies to decrease the risk faced by the retailer is becoming more and more critical in a supply chain, especially in the global marketplace where firm-to-firm competition is being replaced by supply-chain-to-supply-chain The author Charles X. Wang is a PhD Student, School of Management, Syracuse University, Syracuse, New York, USA. Keywords Supply chain, Contracts, Channel management Abstract A supply chain is two or more parties linked by a flow of goods, information, and funds. When one or more parties of the supply chain try to optimize their own profits, system performance may be hurt. Supply chain contract is a coordination mechanism that provides incentives to all of its members so that the decentralized supply chain behaves nearly or exactly the same as the integrated one. We have seen a vast literature on supply chain contracts recently. However, little work has been done on the relationships of those supply chain contract models. In this paper, we provide a general framework that synthesizes existing results for a variety of supply chain contract forms. Electronic access The research register for this journal is available at http://www.emeraldinsight.com/researchregisters The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/1359-8546.htm Research papers The author would like to thank two anonymous referees and Professor Scott Webster for their helpful comments and suggestions. This research is supported by Brethen Institute of Operations Management at Syracuse University in Summer 1999. 302 Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . pp. 302±310 # MCB UP Limited . ISSN 1359-8546 DOI 10.1108/13598540210447746
A general framework of supply chain contract modelsSupply Chain Manaqement: An International JournalCharles X. WangVolume7-Number5-2002-302-310competition (Lee et al., 2000). Among thesynthesizes existing results for a variety ofsolutions, supply chain contracts,whichhavesupply chain contract forms.Based on ourdrawnmuchattentionfromtheresearcherstwo-period supply chain contract model, werecently,are used to provide some incentivesalso derive the optimal solution that couldachieve channel coordination and identifyto adjust the relationship of supply chainpartners to coordinate the supply chain, i.e.some important managerial insights.the total profit of the decentralized supplyThis paper is organized as follows. Sectionchain is equal to that achieved under a2 provides a brief literature review of a varietyof supply chain contract forms includingcentralized system.The format of supply chain contracts variesreturnspolicies,QFcontracts,backupin and across industries.Returns policiesagreements,options,andpriceprotections.Inallow the retailer to return a certainSection 3, we providea general two-periodpercentage of his unsold goods to themodel that synthesizes existing results formanufacturerfor apartial rebate credit.Theysupply chain contracts and identifytheoptimal solution that could achieve supplyarecommoninthedistributionofperishablecommodities, such as books,magazines,chaincoordination.InSection4,weshowhow these existing supply chain contractnewspapers,recorded music,computerhardware and software, greetings cards, andmodels are only special forms of our generalpharmaceuticals (Pasternack, 1985;model. Finally, in Section 5, we discuss somePadmanabhan andPng,1995).Quantityimportant managerial insights and draw ourconclusions.flexibility(QF)contracts defineterms underwhich the quantity a retailer ultimately ordersfromthemanufacturermaydeviatefromaprevious planning estimate (Tsay et al.,Literature review1999). QF contracts are very common in theelectronic industry and used by SunSupply chain contracts have been studiedMicrosystems, Nippon Otis, Solectron, IBM,extensivelyineconomics,operationsHP, and Compaq, etc. (Tsay, 1999).Backupmanagement, and marketing scienceagreements have been used byAnne Klein,literature (see Lariviere (1999)and Tsay etFinity,DKNY,Liz Claiborne, and Catco inal. (1999)for recent surveys).While therethe apparel industry (Eppen and Iyer, 1997).are various types of supply chain contractsItstatesthat,ifaretailercommitstoanumberinthereal world,wefocusonagroupofof units for the season, the manufacturer willclosely related supply chain contracthold back afraction of the commitment andprovisions.the retailer can order up to this backupA returns policy specifies that the retailerquantity at the original purchase price aftercan retum a certain percentage, say p, of hisobserving earlydemand.Barnes-Shuster et al.orderquantityQtothemanufactureratthe(1999) study an option contract whichend of the season for a partial rebate credit b.specifies that, in addition to a firm order at aPasternack (1985) is the first to study aregular price, the retailer can also purchasesingle-periodreturnspolicywithstochasticoptions at an option price at the beginning ofdemand for perishable goods.He shows thatthe selling season.After observing earlyboth fulfill full returns with full rebate creditdemand, the retailer can choose to exerciseand no returns are system suboptimal Thethose options at an exercise price.Finallysupply chain could be coordinated by anprice protection has been commonly usedintermediate returns policy, e.g.partialbetween manufacturers and retailers in thereturns with fulfill full rebate credit. Kandelpersonal computerindustry(Leeet al.,2000)(1996)extendsPasternack(1985)toaprice-It states that the manufacturer pays thesensitivestochasticdemandmodelandretailer a credit applying to the retailer'sconcludes thatthe supply chain cannotbeunsold goods when the wholesale price dropscoordinated by returns policies without retailduring the lifecycle (Taylor, 2001).price maintenance (i.e.allowing theWe have seen a vast literature on supplymanufacturer to dictate the retail price).chain contracts recently.However, little workEmmons and Gilbert(1998)studyahas been done on the relationships of thosemultiplicative model of demand uncertaintysupply chain contract models. In this paper,for catalog goods and demonstratethatwe provide a general framework thatuncertainty tends to increase the retail price.303
competition (Lee et al., 2000). Among the solutions, supply chain contracts, which have drawn much attention from the researchers recently, are used to provide some incentives to adjust the relationship of supply chain partners to coordinate the supply chain, i.e. the total profit of the decentralized supply chain is equal to that achieved under a centralized system. The format of supply chain contracts varies in and across industries. Returns policies allow the retailer to return a certain percentage of his unsold goods to the manufacturer for a partial rebate credit. They are common in the distribution of perishable commodities, such as books, magazines, newspapers, recorded music, computer hardware and software, greetings cards, and pharmaceuticals (Pasternack, 1985; Padmanabhan and Png, 1995). Quantity flexibility (QF) contracts define terms under which the quantity a retailer ultimately orders from the manufacturer may deviate from a previous planning estimate (Tsay et al., 1999). QF contracts are very common in the electronic industry and used by Sun Microsystems, Nippon Otis, Solectron, IBM, HP, and Compaq, etc. (Tsay, 1999). Backup agreements have been used by Anne Klein, Finity, DKNY, Liz Claiborne, and Catco in the apparel industry (Eppen and Iyer, 1997). It states that, if a retailer commits to a number of units for the season, the manufacturer will hold back a fraction of the commitment and the retailer can order up to this backup quantity at the original purchase price after observing early demand. Barnes-Shuster et al. (1999) study an option contract which specifies that, in addition to a firm order at a regular price, the retailer can also purchase options at an option price at the beginning of the selling season. After observing early demand, the retailer can choose to exercise those options at an exercise price. Finally, price protection has been commonly used between manufacturers and retailers in the personal computer industry (Lee et al., 2000). It states that the manufacturer pays the retailer a credit applying to the retailer’s unsold goods when the wholesale price drops during the lifecycle (Taylor, 2001). We have seen a vast literature on supply chain contracts recently. However, little work has been done on the relationships of those supply chain contract models. In this paper, we provide a general framework that synthesizes existing results for a variety of supply chain contract forms. Based on our two-period supply chain contract model, we also derive the optimal solution that could achieve channel coordination and identify some important managerial insights. This paper is organized as follows. Section 2 provides a brief literature review of a variety of supply chain contract forms including returns policies, QF contracts, backup agreements, options, and price protections. In Section 3, we provide a general two-period model that synthesizes existing results for supply chain contracts and identify the optimal solution that could achieve supply chain coordination. In Section 4, we show how these existing supply chain contract models are only special forms of our general model. Finally, in Section 5, we discuss some important managerial insights and draw our conclusions. Literature review Supply chain contracts have been studied extensively in economics, operations management, and marketing science literature (see Lariviere (1999) and Tsay et al. (1999) for recent surveys). While there are various types of supply chain contracts in the real world, we focus on a group of closely related supply chain contract provisions. A returns policy specifies that the retailer can return a certain percentage, say », of his order quantity Q to the manufacturer at the end of the season for a partial rebate credit b. Pasternack (1985) is the first to study a single-period returns policy with stochastic demand for perishable goods. He shows that both fulfill full returns with full rebate credit and no returns are system suboptimal. The supply chain could be coordinated by an intermediate returns policy, e.g. partial returns with fulfill full rebate credit. Kandel (1996) extends Pasternack (1985) to a pricesensitive stochastic demand model and concludes that the supply chain cannot be coordinated by returns policies without retail price maintenance (i.e. allowing the manufacturer to dictate the retail price). Emmons and Gilbert (1998) study a multiplicative model of demand uncertainty for catalog goods and demonstrate that uncertainty tends to increase the retail price. 303 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Management: An International JournalCharles X. WangVolume7-Number5-2002-302-310They also show that, under certaincompanycan orderuptothisbackupconditions, a manufacturer can increase his/quantity for the original purchase cost andher profit by offering a returns policy.receive quick delivery but will pay a penaltyWebster and Weng (2000)takethecost p for any of the backup units it does notbuy.Barnes-Shuster et al. (1999) investigateviewpoint of a manufacturer selling a shortlifecycle product to a singleretailerandthe role of options in a supply chain.Thedescribe risk-free returns policies throughretailer makes a firm order q at the beginningwhich, when compared with no returns, theof the selling season at a wholesale price w.retailer's expected profit is increased and theIn addition, he purchases n options at anmanufacturer's profit is at least as large asoption price wo.In the second period, thewhen no returns are allowed. Lee et al.retailer may choose to exercise n (n ≤ m)(2000)analyze a two-period priceprotectionoptions at an exercise price we.Theypolicy in the personal computer industry.illustratehowoptions provideflexibilitytoaThe basic idea of their single-buying-retailer to respond to market changes in theopportunitymodel is that the retailer orderssecond period quickly.Qproducts from themanufacturer at thebeginning of the first period at a wholesaleprice wr.At the beginning of the secondAgeneral framework of supply chainperiod, the wholesale price of the samecontractmodelsproduct drops to wi because of theintroduction of new products.To sharetheWe consider a supply chain composed of arisk of the retailer, the manufacturer willsingle manufacturer and a single retailerpay a rebate credit b to the retailer for allselling short-lifecycleproducts withunsold inventory at the end of the firststochastic customer demand.The sellingperiod. It is similar to Pasternack (1985),season is short and divided into twobut looking at the dynamic optimal pricecontinuous periods. At the beginning of theprotection policy when the product in thefirst period, the retailer orders Q productsmarkets is faced with obsolescence duringfrom themanufacturer forbothperiods andmultipleperiods.cannot make any changes when the seasonUnlike returns policies which focus onbegins.During thefirstperiod, if realizedflexibility in adjusting price,QFcontractsdemand is higher than Q, all sales are lostfocus on flexibility in adjusting orderingand the retailer will incur a goodwill cost gr.quantity.Lariviere (1999)and Tsay (1999)Ifrealizeddemandislowerthan O,theconsider a single-and a multiple-period QFretailer can return up to PiQ to themodel separately.The basic idea of QF ismanufacturer and get a per unit rebate creditthat, when a retailer places an initial order q,bi.Returned goods are salvaged at a value s1.themanufactureragrees to provide uptoTherest of the leftover inventoryywill be(1 + u)g units to the system. At the samecarried over to the second period and thetime the retailer commits to order at least (1retailer will incur a per unit end-of-period-d)q units.After observing the demand for ainventory holding cost hy.At the beginningshort period, the retailer can decide to orderofthe second period, because oftheproductanyquantitybetween (1-d)gand (1+u)gatobsolescence, theretailer has tomark downthe wholesale price w.Both Lariviere (1999)the product at a retail price r2, which is lowerandTsay(1999)showthatQFcanleadtoathan his retail price ri in the first period.much greater profit of the decentralizedDemand in the second period is stillsupply chain than thatachieved without QF.stochastic but correlated to the first period.EppenandIyer(1997)focusonatwo-If realized demand in the second period isperiod backup agreement between a cataloghigher than the available inventory y, allcompanyand manufacturers.A backupsales are lost and the retailer will incur aagreement states that, if the cataloggoodwill cost g2.If realized demand is lowercompany commits to a number of units forthan y, the retailer will incur an end-of-the season, the manufacturer holds back aperiod inventory holding cost h2and salvageconstant fraction p of the commitment Qthe products at a value s2. No returns areand delivers the remaining units (1 - p)Q atallowed in the second period.Thefollowingthe beginning of the selling season. Aftersubsections formally define our two-periodmodel.observing early demand, the catalog304
They also show that, under certain conditions, a manufacturer can increase his/ her profit by offering a returns policy. Webster and Weng (2000) take the viewpoint of a manufacturer selling a short lifecycle product to a single retailer and describe risk-free returns policies through which, when compared with no returns, the retailer’s expected profit is increased and the manufacturer’s profit is at least as large as when no returns are allowed. Lee et al. (2000) analyze a two-period price protection policy in the personal computer industry. The basic idea of their single-buying- opportunity model is that the retailer orders Q products from the manufacturer at the beginning of the first period at a wholesale price w1. At the beginning of the second period, the wholesale price of the same product drops to w1 because of the introduction of new products. To share the risk of the retailer, the manufacturer will pay a rebate credit b to the retailer for all unsold inventory at the end of the first period. It is similar to Pasternack (1985), but looking at the dynamic optimal price protection policy when the product in the markets is faced with obsolescence during multiple periods. Unlike returns policies which focus on flexibility in adjusting price, QF contracts focus on flexibility in adjusting ordering quantity. Lariviere (1999) and Tsay (1999) consider a single- and a multiple-period QF model separately. The basic idea of QF is that, when a retailer places an initial order q, the manufacturer agrees to provide up to (1 + u)q units to the system. At the same time the retailer commits to order at least (1 – d)q units. After observing the demand for a short period, the retailer can decide to order any quantity between (1 – d)q and (1 + u)q at the wholesale price w. Both Lariviere (1999) and Tsay (1999) show that QF can lead to a much greater profit of the decentralized supply chain than that achieved without QF. Eppen and Iyer (1997) focus on a two- period backup agreement between a catalog company and manufacturers. A backup agreement states that, if the catalog company commits to a number of units for the season, the manufacturer holds back a constant fraction » of the commitment Q and delivers the remaining units (1 – »)Q at the beginning of the selling season. After observing early demand, the catalog company can order up to this backup quantity for the original purchase cost and receive quick delivery but will pay a penalty cost p for any of the backup units it does not buy. Barnes-Shuster et al. (1999) investigate the role of options in a supply chain. The retailer makes a firm order q at the beginning of the selling season at a wholesale price w. In addition, he purchases n options at an option price wo . In the second period, the retailer may choose to exercise n (n µ m) options at an exercise price we. They illustrate how options provide flexibility to a retailer to respond to market changes in the second period quickly. A general framework of supply chain contract models We consider a supply chain composed of a single manufacturer and a single retailer selling short-lifecycle products with stochastic customer demand. The selling season is short and divided into two continuous periods. At the beginning of the first period, the retailer orders Q products from the manufacturer for both periods and cannot make any changes when the season begins. During the first period, if realized demand is higher than Q, all sales are lost and the retailer will incur a goodwill cost g1. If realized demand is lower than Q, the retailer can return up to »1Q to the manufacturer and get a per unit rebate credit b1. Returned goods are salvaged at a value s1. The rest of the leftover inventory y will be carried over to the second period and the retailer will incur a per unit end-of-period inventory holding cost h1 . At the beginning of the second period, because of the product obsolescence, the retailer has to mark down the product at a retail price r2, which is lower than his retail price r1 in the first period. Demand in the second period is still stochastic but correlated to the first period. If realized demand in the second period is higher than the available inventory y, all sales are lost and the retailer will incur a goodwill cost g2. If realized demand is lower than y, the retailer will incur an end-of- period inventory holding cost h2 and salvage the products at a value s2. No returns are allowed in the second period. The following subsections formally define our two-period model. 304 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Management: An International JournalCharles X. WangVolume7-Number 5-2002-302-310Notationretailer can makea profit from selling theWe define the following quantities:product. Similarly, we assume thewholesaleprice is higher thanthecmanufacturer's production costproduction cost. The rebate credit isin the first period;lower than the production cost.wmanufacturer's wholesale priceg2S2,andr>S1.Thisin the first period;assumption states that the goodwill costretail price in period i=1,2;4in the second period is less than the firstbimanufacturer's rebatecreditforperiod and the retail price is higher thanthe salvage value in each period.returned goods in the first period;There is no information asymmetry soretailer's total order quantity atQthat information on price, costs, andthe beginning of the first period;demand is commonknowledge.amount left after the end of theJfirst period at the retailerThe timingpercentage of Q that can beThe timing of the events is as follows:pireturned to the manufacturer at(1) The manufacturer moves first as theStackelberg leader offering the retailer athe end of the first period;take-it-or-leave-it contract which specifiesretailer's goodwill cost in periodgia wholesale price w, a rebate credit bi,i= 1,2;and the returns percentage pi for the firsthiretailer's end-of-period inventoryperiod.holding cost in period i= 1,2;(2)In response, theretailer ordersQfromthesalvage value in period i = 1, 2;manufacturer before the beginning of thesiX;first period.non-negative random variable for(3)Production takes placeat thecustomer demand in period l;manufacturer and finished products areprobability density functionfi(x1)sent to the retailer at the beginning of the(PDF)for realized demand xinfirst period.period l;(4) Demand in the first period is realized.Fi(x1)cumulative distribution functionSome of leftover inventories are returned(CDF) for realized demand x1to the manufacturer and salvaged. Othersthat cannot be returned are carried overin period l;to the second period.conditional PDF for demand x2f2(x2|x1)(5) Demand in the second period is realized.in period 2, given x1;Leftover inventories are salvaged at theF2(x2|x1)conditional CDFfordemand x2retailer.in period 2, given xThe integrated supply chainAssumptionsIn the integrated supply chain, theWewill use the following assumptionsmanufacturer acts as his own retailer (i.e.throughout the remainder of the paper:company store). This model will enable us to.Both the manufacturer and the retailerdetermine the optimal policy for the system asare risk-neutral so that maximizinga whole.In this setting,the integrated firmexpected utilities would be equivalent toproduces Q products at a per unit productionmaximizing expected profits.cost c and sells them to the public directly at aWeassumebothmanufacturerandretail price r and r2 in the first and secondretailer have full controls over theperiod respectively.The firm's objective is towholesale price and retail prices in bothchooseanoptimalproductionquantitythatperiods. These prices are exogenous.maximizes his expected profit.r>r2>w>c>b.WeassumetheretailToanalyze the model, we work backwardprice in the second period is lower thanstarting with period 2. At the end of period 1,thefirst period because of the productif the leftover stock is y,the integrated firm'sobsolescence. Retail prices are higherexpected profitII(y)inthe second period isthan the wholesale price so that thegiven by:305
Notation We define the following quantities: c manufacturer’s production cost in the first period w manufacturer’s wholesale price in the first period; ri retail price in period i ˆ 1; 2 b1 manufacturer’s rebate credit for returned goods in the first period; Q retailer’s total order quantity at the beginning of the first period; y amount left after the end of the first period at the retailer; »1 percentage of Q that can be returned to the manufacturer at the end of the first period; gi retailer’s goodwill cost in period i ˆ 1; 2 hi retailer’s end-of-period inventory holding cost in period i ˆ 1; 2 si salvage value in period i ˆ 1; 2 Xi non-negative random variable for customer demand in period 1; f1.x1† probability density function (PDF) for realized demand x1 in period 1; F1.x1† cumulative distribution function (CDF) for realized demand x1 in period 1; f2.x2jx1† conditional PDF for demand x2 in period 2, given x1 F2.x2jx1† conditional CDF for demand x2 in period 2, given x1 Assumptions We will use the following assumptions throughout the remainder of the paper: Both the manufacturer and the retailer are risk-neutral so that maximizing expected utilities would be equivalent to maximizing expected profits. We assume both manufacturer and retailer have full controls over the wholesale price and retail prices in both periods. These prices are exogenous. r1 > r2 > w > c > b1. We assume the retail price in the second period is lower than the first period because of the product obsolescence. Retail prices are higher than the wholesale price so that the retailer can make a profit from selling the product. Similarly, we assume the wholesale price is higher than the production cost. The rebate credit is lower than the production cost. g2 s2, and r1 > s1. This assumption states that the goodwill cost in the second period is less than the first period and the retail price is higher than the salvage value in each period. There is no information asymmetry so that information on price, costs, and demand is common knowledge. The timing The timing of the events is as follows: (1) The manufacturer moves first as the Stackelberg leader offering the retailer a take-it-or-leave-it contract which specifies a wholesale price w, a rebate credit b1, and the returns percentage »1 for the first period. (2) In response, the retailer orders Q from the manufacturer before the beginning of the first period. (3) Production takes place at the manufacturer and finished products are sent to the retailer at the beginning of the first period. (4) Demand in the first period is realized. Some of leftover inventories are returned to the manufacturer and salvaged. Others that cannot be returned are carried over to the second period. (5) Demand in the second period is realized. Leftover inventories are salvaged at the retailer. The integrated supply chain In the integrated supply chain, the manufacturer acts as his own retailer (i.e. company store). This model will enable us to determine the optimal policy for the system as a whole. In this setting, the integrated firm produces Q products at a per unit production cost c and sells them to the public directly at a retail price r1 and r2 in the first and second period respectively. The firm’s objective is to choose an optimal production quantity that maximizes his expected profit. To analyze the model, we work backward starting with period 2. At the end of period 1, if the leftover stock is y, the integrated firm’s expected profit I 2 .y† in the second period is given by: 305 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Management: An International JourmalCharles X. WangVolume7-Number5-2002-302-310Similarly, we work backward starting() =x2r2 - (y - x2)(h2 = s2)with period 2. At the end of period 1, if the(1)leftover stock is y, the retailer's expectedf2(x2|x1)dx2profit IIs() in the second period is given by:Moving back to the first period, the expected() =[r2x2 - (y - x2)(h2 - s2)]profit of the integrated firm is given by:f2(x2|x1)dx2(4)I(Q) = -cQ +[xii +(Q-x)[yr2 - (x2 -y)g2]f2(x2|x1)dx2(2)- (Q-xi)hifi(x1)dx)[Qrn +I(0) - (x1 - Q)gi]i(x1)dx1-Moving back to the first period, the expectedprofit of the retailer is given by:rQrProperty1I (Q) = -cQ, +The integrated supply chain's expected profit[x1r1 +I(Qr - x1) - (O, - x1)hi]function is concavein thedecision variableQ(5)fi(x1)dx1and hence there is a unique optimal solutionQ* that maximizes the integrated supply[Qrr +I(0)chain's expected profitJOProof. We take the first derivative of I(Q)- (x1 - O,)gilfi(x1)dx1with respect to Q and set this amount equal to0. This gives:Property 2dII)(Q)/dQ= n1 + g1 - cThe independent retailer's expected profitfunction is concave in the decision variable Q,- (r - r2 + g1 - g2 + hi)Fi(Q)and hence there is a unique optimal solution(3)0F2(Q - x1)- (r2 + g2 + h2 - s2)Q, that maximizes the retailer's expectedprofit.fi(xi)dx1 = 0.Proof. Similar to Property 1.From Property 2, we can derive that theWe take the second derivative of II(Q) withretailer's optimal order quantity , satisfies:respect to Q. This gives:dlli(Q,)/dQ, = + g1 -wd(Q)/dg =- (1 - r2 + g1 - g2 + hi)Fi(Q.)- (n - r2 + g1 - g2 + h1)fi(Q)(6)- (r2 + g2 + h2 - 52)- (r2 + g2 + h2 - S2)rOrrOF2(Q, - x1)fi(x1)dx1 = 0.f2(Q-x1)fi(x1)dx1 0to maximize his expected profit.306
I 2 .y† ˆ Z y 0 ‰x2r2 ¡ .y ¡ x2†.h2 ¡ s2†Š f2.x2jx1†dx2: .1† Moving back to the first period, the expected profit of the integrated firm is given by: I2.Q† ˆ ¡cQ ‡ Z Q 0 ‰x1r1 ‡ I2.Q ¡ x1† ¡ .Q ¡ x1†h1Šf1.x1†dx1 ‡ Z 1 Q ‰Qr1 ‡ I2.0† ¡ .x1 ¡ Q†g1Šf1.x1†dx1: .2† Property 1 The integrated supply chain’s expected profit function is concave in the decision variable Q and hence there is a unique optimal solution Q* that maximizes the integrated supply chain’s expected profit. Proof. We take the first derivative of I 1 .Q† with respect to Q and set this amount equal to 0. This gives: d I 1 .Q†=dQ ˆ r1 ‡ g1 ¡ c ¡ .r1 ¡ r2 ‡ g1 ¡ g2 ‡ h1†F1.Q† ¡ .r2 ‡ g2 ‡ h2 ¡ s2† Z Q 0 F2.Q ¡ x1† f1.x1†dx1 ˆ 0: .3† We take the second derivative of I 1 .Q† with respect to Q. This gives: d 2 I 1 .Q†=dQ2 ˆ ¡ .r1 ¡ r2 ‡ g1 ¡ g2 ‡ h1†f1.Q† ¡ .r2 ‡ g2 ‡ h2 ¡ s2† Z Q 0 f2.Q ¡ x1†f1.x1†dx1 0: 306 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Manaqement: An International JournalCharles X. WangVolume7-Number5-2002-302-310So dll;(Q*)/dQ = 0 < dll;(Q:)/dQ. NoticeCondition1The manufacturer's returns policy (br pi)that dll,(Q)/dQis strictly decreasing inQ;wesatisfies:get Q < QProperty 3 shows that, without supply(1 - p1)2(r2 + g2 - b - h1)fichain coordination, the independent retailer((1 - p1)8) - (r + g1 - bi)fi(α)will always order less than thetotal supply(9)(1-p1)2chain's optimal quantity.The decentralized-(1 - p1)(r2 + g2 + h2) supply chain's expected profitwill belowerthan an integrated supply chain. Thisf2(1 - p1), - x1)fi(x1)dx1 < 0.phenomenon iswell-known as“doublemarginalization"(Spengler, 1950).In theProperty4next subsection, we will provide a supplyUnderCondition 1,theexpectedprofitchain contract model where thefunction of the independent retailer with amanufacturerprovidesareturnspolicytoreturnspolicy(bi,pr)isconcaveintheencourage the retailer to order more so thatdecision variable O, and hence there is athe supply chain is coordinated.unique optimal solution , that maximizeshis expected profit.Independent retailer with returnsProof. We take the first derivative of f(Q)To encourage the retailer to order more, thewith respect to Q, and set this amount equalmanufacturer offers a returns policy thatto 0. This gives:specifies that the retailer can return adfr(α)/do,= ri +g1 -w+ (1 -p1)percentage ofhis initial orders, say pi, to get aper unit rebate credit b, from the(r2 +g2 - bi - hi)Fi(1 - p1)O,)manufacturer at the end of the first period. In- (rni + g1 - b1)Fi(α.)this way, the manufacturer shares the risk(10)- (r2 + g2 + h2)faced by the retailer.(1-p1)0,To analyze themodel, again, we start fromF2((1 - p1)Qr - x1)(1 - p1)period 2. At the end of period 1, if the leftoverstock is y, the retailer's expected profit frs(y)fi(x1)dx1 = 0.in the second period is given by:After taking the second derivative of f (Q)() =with respect to Qr, this gives:dr()/-(1-p1)2(7)[r2x2 - (y - x2)h2]f2(x2|x1)dx2(r2 + g2 - b1 -hi)fi(1 - p1))[yr2 — (x2 - J)g2]f2(x2|x1)dx2- (n1 + g1 - b1)fi()(1-p)0,Moving back to the first period, the expected- (1 - p1)(r2 + g2 + h2)profit to the retailer when he orders , isgiven by:f2(1 - p1)Q, - x1)fi(x1)dx1.R(O)= -wOAccording to Condition 1, d?fr (.)/d2 < 0.(1-pi)oThis leads to the Property.[x+p1orbGiven the integrated supply chain's optimal- (1 - p1)Q, - x1)hiproduction quantity Q* and the independent+R(1 - p1), -x1)Ifi(x1)dx1retailer's optimal order quantity O,, the(8)manufacturer's objective is to provide thero.[r1x]retailer with a returns policy (bi, pi) that(1-p1)0satisfies Q, = Q* so that the supply chain is+ (@, - x1)b1 + frs(0)fi(x1)dx1 +coordinated.ThefollowingPropertyformallydefines the optimal returns policy.[Or1 - (x1 - Q,)g1 +I(0)f(x1)dx1.Property 5Under Condition 1, a returns policy (bi,pi)Before going to Property 4, we define thefollowing condition that will ensure anthat satisfies the following equation couldinterior optimal solution for this model.coordinate the supply chain, i.e. Q, =- Q*:307
So d I 1 .Q¤†=dQ ˆ 0 < d I 1 .Q¤ r†=dQ. Notice that d I 1 .Q†=dQ is strictly decreasing in Q; we get Q¤ r < Q¤ : Property 3 shows that, without supply chain coordination, the independent retailer will always order less than the total supply chain’s optimal quantity. The decentralized supply chain’s expected profit will be lower than an integrated supply chain. This phenomenon is well-known as ‘‘double marginalization’’ (Spengler, 1950). In the next subsection, we will provide a supply chain contract model where the manufacturer provides a returns policy to encourage the retailer to order more so that the supply chain is coordinated. Independent retailer with returns To encourage the retailer to order more, the manufacturer offers a returns policy that specifies that the retailer can return a percentage of his initial orders, say »1, to get a per unit rebate credit b1 from the manufacturer at the end of the first period. In this way, the manufacturer shares the risk faced by the retailer. To analyze the model, again, we start from period 2. At the end of period 1, if the leftover stock is y, the retailer’s expected profit r2 .y† in the second period is given by: r2 .y† ˆ Z y 0 ‰r2x2 ¡ .y ¡ x2†h2Šf2.x2jx1†dx2 ‡ Z 1 y ‰yr2 ¡ .x2 ¡ y†g2Šf2.x2jx1†dx2: .7† Moving back to the first period, the expected profit to the retailer when he orders Qr is given by: R 1 .Qr† ˆ ¡wQr ‡ Z .1¡»1†Qr 0 ‰x1r1 ‡ »1Qrb1 ¡ .1 ¡ »1†Qr ¡ x1†h1 ‡ R 2 .1 ¡ »1†Qr ¡ x1†Šf1.x1†dx1 ‡ Z Qr .1¡»1†Qr ‰r1x1 ‡ .Qr ¡ x1†b1 ‡ r2 .0†Šf1.x1†dx1 ‡ Z 1 Qr ‰Qrr1 ¡ .x1 ¡ Qr†g1 ‡ R 2 .0†Šf1.x1†dx1: .8† Before going to Property 4, we define the following condition that will ensure an interior optimal solution for this model. Condition 1 The manufacturer’s returns policy (b1, »1) satisfies: .1 ¡ »1†2 .r2 ‡ g2 ¡ b1 ¡ h1†f1 .1 ¡ »1†Qr† ¡ .r1 ‡ g1 ¡ b1†f1.Qr† ¡ .1 ¡ »1†2 .r2 ‡ g2 ‡ h2† Z .1¡»1 †Qr 0 f2.1 ¡ »1†Qr ¡ x1†f1.x1†dx1 < 0: .9† Property 4 Under Condition 1, the expected profit function of the independent retailer with a returns policy (b1, »1) is concave in the decision variable Qr and hence there is a unique optimal solution Q¤ r that maximizes his expected profit. Proof. We take the first derivative of r1 .Qr† with respect to Qr and set this amount equal to 0. This gives: d r1 .Qr†=dQr ˆ r1 ‡ g1 ¡ w ‡ .1 ¡ »1† .r2 ‡ g2 ¡ b1 ¡ h1†F1.1 ¡ »1†Qr† ¡ .r1 ‡ g1 ¡ b1†F1.Qr† ¡ .r2 ‡ g2 ‡ h2† .1 ¡ »1† Z .1¡»1†Qr 0 F2.1 ¡ »1†Qr ¡ x1† f1.x1†dx1 ˆ 0: .10† After taking the second derivative of r1 .Qr† with respect to Qr, this gives: d 2 r1 .Qr†=dQ 2 r ¡ .1 ¡ »1†2 .r2 ‡ g2 ¡ b1 ¡ h1†f1.1 ¡ »1†Qr† ¡ .r1 ‡ g1 ¡ b1†f1.Qr† ¡ .1 ¡ »1†2 .r2 ‡ g2 ‡ h2† Z .1¡»1 †Qr 0 f2.1 ¡ »1†Qr ¡ x1†f1.x1†dx1: According to Condition 1, d 2 r1 .Qr†=dQ2 r < 0. This leads to the Property. Given the integrated supply chain’s optimal production quantity Q¤ and the independent retailer’s optimal order quantity Q¤ r , the manufacturer’s objective is to provide the retailer with a returns policy (b1, »1) that satisfies Q¤ r ˆ Q¤ so that the supply chain is coordinated. The following Property formally defines the optimal returns policy. Property 5 Under Condition 1, a returns policy (b ¤1 ; » ¤1 ) that satisfies the following equation could coordinate the supply chain, i.e. Q¤ r ˆ Q¤ : 307 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Management: An International JournalCharles X. WangVolume 7-Number 5-2002-302-310Returns policies suchas Pasternack(1985)w - c - (r2 - 2ri - 2g1 + g2 - b, - h1)are single-period newsvendor models. In ourrQFi(Q) - (r2 + g2 + h2)F2(Q- xi)model, if we allow backorders at thebeginning of the second period and assumefi(xi)dx1retailer prices in both periods are constant,= (1 - pi)(r2 + g2 - bt - hi)(11)i.e. ry = r2, then our model reduces to theFi((1 - pi)Q)returns policy.(1-pi)QThe two-period single-order-opportunity+ (r2 + g2 + h2)(1 - pi)price protection contract such as Lee et al.(2000)assumes demands in both periods areF2((1 - pi)Q-x1)fi (x1)dx1.independent and the return percentage is 100per cent, whereas, in our model, demand inProof. If Q* =Q,, Equations (8) and (9)both periods is correlated and we allow anyshould coincide. This leads to Equation (11).percentage of returns.If we the correlationcoefficient of the demand in both periods bezero and the returns percentage pi = 100 perRelationshipwithmodelsfromthecent, then our model reduces to a priceliteratureprotection contract.Thetwo-period backupagreement assumesIn this section, we will show how returnsdemands in both periods are correlated andpolicies,QF,backup agreements,options,retail prices in both periods are constant. Itand the single-order-opportunity pricestates that, if the retailer orders Q from theprotection contract are only special forms ofmanufacturer at the beginning of the firstour general model.The correspondencesperiod, he/she can choose to order less thanbetween our general model and these supplythe backup quantity pQ at the beginning ofchain contracts are summarized in TableIthe second period after observing earlyWe begin our analysis with identifying somedemand, butwill pay a penalty cost p foranycommon features among these supply chainof the backup units he/she does not buy.It iscontract models and ourgeneral model.Theequivalent that the retailer orders Q from thesupply chain studied in all these models ismanufactureratthebeginning of thefirstcomposed of a single retailer and a singleperiod and returns up to pQ to themanufacturer selling short-lifecycle productsmanufacturer at a rebate credit w-p. In ourwith stochastic demand.The wholesale price,model,ifwelet ri= r2,bi=w-p,andpr=p,retail price, production cost, inventorythen it reduces to the backup agreement.holding cost, goodwill cost, and salvage valueOption contract is a two-period model likeare exogenous.The manufacturer acts as theours.Itassumes demands inbothperiods aresupply chain leader and offers the retailer acorrelated and retail prices in both periods aretake-it-or-leave-it contract. These contractsconstant It states that the retailer orders afirm order g at the regular wholesale price andimplicitly orexplicitlyallowtheretailertooptions m at an option pricefrom thereturn certain percentage of his initial ordermanufacturer. In the second period, thequantity to the manufacturer. The mainretailermay choose to exercise n(n< m)differences among these supply chainoptions at an exercise price weThen it iscontracts are:equivalent that the retailer's orders totalreturns policies are single-period modelsQ= q + m from the manufacturer at thewhereas others are two-period models;beginning of the first period and could returndemands in returns policies and priceuptop=m/(q+m)ofQtothemanufacturerprotection contracts are independentwith a rebate credit we. In our model, if we letwhereas others are correlated; andri=r2,b=wesandpi=m/(q+m),thenourin priceprotection and our model, wemodelreducestotheoptioncontractallow different retailer prices in periodsA two-period QF model assumes demandswhereas others assume constant retailerin the two periods are correlated and retailprices in periods.prices in both periods are constant. If theWe will show how our model is generalretailer orders q from the manufacturer at theenough to synthesize all these supply chainbeginning of thefirst period, he can choosetocontract models.buy any amount between (1 -d)q and (1 + u)q308
w ¡ c ¡ .r2 ¡ 2r1 ¡ 2g1 ‡ g2 ¡ b ¤1 ¡ h1† F1.Q† ¡ .r2 ‡ g2 ‡ h2† Z Q 0 F2.Q ¡ x1† f1.x1†dx1 ¡ .1 ¡ » ¤1 †.r2 ‡ g2 ¡ b ¤1 ¡ h1† F1.1 ¡ » ¤1 †Q† ‡ .r2 ‡ g2 ‡ h2†.1 ¡ » ¤1 † Z .1¡» ¤1 †Q 0 F2.1 ¡ » ¤1 †Q ¡ x1†f1.x1†dx1: .11† Proof. If Q¤ ˆ Q¤ r , Equations (8) and (9) should coincide. This leads to Equation (11). Relationship with models from the literature In this section, we will show how returns policies, QF, backup agreements, options, and the single-order-opportunity price protection contract are only special forms of our general model. The correspondences between our general model and these supply chain contracts are summarized in Table I. We begin our analysis with identifying some common features among these supply chain contract models and our general model. The supply chain studied in all these models is composed of a single retailer and a single manufacturer selling short-lifecycle products with stochastic demand. The wholesale price, retail price, production cost, inventory holding cost, goodwill cost, and salvage value are exogenous. The manufacturer acts as the supply chain leader and offers the retailer a take-it-or-leave-it contract. These contracts implicitly or explicitly allow the retailer to return certain percentage of his initial order quantity to the manufacturer. The main differences among these supply chain contracts are: returns policies are single-period models whereas others are two-period models; demands in returns policies and price protection contracts are independent whereas others are correlated; and in price protection and our model, we allow different retailer prices in periods whereas others assume constant retailer prices in periods. We will show how our model is general enough to synthesize all these supply chain contract models. Returns policies such as Pasternack (1985) are single-period newsvendor models. In our model, if we allow backorders at the beginning of the second period and assume retailer prices in both periods are constant, i.e. r1 = r2, then our model reduces to the returns policy. The two-period single-order-opportunity price protection contract such as Lee et al. (2000) assumes demands in both periods are independent and the return percentage is 100 per cent, whereas, in our model, demand in both periods is correlated and we allow any percentage of returns. If we the correlation coefficient of the demand in both periods be zero and the returns percentage »1 = 100 per cent, then our model reduces to a price protection contract. The two-period backup agreement assumes demands in both periods are correlated and retail prices in both periods are constant. It states that, if the retailer orders Q from the manufacturer at the beginning of the first period, he/she can choose to order less than the backup quantity »Q at the beginning of the second period after observing early demand, but will pay a penalty cost p for any of the backup units he/she does not buy. It is equivalent that the retailer orders Q from the manufacturer at the beginning of the first period and returns up to »Q to the manufacturer at a rebate credit w – p. In our model, if we let r1 = r2, b1 = w – p, and »1 = », then it reduces to the backup agreement. Option contract is a two-period model like ours. It assumes demands in both periods are correlated and retail prices in both periods are constant. It states that the retailer orders a firm order q at the regular wholesale price and options m at an option price from the manufacturer. In the second period, the retailer may choose to exercise n.n µ m† options at an exercise price we. Then it is equivalent that the retailer’s orders total Q = q + m from the manufacturer at the beginning of the first period and could return up to » = m/(q + m) of Q to the manufacturer with a rebate credit we. In our model, if we let r1 = r2, b1 = we, and »1 = m/(q + m), then our model reduces to the option contract. A two-period QF model assumes demands in the two periods are correlated and retail prices in both periods are constant. If the retailer orders q from the manufacturer at the beginning of the first period, he can choose to buy any amount between (1 – d)q and (1 + u)q 308 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
A general framework of supply chain contract modelsSupply Chain Management: An International JournalCharles X. WangVolume7-Number 5-2002-302-310TableIRelationshipbetweenthegeneralmodelandothersupplychaincontractsRetailRetailOrderRebateprice inprice inDemands inModelcreditquantityReturns percentageperiod 1period 2both periodsQbiGeneral modelr12CorrelatedP1QbiReturns PolicyP1[1[2 = riIndependentQFQ= (1 + u)q p = (u + d)/(1 + u)bi = w.Correlatedr1[2 = 11QCorrelatedBackupagreementbi=w-pr1p112=1OptionsQ=q+mP1 = m(q + m)b, = We11[2 = [iCorrelatedQb,Priceprotection512IndependentP1markdowns.Consequently,adynamicpricinglater.It is equivalent thattheretailer commitstobuyQ=g(l+u)atthebeginning of thepolicy which allows the retail price to changefirst period, and could return up to (u+ d)qfromtimetotimemaybehavemuchbetteritems to the manufacturer with a rebate creditthan a static retail price (see Gallego and vanw.Inourmodel, ifweletry=r2,b,=w,andRyzin (1994);Bitran and Mondscheinpi= (u + d)/(1 + u), then our model reduces(1997);ZhaoandZheng(2000)forrecenttotheQFcontract.discussions on dynamicpricing).In addition,we have overlooked competition, eitheramong multiple retailers, or among multipleDiscussion and conclusionmanufacturers. That is another possiblefuture research area.Wehave investigated different supply chaincontract models in the literature.Thelimitation of the single-period returns policy isReferencesthat, even if the retailer has observed themarket signal at the very beginning of theBarnes-Shuster, D., Bassok, Y. and Anupindi, R. (1999),selling season and wants to make some"Coordination and flexibility in supply contractsadjustments of his/her initial order quantitywith options", University of Chicago working paper,Chicago, IL.he/she cannot do that under the single-periodBitran, G.R. and Mondschein, S.V. (1997), "Periodicreturns policy.Price protection extends thepricing of seasonal products in retailing,single-period returns policy to a multi-periodManagement Science, Vol. 43, pp. 64-79.setting, but it neglects that demands inEmmons, H. and Gilbert, S.M. (1998), "Note. The role ofmultiple periods may be correlated. Inreturns policies in pricing and inventory decisionsfor catalogue goods", Management Science,addition,manufacturerssometimesmaynotVol. 44, pp. 276-83.have incentives to offer a generous full returnsEppen, G.D. and lyer, A.V. (1997),"Backup agreements inpolicy to theretailer.The QF, backupfashion buying - the value of upstream flexibility',.agreement and option models focus on theManagement Science, Vol. 43, pp. 1469-84.flexibility of adjusting the order quantityFisher, M.L., Raman, A. and McClelland, A.S. (2000),They all assume retail pricedoes not change"Rocket science retailing is almost here - are youin the selling season. This is a very restrictiveready?", Harvard Business Review, July-August,assumption in the real world, especially inpp.115-24.Gallego, G. and van Ryzin, G. (1994), "Optimal dynamicretailingindustrieswherepricediscountsarepricing of inventories with stochastic demand oververy common.Our model overcomes thefinite horizons, Management Science, Vol. 40,limitations of those supply chain contractspp.999-1020.and extends them to a more general andJohnson, M.E. (1999),"Lessons in managing demand fromrealistic setting.It is very flexible for managersthe toy industry", Discount Merchandiser, February.to make decisions under different scenarios.Kandel, E. (1996),"The right to retum, Journal of Lawand Economics, Vol. 39, pp. 329-56.In our model, we assume the retail price inLariviere, M.A. (199), "Supply chain contracting andeach period is fixed and exogenous.Ifcoordination with stochastic demand", in Tayur, S.,demand is price-sensitive and stochastic, thenGaneshan, R. and Magazine, M. (Eds), Quantitativea time-invariant fixed price may not be in theModels for Supply Chain Management, Kluwerretailer's interest, especially in a volatileAcademic Publishers, Boston, MA, pp. 233-68.market where the retailer often facesLee, H.L, Padmanabhan, V., Taylor, T.A. and Whang, S.temporary promotions or significant(2000),"Price protection in the personal computer309
later. It is equivalent that the retailer commits to buy Q = q(1 + u) at the beginning of the first period, and could return up to (u + d)q items to the manufacturer with a rebate credit w. In our model, if we let r1 = r2, b1 = w, and »1 = (u + d)/(1 + u), then our model reduces to the QF contract. Discussion and conclusion We have investigated different supply chain contract models in the literature. The limitation of the single-period returns policy is that, even if the retailer has observed the market signal at the very beginning of the selling season and wants to make some adjustments of his/her initial order quantity, he/she cannot do that under the single-period returns policy. Price protection extends the single-period returns policy to a multi-period setting, but it neglects that demands in multiple periods may be correlated. In addition, manufacturers sometimes may not have incentives to offer a generous full returns policy to the retailer. The QF, backup agreement and option models focus on the flexibility of adjusting the order quantity. They all assume retail price does not change in the selling season. This is a very restrictive assumption in the real world, especially in retailing industries where price discounts are very common. Our model overcomes the limitations of those supply chain contracts and extends them to a more general and realistic setting. It is very flexible for managers to make decisions under different scenarios. In our model, we assume the retail price in each period is fixed and exogenous. If demand is price-sensitive and stochastic, then a time-invariant fixed price may not be in the retailer’s interest, especially in a volatile market where the retailer often faces temporary promotions or significant markdowns. Consequently, a dynamic pricing policy which allows the retail price to change from time to time may behave much better than a static retail price (see Gallego and van Ryzin (1994); Bitran and Mondschein (1997); Zhao and Zheng (2000) for recent discussions on dynamic pricing). In addition, we have overlooked competition, either among multiple retailers, or among multiple manufacturers. That is another possible future research area. References Barnes-Shuster, D., Bassok, Y. and Anupindi, R. (1999), ``Coordination and flexibility in supply contracts with options’’, University of Chicago working paper, Chicago, IL. Bitran, G.R. and Mondschein, S.V. (1997), ``Periodic pricing of seasonal products in retailing’’, Management Science, Vol. 43, pp. 64-79. Emmons, H. and Gilbert, S.M. (1998), ``Note. The role of returns policies in pricing and inventory decisions for catalogue goods’’, Management Science, Vol. 44, pp. 276-83. Eppen, G.D. and Iyer, A.V. (1997), ``Backup agreements in fashion buying ± the value of upstream flexibility’’, Management Science, Vol. 43, pp. 1469-84. Fisher, M.L., Raman, A. and McClelland, A.S. (2000), ``Rocket science retailing is almost here ± are you ready?’’, Harvard Business Review, July-August, pp. 115-24. Gallego, G. and van Ryzin, G. (1994), ``Optimal dynamic pricing of inventories with stochastic demand over finite horizons’’, Management Science, Vol. 40, pp. 999-1020. Johnson, M.E. (1999), ``Lessons in managing demand from the toy industry’’, Discount Merchandiser, February. Kandel, E. (1996), ``The right to return’’, Journal of Law and Economics, Vol. 39, pp. 329-56. Lariviere, M.A. (1999), ``Supply chain contracting and coordination with stochastic demand’’, in Tayur, S., Ganeshan, R. and Magazine, M. (Eds), Quantitative Models for Supply Chain Management, Kluwer Academic Publishers, Boston, MA, pp. 233-68. Lee, H.L., Padmanabhan, V., Taylor, T.A. and Whang, S. (2000), ``Price protection in the personal computer Table I Relationship between the general model and other supply chain contracts Model Order quantity Returns percentage Rebate credit Retail price in period 1 Retail price in period 2 Demands in both periods General model Q »1 b1 r1 r2 Correlated Returns Policy Q »1 b1 r1 r2 = r1 Independent QF Q = (1 + u)q »1 = (u + d)/(1 + u) b1 = w r1 r2 = r1 Correlated Backup agreement Q »1 b1 = w ± p r1 r2 = r1 Correlated Options Q = q + m »1 = m/(q + m) b1 = we r1 r2 = r1 Correlated Price protection Q »1 b1 r1 r2 Independent 309 A general framework of supply chain contract models Charles X. Wang Supply Chain Management: An International Journal Volume 7 . Number 5 . 2002 . 302±310
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