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2013 Coordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition Jennifer K. Ryan Rensselaer Polytechnic Institute, [email protected]
Daewon Sun University of Notre Dame, [email protected]
Xuying Zhao University of Notre Dame, [email protected]
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Ryan, Jennifer K.; Sun, Daewon; and Zhao, Xuying, "Coordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition" (2013). Supply Chain Management and Analytics Publications. 5. https://digitalcommons.unl.edu/supplychain/5
This Article is brought to you for free and open access by the Business, College of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Supply Chain Management and Analytics Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 60, NO. 2, MAY 2013 247 Coordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition Jennifer K. Ryan, Daewon Sun, and Xuying Zhao
Abstract—We consider a dual channel supply chain in which a product selection, and enabling the manufacturer to reach a manufacturer sells a single product to end-users through both a wider segment of customers and to engage in price discrimina- traditional retail channel and a manufacturer-owned direct online tion. Of course, adding an online channel also has a number of channel. We adopt a commonly used linear demand substitution model in which the mean demand in each channel is a function of potential disadvantages, including the introduction of competi- the prices in each channel. We model each channel as a newsvendor tion into the system, which may lead to lower prices and po- problem, with price and order quantity as decision variables. In ad- tentially reduced profits for both channels [3]. Understandably, dition, the manufacturer must choose the wholesale price to charge retailers often view manufacturer-owned direct online channels to the independent retailer. We analyze the optimal decisions for as a competitive threat [2], [4]. each channel and prove the existence of a unique equilibrium for the system. We compare this equilibrium solution to the solution While there has been significant previous literature weigh- for an integrated system, in which the manufacturer owns both the ing these advantages and disadvantages to consider the question online store and the retailer. To enable supply chain coordination, of whether or not it is beneficial for a manufacturer to add a we propose two contract schemes: a modified revenue-sharing con- direct online channel, as well as assessing the impact of the tract and gain/loss sharing contract. We show that, in cases where dual-channel approach on the retailer, little of this previous the retail channel has a larger market than the online channel, such contracts enable the manufacturer to maintain price discrimina- literature addresses the obvious next questions: given that the tion, selling the products in different channels at different prices. manufacturer has chosen to take a dual-channel approach to Finally, we perform a comprehensive numerical study to consider distribute his product, how can the system be designed in order the impact of the model parameters on the equilibrium and to to achieve supply-chain coordination? What kinds of mecha- demonstrate the performance of the proposed coordination con- nisms can be designed to reduce or eliminate channel conflict? tracts. We conclude that coordination is most critical for products which are highly price sensitive and for systems in which the online Addressing these questions is the primary focus of this paper. and traditional retail channels are not viewed as close substitutes. Thus, we focus our analysis on systems in which there already exist dual channels of distribution, a traditional retail channel Index Terms—Competition, coordination, eBusiness, game theory, newsvendor problem with pricing, online direct channel. and a manufacturer-owned direct online channel, e.g., HP, Dell, Nike, and Apple. Because we consider a single period setting, our model is particularly appropriate for apparel, publishing, I. INTRODUCTION AND MOTIVATION and electronics supply chains. As noted in [2] and [5], ap- HIS paper considers competition and coordination in a parel manufacturers such as Polo Ralph Lauren, DKNY,and Liz T retail supply chain with dual channels of distribution. A Claiborne distribute their products through both manufacturer- manufacturer distributes his products through both a traditional owned channels (outlet stores and, more recently, online stores) (independent) retail channel, e.g., a department store, as well as as well as through major department store chains, such as Macy’s through a manufacturer-owned direct online channel. The past and Kohl’s. two decades have seen rapid growth in online channels, for a In this paper, we model the horizontal price competition be- variety of reasons, including the development of the internet and tween the manufacturer-owned direct channel and the traditional information technology and the growth of third-party logistics retailer, and the vertical competition between the manufacturer providers [1], [2]. Adding a direct online channel has a num- and the retailer (e.g., [6]). We seek to understand how the equi- ber of advantages, such as increasing control over pricing and librium behavior of this supply chain will depend on a number of problem parameters. We study the impact of price compe- tition on the profits of each firm and we investigate methods for achieving supply-chain coordination. As detailed in the next Manuscript received September 21, 2011; revised April 24, 2012; accepted section, we believe we are the first to consider the problem of June 21, 2012. Date of publication August 14, 2012; date of current version supply-chain coordination for a dual-channel supply chain in April 13, 2013. Review of this manuscript was arranged by Department Editor S. (Sri) Talluri. which the direct and retail channels compete on price. We do J. K. Ryan is with the Rensselaer Polytechnic Institute, Troy, NY 12180 USA so in a setting in which demand is uncertain and in which both (e-mail: [email protected]). channels must make both price and quantity decisions. D. Sun and X. Zhao are with the University of Notre Dame, Notre Dame, IN 46556 USA (e-mail: [email protected]; [email protected]). Specifically, we consider a dual-channel supply chain in This paper has supplementary downloadable material available at which demand in each channel is a random variable whose http://ieeexplore.ieee.org. expected value is a function of the prices charged in each Digital Object Identifier 10.1109/TEM.2012.2207903
0018-9391/$31.00 © 2012 IEEE 248 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 60, NO. 2, MAY 2013 channel. Thus, the channels compete on price. In addition, de- and the locations compete on price (e.g., [13] and [14]), or on mand in each channel will depend on customers’ preferences both price and inventory (e.g., [9] and [15]). regarding purchasing online versus in a traditional retail setting. For example, some customers may prefer the convenience and A. Competition Between Direct and Retail Channels lower search cost associated with the online channel, while other We next review the literature on dual-channel supply chains customers may prefer the ability to immediately obtain the prod- in which the manufacturer sells directly to the end-users, either uct through the retail channel. To reflect this, we adopt a com- through online sales or through a manufacturer-owned store, monly used linear demand substitution model (e.g., [7]Ð[9]). as well as through an independent retailer. Unless specifically Given the uncertainty in demand, each channel’s decision prob- mentioned (e.g., [2] and [3]), none of these papers considers lem can be formulated as a newsvendor problem in which both supply-chain coordination, the primary focus of this paper. The price and order quantity are decision variables. In addition, the most relevant papers are those that consider dual channels that manufacturer sets the wholesale price. compete on price; most of these, however, do not consider Our equilibrium analysis is composed of multiple steps. First, production/order quantity decisions. For example, Dumrongsiri for a given wholesale price, we characterize the Nash equilib- et al. [16] assume that the manufacturer fills direct sales demand rium decisions for the system, i.e., we determine the equilibrium on a make-to-order basis and must always fill the retailer’s order. price and quantity decisions for each channel and, under certain Thus, the manufacturer’s production quantity is not a decision conditions, prove the existence of a unique equilibrium for the variable. Chiang et al. [1] assume the market share for each system. Next, we formulate a Stackelberg game to consider the channel is a deterministic function of the prices and thus there manufacturer’s choice of the wholesale price. We then study the is no quantity decision. Cattani et al. [4] also consider a dual- equilibrium behavior of the system as a function of the problem channel model in which the market share is deterministic. Like parameters. We also compare this equilibrium solution to the us, they use a Stackelberg game model with the manufacturer as solution for an integrated system, in which the manufacturer leader and retailer as follower. Bell et al. [17] consider the im- owns both the direct channel and the retailer. Given the solution pact of the introduction of a manufacturer-owned channel on the to the integrated system, we propose a modified revenue-sharing pricing strategies of the existing retailers under the assumption contract, in which the manufacturer imposes a minimum retail that demand is a deterministic function of prices and marketing price on the retailer, to enable supply-chain coordination. effort. In cases where the retail channel has a larger market than The aforementioned papers, as well as this paper, all take re- the online channel, such a contract enables the manufacturer to tail price as a decision variable, and thus, the channels compete maintain a minimum price differential between the retailer and on price. Other research on manufacturerÐretailer competition the online store, which helps to achieve price discrimination. In in dual-channel supply chains takes price as fixed. Here, the addition, we show that a gain/loss (GL) sharing contract can be locations may compete on inventory or on other factors such used to coordinate the system. Finally, through a comprehensive as sales effort. The authors in [3] and [18] seek to coordinate a numerical study, we consider how the equilibrium varies with system in which the channels compete only on inventory. The the key model parameters and demonstrate that the proposed co- authors in [2] and [19] consider a manufacturer who sells his ordination contracts can improve the system’s profit by 12.44%, product through one of three systems: retailer-only, direct sales- on average, for 1080 problems tested. only, or a system with both retail and direct sales. Tsay and The main contribution of this paper is the development of co- Agrawal [2] consider the impact of sales effort, while Hender- ordination schemes for a dual-channel system under price com- shott and Zhang [19] consider the impact of search costs. Tsay petition and demand uncertainty. As noted in the next section, and Agrawal [2] use their model to study channel coordination while several authors have considered the problem of competi- mechanisms, including a wholesale pricing scheme and two tion between online and traditional retail channels, to the best referral schemes. of our knowledge, none have considered coordination when the channels compete on price. In addition, we introduce a new mod- B. Supply-Chain Coordination ification to the classic revenue-sharing contract, which imposes a minimum retail price. In a single-channel supply chain, with one manufacturer and one retailer, operating under a wholesale price contract, it is known that the retailer will order less than the system optimal quantity. When demand is not dependent on retail price, several ITERATURE REVIEW II. L contract types have been shown to coordinate the supply chain We next review the literature on competition in supply chains and to arbitrarily divide its profit: buy back [20], revenue shar- with multiple channels of distribution. While we focus on com- ing [21], quantity flexibility [22], [23], sales rebate [24], [25], petition between a manufacturer-owned direct channel and an and quantity discount [26]. With price-dependent demand, a key independent retailer, our research has some similarities to the question is whether contracts that coordinate the order quantity literature on competition in a single supplier, n-retailer sup- also coordinate the pricing decision. It is known that buy back, ply chain. While much of this literature considers retailers who quantity flexibility, and sales-rebate contracts do not coordi- compete only on inventory (e.g., [10]Ð[12]), the most relevant nate in this setting, while revenue sharing and quantity discount papers for our purpose are those in which demand is stochastic contracts achieve coordination under certain conditions [27]. RYAN et al.: COORDINATING A SUPPLY CHAIN WITH A MANUFACTURER-OWNED ONLINE CHANNEL 249
A second segment of this literature considers coordination Since our goal is to investigate the impact of manufacturer- with multiple retailers. Research in this area includes a buyback owned online stores in a competitive market environment, our contract to coordinate newsvendors who compete on both price demand model must adequately reflect the substitutability of the and inventory [9], a wholesale price contract to coordinate retail- two channels. Thus, we adopt a typical linear demand substi- ers who compete only on inventory [28], a revenue-sharing con- tution model. If we let DR (pR ,pO ) (DO (pR ,pO )) denote the tract to coordinate retailers who compete on quantity [21], and total market demand seen by the retailer (online store) given the coordinating retailers who compete on price [14]. Cachon [29] prices charged by the retailer pR and the online store pO ,we provides a review of this literature. can write One of the coordination contracts considered in this paper is − · · the revenue-sharing contract. Numerous authors have consid- DR (pR ,pO )=δR αR pR + βR pO (1) ered this type of contract (e.g., [30]Ð[32]). We also consider a DO (pR ,pO )=δO − αO · pO + βO · pR . (2) GL sharing contract, which is commonly observed in practice, although there are very few papers studying contracts of this The parameters αi and βi , i ∈{R, O}, represent the own-price form (e.g., [33]Ð[35]). In some industries, GL sharing contracts and cross-price sensitivities of demand. Generally, one would are referred to as profit-sharing contracts. Weinstein [36] ex- expect the retail demand to be more sensitive to the retail price amines profit-sharing contracts in the motion picture industry. than to the online price. Similarly, the online demand would be In the supply-chain literature, Wang and Webster [5] investi- more sensitive to the online price than to the retail price. This gate the GL sharing contract in a decentralized supply chain would imply αR >βR and αO >βO .Also,δi represents the including one manufacturer and one loss-averse retailer. They base market size and captures the customers’ base utility gained show that such a contract can coordinate the supply chain under from purchasing through channel i. The parameter βi captures certain conditions. the substitutability between the two channels, i.e., higher values A final segment of the literature considers a manufacturer of βi imply that the channels are viewed as closer substitutes. who owns a direct sales channel, which competes with a tradi- Thus, δi and βi will depend on the customers’ preferences re- tional retail channel. Here, the supply chain experiences both garding purchasing online versus in a traditional retail setting. vertical (between manufacturer and retailer) and horizontal (be- For example, some customers may prefer the convenience and tween direct channel and traditional retail channel) competition. lower search cost associated with the online channel, while other Coordination in this setting has received little attention. Boy- customers may prefer the ability to immediately obtain the prod- aci [3] shows that if the selling prices are fixed, the price-only, uct through the retail channel. The value of βi, in particular, will buy-back, rebate, and revenue-sharing contracts cannot coordi- reflect this tradeoff. nate the supply chain. Boyaci proposes a new type of contract, We now outline the sequence of events for our model and the compensation-commission contract, which can coordinate define some additional notation. the system. Tsay and Agrawal [2] also consider this context, but 1) Prior to the start of the selling season, the manufacturer assume deterministic demand (which is influenced by sales ef- sets the wholesale price cR charged to the retailer. fort) and fixed prices. If the selling prices are decision variables 2) The retailer sets the retail price pR and orders QR from and demands are price dependent, then coordination is challeng- the manufacturer at the wholesale price of cR per unit. ing because it requires the price and inventory decisions in each 3) At the same time, the manufacturer sets the online store channel to be system-optimal. Coordination in this environment, price pO and chooses a production quantity to be shipped in which the supply chain experiences both horizontal and ver- to the online store QO . tical competition, and in which the decision-makers must make 4) The manufacturer produces QM = QR + QO , with unit both pricing and quantity decisions, is the focus of this paper. production cost of cM . We assume unlimited capacity at To the best of our knowledge, we are the first to study this prob- the manufacturer. Thus, the manufacturer is always able lem, and the first to provide contracts which can coordinate the to produce the full quantity QM in time for the start of the system and arbitrarily allocate profits between the manufacturer selling season. and retailer. 5) End-user demands occur simultaneously at the retailer and the online store. We first derive the best response function for the retailer III. MODEL FORMULATION AND ANALYSIS: given the price for the manufacturer, i.e., we characterize the DETERMINISTIC DEMAND optimal pR for a given value of pO . Since, given the prices, We consider a supply chain consisting of a manufacturer demand is known with certainty, the retailer will choose to (he), which we denote with the subscript M, who distributes order a quantity QR just equal to demand. Thus, given pO , his product through two channels: an independently owned and the expected profit for the retailer ΠR is ΠR (pR |pO )=(pR − operated retailer (she), which we denote with the subscript R, cR )QR , and the retailer will choose pR to maximize ΠR (pR |pO ) and a manufacturer-owned online store, which we denote with subject to QR = δR − αR · pR + βR · pO . It is easy to show that the subscript O. Demand through each channel is dependent on ΠR (pR |pO ) is concave in pR and that the optimal retail price is δR +α R cR +βR pO the prices charged in both channels. Each channel must make pR (pO )= . 2α R both pricing and quantity decisions, while the manufacturer also We next characterize the manufacturer’s best response func- sets the wholesale price charged to the retailer. tion given the retailer’s price, taking the wholesale price as 250 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 60, NO. 2, MAY 2013
fixed. Later, we will consider how the manufacturer chooses QR and QO are increasing in β and decreasing in α.3)The the optimal wholesale price. Since, given the prices, demand equilibrium pR is increasing in β and decreasing in α.4)The is known with certainty, the retailer will choose to order equilibrium cR is increasing in cM . 5) The equilibrium ΠR a quantity QR just equal to demand. Thus, given pR ,we increases in β and decreases in α. can write the expected profit for the manufacturer ΠM as All proofs are provided in the online Supplement Material. ΠM (pO |pR )=(pO − cM )QO +(cR − cM )QR , and the man- The proof of Theorem 1 contains expressions for the equilib- ufacturer will choose pO to maximize ΠM (pO |pR ) subject rium prices, order quantities, and profits. The condition α>β to QO = δO − αO · pO + βO · pR . It is easy to show that implies that each channels’ demand is more sensitive to its own ΠM (pO |pR ) is concave in pO and that the optimal retail prices price than to the other channel’s price. ∗ δO +α O cM +βO pR +(cR −cM )βR is p (pO )= . We next note that, The results of Theorem 1 are intuitive. Point 1 says that the R 2α O since both profit functions are strictly concave in price, for a optimal order quantity in each channel is decreasing in its own given wholesale price cR , a unique equilibrium exists for the price, but increasing in the other channel’s price. Point 2 says game between the retailer and manufacturer. Thus, the equilib- that the equilibrium order quantity in each channel is decreas- rium prices can be found at the intersection of the best response ing in its own-price sensitivity and increasing in the competitor- functions, and can be written as follows: price sensitivity. Point 3 says that the equilibrium retail price is decreasing in its own-price sensitivity and increasing in the ∗ βR − pR = [δO + αO cM +(cR cM )βR ] competitor-price sensitivity. Point 4 says that the equilibrium 4αO αR − βO βR wholesale price charged to the retailer is increasing in the man- 2αO ufacturer’s unit production costs. Point 5 says that the retailer’s + [δR + αR cR ] (3) 4αO αR − βO βR equilibrium profit is decreasing in its own-price sensitivity and increasing in the competitor-price sensitivity. ∗ βO Finally, we consider how this system can be coordinated, i.e., pO = [δR + αR cR ] 4αO αR − βO βR we consider the type of contract that can make the decentralized system perform as well as an integrated system, in which the 2αR − + [δO + αO cM +(cR cM )βR ]. manufacturer owns both the retailer and the online channel. For 4αO αR − βO βR this deterministic model, it is straightforward to see that a profit- (4) sharing contract can coordinate the system. In such a contract, ∗ ≥ ∗ ≥ the manufacturer sets the wholesale price at c = c . Then, Notice that in order to have pR 0 and pO 0, we require R M 4αO αR − βO βR > 0. This condition will be satisfied if αR > at the end of the selling season, the retailer keeps φ percent of − βR and αO >βO , i.e., if the retail demand is more sensitive the total system profit, while the manufacturer receives 1 φ to the retail price than to the online price and, similarly, if the percent of the total system profit. Given that coordination can online demand is more sensitive to the online price than to the be achieved for our deterministic model, we have the following retail price. result. We next consider how the manufacturer will set the wholesale Theorem 2: Suppose δR = δO = δ, αR = αO = α, and βR = price for the retailer. To answer this question, we consider a βO = β. Then, the retail and online prices in the coordinated Stackelberg game between the manufacturer and retailer. In this (integrated) system are lower than the equilibrium retail and game, the manufacturer sets the wholesale price taking into online prices in the decentralized system. consideration the equilibrium prices, i.e., we are interested in Theorem 2 indicates that coordination not only improves the the value of cR that maximizes the manufacturer’s profits, given overall system profit, but also makes the consumer better off by ∗ ∗ lowering the prices on both channels. pR and pO . By checking the second-order conditions, it is easy to show that the manufacturer’s profits will be concave in cR , Finally, we note that a profit-sharing contract will require both and thus, there will exist a unique optimal cR , as long as αi >βi parties to honestly share cost and profit information, which may and αj >βi for all i ∈{R, O} and i ∈{R, O}. Unfortunately, create difficulties in implementation. In addition, when demand while we can obtain a closed-form expression for the optimal cR is stochastic, as in the next section, coordination is more difficult. (see the online Supplementary Material), the exact expression However, we propose two contracts that coordinate the system is quite complex. However, if we consider a symmetric setting and that are relatively easy to implement in practice. with δR = δO = δ, αR = αO = α, and βR = βO = β, we can simplify the expression for the optimal cR to the following: (8α3 + β3 )δ +(α − β)(8α3 +2αβ − β3 )c c∗ = M . (5) R 2α(α − β)(8α2 + β2 ) IV. MODEL FORMULATION AND ANALYSIS: We next present sensitivity analysis for this symmetric model STOCHASTIC DEMAND with deterministic demand. We next extend the model considered in Section III to the case Theorem 1: Suppose δR = δO = δ, αR = αO = α, and βR = of uncertain demand so that we may use the model to capture the βO = β. Then, if α>β: critical tradeoff between overstocking and understocking. To do 1) QR is decreasing in pR and increasing in pO . Similarly, QO so, we will use an additive model of uncertainty (see, e.g., [37]) is decreasing in pO and increasing in pR . 2) The equilibriums and thus our demand functions can be rewritten as follows: RYAN et al.: COORDINATING A SUPPLY CHAIN WITH A MANUFACTURER-OWNED ONLINE CHANNEL 251
DR (pR ,pO )=δR − αR · pR + βR · pO + R (6) 2) The demand and cost parameters must satisfy: δR + β p − α c + A > 0. D (p ,p )=δ − α · p + β · p + (7) R O R R R O R O O O O O R O The first condition will be satisfied for a variety of dis- tributions, including the normal and log-normal. For the where i , i ∈{R, O}, is a random variable defined on the range second condition, notice that, for any reasonable p and [Ai ,Bi ].Weletfi (·) and Fi(·) denote the probability density R p , we should require D ≥ 0. This implies that δ + function and cumulative distribution function of i, with mean O R R β p − α p + A > 0. We also require p >c . Thus, μi and standard deviation σi . To ensure that, for all values of R O R R R R R we can safely assume that δ − α c + β p + A >δ − pj , there exists some range of pi for which Di (pi ,pj ) > 0,we R R R R O R R α p + β p + A ≥ 0, and under reasonable conditions, the require Ai > −δi , for all i ∈{R, O}. R R R O R The sequence of events in this model is identical to that in second condition should hold. Section III, with the additional assumption that, at the end of Finally, from Theorem 1 in P&D, we have the first-order the selling season, any excess inventory is salvaged with values condition for zR vR and vO per unit at the retailer and online store, respec- ∂ΠR − − 0 − − ΘR (zR ) tively. In addition, as noted previously, like much of the liter- = (cR vR )+ pR (pO ) vR ature on supply-chain coordination, we assume a single-period ∂zR 2αR newsvendor setting, and thus, our model will be most applica- × (1 − FR (zR )) = 0. (9) ble for products with a short life cycle. Finally, to simplify the − ∗ analysis, it is useful to write QR = δR αR pR + βR pO + zR Let zR (pO ) denote the value of zR that satisfies this condition − ∗ and QO = δO αO pO + βO pR + zO , where zi represents the for a given pO .GivenzR (pO ), the retailer’s order quantity can ∈{ } ∗ − ∗ ∗ amount of safety stock held at location i, i R, O . With this be written as QR = δR αR pR (zO )+βR pO + zR (pO ). reformulation, the decision variables for each player are (zi ,pi ), i ∈{R, O}. B. Manufacturer’s Best Response Function
A. Retailer’s Best Response Function We will first analyze the manufacturer’s problem taking the wholesale price as fixed and deriving the best response function We first derive the best response function for the retailer, i.e., for the manufacturer given the price and order quantity for the we characterize the optimal p and z for given values of p R R O retailer, i.e., we characterize the optimal pO and zO for given and z . We can write the expected profit for the retailer Π as O R values of pR and zR . To do so, we can write the expected profits for the manufacturer ΠM ,givenpR and zR , as follows: ΠR (pR ,QR |pO ,zO )=E (−cR QR + pR min[DR ,QR ]
+ vR max[QR − DR , 0]) . ΠM (pO ,QO |pR ,zR )=E (cR QR − cM QM − We can now apply the results obtained by Petruzzi and + pO min[DO ,QO ]+vO max[QO DO , 0]) Dada [37], henceforth denoted as P&D. Specifically, our prob- lem is the same as P&D, Section 1.1, but with the follow- where QM = QO + QR . Although the manufacturer’s profit has additional terms to capture manufacturing costs and revenue ing notation: h = −vR ,s=0,μ= μR ,a= δR + βR pO ,b= from the retailer, its form is the same as the retailer’s profit. Thus, αR ,c= cR ,A= AR , and B = BR . Thus, Lemma 1 and The- we have the following optimal online price as a function of zO orem 1 in P&D apply and we can write the optimal pR given zR and pR : and pO as follows: Θ (z ) ∗ | 0 − ΘR (zR ) ∗ | 0 − O O pR (zR pO )=pR (pO ) (8) pO (zO pR )=pO (pR ) (10) 2αR 2αO B R − 0 B O 0 where ΘR (zR )= (R zR )fR (R )dR and pR (pO )= where ΘO (zO )= (O − zO )fO (O )dO and p (pR )= zR zO O δ +α c +β p +μ R R R R O R δO +α O cM +βO pR +(cR −cM )βR +μO 2α is the optimal riskless price, which depends is the optimal riskless price. R 2α O on the price charged by the online channel. Notice that this opti- Finally, the first-order conditions for zO are mal price for the retailer depends only on the price at the online store, not on the order quantity. ∂ΠM − − 0 − − ΘO (zO ) ∗ | = (cM vO )+ pO (pR ) vO We can plug pR (zR pO ) back into the profit function to get the ∂zO 2αO profit as a function of just z , i.e., we can convert the retailer’s R × − 2-D strategy space into a single dimension, which will simplify (1 FO (zO )) = 0. (11) our analysis. We apply Theorem 1 in P&D, which provides ∗ Let zO (pR ) denote the value of zO that satisfies this condition conditions under which there is a unique solution to the first- ∗ for a given pR .GivenzO (pR ), the retailer’s order quantity can order condition for zR . ∗ − ∗ ∗ 2 be written as QO = δO αO pO (pR )+βO pR + zO (pR ).The 1) FR (·) should satisfy the following: 2rR (zR ) + drR (zR ) conditions needed to guarantee that there is a unique solution > 0 for all AR ≤ zR
C. Equilibrium Analysis The first result indicates that safety stock at the retailer (online store) decreases (increases) as the wholesale price increases. We next show that, for a given wholesale price cR ,thegame between the retailer and manufacturer is supermodular and thus The second result says that, as expected, as the salvage value increases, the retailer’s safety stock will increase. The third an equilibrium exists. In addition, under certain conditions, this result also confirms our intuition that the online store’s safety equilibrium is unique. We start by noting that any equilibrium must satisfy the first-order conditions, which define the players’ stock decreases as the production cost increases. best response functions, specified in (8)Ð(11). Next, using (8) and (10), we can jointly solve for the prices for any given values D. Setting the Wholesale Price of zR and zO We next consider a Stackelberg game between the manu- facturer and retailer to characterize the equilibrium wholesale ∗ βR price. Thus, we are interested in the value of cR that maximizes pR (zO ,zR )= − [δO + αO cM + μO 4αO αR βO βR the manufacturers profits, given the equilibrium price and order quantities, p∗ ,Q∗ ,p∗ ,Q∗ . We start by proving the existence +(cR − cM )βR − ΘO (zO )] R R O O of a Stackelberg equilibrium: 2αO Theorem 6: There exists a Stackelberg equilibrium for the + − 4αO αR βO βR game in which the manufacturer chooses the wholesale price cR to maximize his own profits given (p∗ ,z∗ ,p∗ ,z∗ ). × [δR + αR cR + μR − ΘR (zR )] (12) R R O O The proof of Theorem 6 follows [39], i.e., existence of an ∗ βO equilibrium cR is guaranteed due to the fact that 1) the profit pO (zO ,zR )= − 4αO αR βO βR functions are real valued and continuous and 2) the strategy spaces are compact. This result only guarantees the existence × [δR + αR cR + μR − ΘR (zR )] of an equilibrium for the Stackelberg game, but says nothing 2αR about the uniqueness of such an equilibrium. While we are + − [δO + αO cM + μO 4αO αR βO βR unable to prove uniqueness, our numerical results indicate that the equilibrium c appears to be unique. Specifically, to find +(cR − cM )βR − ΘO (zO )]. (13) R the equilibrium cR , we must solve a system of equations. The Given the game defined by (9) and (11)Ð(13), we can now prove value of cR that satisfies this system of equations appears to be the following result. unique. − To find the cR chosen by the manufacturer to maximize his Theorem 3: If 4αO αR βO βR > 0, then the game between ∗ ∗ ∗ ∗ the retailer and manufacturer is a supermodular game. Thus, own profits given (pR ,zR ,pO ,zO ), we write the first-order con- dition, ∂ ΠM =0 there exists at least one equilibrium. ∂cR The proof of Theorem 3 shows that the profit functions have 2 ∂ΠM ∂pO ∂ Πi − − increasing differences in zR and zO , i.e., satisfy ≥ 0,for = (δO αO pO + βO pR + zO )+(pO cO ) ∂zR ∂zO ∂c ∂c i ∈{R, O} [38]. This result implies that the decision variables R R are complements, i.e., an increase in zO will cause the retailer to ∂pO ∂pR ∂zO × −αO + βO + want to increase (or not decrease) zR . The condition 4αO αR − ∂cR ∂cR ∂cR βO βR > 0 will be satisfied if αR >βR and αO >βO , which, as zO ∂pO discussed in Section III, is likely to hold. We next demonstrate − (z − )f( )d ∂c O O O O that, under certain conditions, the equilibrium will be unique. R A O Theorem 4: A unique Nash equilibrium exists under the fol- ∂zO − (pO − vO ) FO (zO ) lowing conditions: ∂cR 1) 4αO αR − βO βR > 0, cR >vR , and cM >vO ; +(δR − αR pR + βR pO + zR )+(cR − cM ) 2 dri (zi ) 2) 2ri (zi ) + > 0, i ∈{R, O}; dzi ∂p ∂p ∂z 3) δi − αi ci + Ai > 0, i ∈{R, O}. R O R × −αR + βR + =0. (14) While the condition in Theorem 3 guarantees the existence ∂cR ∂cR ∂cR of an equilibrium, the additional conditions in Theorem 4 guar- Since we do not have closed-form solutions for the equilibrium antee that the equilibrium will be unique. If these conditions are prices and quantities at the retailer and manufacturer, we use the not satisfied, the profit functions Π and Π may not be uni- R M implicit function theorem to write the partial derivatives of p , modal, and thus there could potentially be multiple equilibria. R p , z , and z with respect to c . A more detailed discussion In that case, it becomes difficult to make specific predictions O R O R of our solution approach for finding the optimal wholesale price regarding the behavior of the system equilibrium in practice. ∗ c can be found in the online Supplement Material. Finally, we can show the following properties of the equilib- R rium solution. V. I NTEGRATED SYSTEM AND SUPPLY-CHAIN COORDINATION Theorem 5: Under the conditions specified in Theorem 4: 1) ∗ ∗ zR is nonincreasing in cR , while zO is nondecreasing in cR ;2) We are interested in understanding how this dual-channel sup- ∗ ∗ zR is nondecreasing in vR ; and 3) zO is nonincreasing in cM . ply chain can be coordinated. We start by analyzing an integrated RYAN et al.: COORDINATING A SUPPLY CHAIN WITH A MANUFACTURER-OWNED ONLINE CHANNEL 253
system in which the manufacturer owns both the retailer and the βR + βO + 2 online channel. We then propose two contracting schemes to 4αR αO − (βR + βO ) achieve coordination. ×{δR +(αR − βO )cM + μr − ΘR (zR )}. I I A. Integrated System It is difficult to analytically compare the pR and pO . However, I I our numerical study indicates that whether or not pR >pO will We consider an integrated system under the assumption that depend on the parameters of the model. the manufacturer owns both the retailer and the online store. Finally, we compare the optimal solution for the integrated Prior to observing demand, the manufacturer chooses the pro- system with the Nash equilibrium solution for the decentralized duction quantities and prices for each location. Demand is then system. As discussed in detail in Section VI-B, our numerical re- observed and any excess demand at each location is salvaged. sults indicate that p∗ >pI , p∗ >pI , z∗
=(pR − cM )(δR − αR pR + βR pO + zR ) − (pR − vR ) B. Coordination Using a Modified Revenue-Sharing Contract zR × (zR − R )fR (R )dR Having analyzed the equilibrium behavior for the dual- A R channel model and having characterized the optimal system +(pO − cM )(δO − αO pO + βO pR + zO ) − (pO − vO ) behavior for the integrated system, we now investigate a con- zO tracting scheme that will enable supply-chain coordination. × (zO − O )fO (O )dO . (15) Specifically, we consider a modified revenue-sharing contract A O in which the retailer shares a fixed portion of her revenue with In the following, we characterize the optimal solution of the the manufacturer. Under this contract, defined by the parameters I I integrated system. (pR ,pO ,φ), the manufacturer imposes a minimum retail price I Theorem 7: If the following conditions are met, the expected pR on the retailer, i.e., the retailer may choose to price at any ≥ I profit for the integrated system is unimodal (quasi-concave) level pR pR , and the manufacturer sets his own online price I I I at pI . Then, at the start of the selling season, the retailer chooses and the optimal prices (pR and pO ) and order quantities (QR O I her order quantity Q for which the manufacturer charges the and QO ) can be found as the unique solution to the first-order R conditions: unit wholesale price cR = φcM . Then, at the end of the selling 2 1) 4αR αO − (βR + βO ) > 0; season, the retailer keeps a fraction φ of her revenue and gives a − 2) cM >vi, i = R, O; fraction (1 φ) of her revenue to the manufacturer. We call this 2 dri (zi ) contract a minimum retail-price-constrained revenue-sharing 3) 2ri (zi ) + > 0, i = R, O; zi contract. 4) δi − αi cM + Ai > 0, i = R, O. To understand the first condition, consider the case in which The minimum retail price constraint is commonly observed in practice. Lynette [40] studied 203 resale price maintenance βR = βO = β. In this case, the first condition in the theorem cases and found that approximately 80% of the cases involved will hold if αR >βand αO >β, i.e., if each channel’s demand is more sensitive to its own price than to the other channel’s a minimum resale price requirement specified by the manufac- price. Conditions 3 and 4 of the theorem are analogous to the turers to reduce price competition among the retailers. In the conditions for unimodality required in Sections IV-A and IV-B. bicycle industry, some suppliers have been known to enforce Theorem 7 indicates that the integrated systems has a unique minimum pricing, although not overtly [41]. In the automotive optimal solution. As shown in the proof of the theorem, the industry, car manufacturers have a long history of specifying a “manufacturer suggested retail price.” They are now consid- optimal prices for the integrated system, given zR and zO ,are ering efforts to enforce the minimum retail price [42]. In the I βR + βO video game industry, Nintendo has been known to occasionally pR (zR ,zO )= 2 4αR αO − (βR + βO ) institute minimum price requirements [43]. Similar minimum price requirements are common for electronic goods, software, ×{δO +(αO − βR )cM + μO − ΘO (zO )} books, and pharmaceuticals.1 2αO Minimum retail price constraint makes intuitive sense in a + 2 4αR αO − (βR + βO ) dual-channel supply chain in which the manufacturer distributes products through a traditional retailer and a manufacturer-owned ×{δR +(αR − βO )cM + μr − ΘR (zR )} online store. In such a system, the manufacturer will likely be I 2αR pO (zR ,zO )= 2 1 4αR αO − (βR + βO ) “Century-Old Ban Lifted on Minimum Retail Pricing,” by S. Labaton, New York Times, 06/29/2007 and “Justices Hear Arguments About Pacts on Pricing,” ×{δO +(αO − βR )cM + μO − ΘO (zO )} by L. Greenhouse, New York Times, 06/27/2007. 254 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 60, NO. 2, MAY 2013
I ∗ I ∗ interested in ensuring that the retailer does not undercut his 2) When ΠR > ΠR and ΠM > ΠM , a feasible φ may be price or, going even further, he may be interested in maintaining greater than 1, depending on the negotiating power of price discrimination, i.e., ensuring that the retail price is strictly each party, e.g., when the retailer has more negotiating greater than the online price. Our numerical study results indi- power, we would expect her to extract more of the system cate that the minimum price-constrained revenue-sharing con- profits and thus φ may exceed 1. I ∗ I ≤ ∗ tract enables this sort of price discrimination for cases in which 3) When ΠR > ΠR and ΠM ΠM , a feasible φ will always the retail channel has a larger market than the online channel, be less than or equal to 1, as in a traditional revenue- i.e., when δR ≥ δO . sharing contract. In this case, the integrated system pro- To analyze this contract, we first show that, when the manu- vides no benefit to the manufacturer over the decentral- facturer imposes a minimum retail price, the retailer will always ized system. Therefore, in order to motivate the manufac- choose to price at exactly this minimum level. turer to participate, the retailer must share some of the Theorem 8: Under the revenue-sharing contract defined by benefits she obtains from the integrated system with the I I I (pR ,pO ,φ), where pR is the minimum retail price imposed manufacturer. by the manufacturer, the retailer will always choose to price While the value of φ may theoretically be greater than 1, in I at pR . our numerical results, as described in Section VI, the Pareto- To understand this result, note that if the retailer operated improving region for φ ranged from 15% to 51%. under a revenue-sharing contract with no constraint on her price, 1) Implementation and Legal Considerations: The mini- I given that the online channel prices at pO , her optimal price mum price-constrained revenue-sharing contract proposed here I would be less than pR . Since her profit is unimodal in price, is different from what is known as a “minimum resale price under the minimum price contract, the retailer would choose maintenance contract.” In Dr. Miles Medical Co. v. John D. I to set her price equal to the minimum level, pR . We also note Park and Sons (1911), the Supreme Court found that mini- that this result does not require any assumptions regarding the mum resale price maintenance contracts violate the Sherman I I I I size of pR relative to pO , i.e., we do not require pR >pO . Antitrust Act [45]. However, that ruling has been a source of Finally, this result coincides with what is generally observed debate (see [46] and [47]). In a June 2007 ruling, the Supreme in practice, i.e., when manufacturers impose a minimum retail Court overturned Dr. Miles, concluding that vertical price re- price on their retailers, the retailers generally choose to set their straints are not illegal across the board, but must be judged on price at exactly that minimum level [44]. an individual basis. The ruling came in the case Leegin Creative We can now demonstrate that a revenue-sharing contract of Leather Products,2 a manufacturer of fashion accessories, who the form described previously can coordinate the supply chain. wanted to target customers willing to pay a higher price for extra ∗ ∗ We first define the following notation: let ΠR (ΠM ) denote the service. The company instituted a policy that required retailers retailer’s (manufacturer’s) optimal expected profit without the to adhere to a minimum price and refused to sell to the retailer ∗ revenue-sharing contract, when cR = cR , the optimal wholesale who filed suit because that retailer sold goods at prices below I I price for the decentralized dual-channel model, and let ΠR (ΠM ) the manufacturer’s minimum price. denote the retailer’s (manufacturer’s) expected profit if both Thus, in a minimum resale price maintenance contract, the parties use the optimal solution for the integrated system, when manufacturer refuses to sell products to a retailer if the re- cR = cM . tailer does not accept and execute the minimum retail price. Theorem 9: When cR = φcM , the revenue-sharing con- Our proposed contract is different because the retailer is given I I tract defined by (pR ,pO ,φ) coordinates the dual-channel two options: 1) she could buy from the manufacturer under Π∗ ΠI +ΠI −Π∗ ∈ R R M M the existing wholesale price contract or 2) she may participate model. If φ ΠI , ΠI , the contract will be Pareto- improving. R R in the price-constrained revenue-sharing contract. In order to As shown in the proof of Theorem 9, the Pareto-improving increase his profits, the manufacturer seeks to motivate the re- region for φ is always nonempty, i.e., there always exists some tailer to choose option 2). Therefore, the manufacturer designs value of φ that makes both parties better-off. the revenue-sharing contract in a manner that is beneficial to the Next, we note that, depending on the relationships among retailer, i.e., so that the profits earned by the retailer under 2) ∗ I ∗ I are at least as high as under 1). ΠR , ΠR , ΠM , and ΠM , the parameter φ may be larger than 1, as discussed in the following. Finally, since the prices charged by both channels under the I ≤ ∗ minimum price-constrained revenue-sharing contract are equal 1) When ΠR ΠR , a feasible φ will always be greater than or equal to 1. In this case, the integrated system provides to the optimal prices for the integrated system, these prices no benefit to the retailer over the decentralized system. will likely be less than those charged without the contract, i.e., I ∗ I ∗ Therefore, in order to motivate the retailer to participate, pR C. GL Sharing Contract will be shared with the manufacturer WG , in those instances in which the retailer does better under the contract, will be larger In this section, we propose a GL sharing contract to coordinate the dual-channel model. In a GL sharing contract, the upstream than the percentage of the retailer’s loss that would be paid to the retailer by the manufacturer W in those instances in which player (manufacturer) shares the gain or loss incurred by the L the retailer does worse under the contract. downstream player (retailer). Such GL contracts are commonly observed in the insurance, banking, and third-party logistics industries [5], [33], [48], [49]. D. Comparison of Coordinating Contracts We assume that the manufacturer offers a GL sharing contract We have presented two contracts, the minimum price- (WL ,WG ,T) to the retailer. The parameter T is the retailer’s ex- pected optimal profit without the contract, which can be thought constrained revenue-sharing contract and the GL sharing con- of as the retailer’s target profit. At the beginning of the selling tract, that can coordinate the dual-channel model. In addition, I both contracts are completely flexible in dividing system profits season, the manufacturer sends the quantity QR to the retailer ∗ between the players. Depending on the negotiation power of at the wholesale price cR , as specified in Section IV-D, and asks the retailer to sell the product at the price pI . The online each party, under either contract, the manufacturer’s profit can R range from Π∗ (i.e., the manufacturer gets no gain from coor- store stocks the quantity QI and sells at price pI . At the end M O O dination) to ΠI +ΠI − Π∗ (i.e., the manufacturer takes all of of the selling season, if the retailer’s realized profit is less than M R R T , then the manufacturer pays the retailer W times the dif- the gain from coordination). Similarly, the retailer’s profit can L range from Π∗ to ΠI +ΠI − Π∗ . One difference between ference between the retailer’s realized profit and T . Otherwise, R M R M the two contracts is the wholesale price. Under the revenue- the retailer pays the manufacturer WG times the difference be- tween the retailer’s realized profit and T . Notice that, as with the sharing contract, the wholesale price is linearly increasing with φ minimum price-constrained revenue-sharing contract, the issue the fraction of revenue that is kept by the retailer. Under the GL sharing contract, the wholesale price is fixed at c∗ , the opti- arises of whether such a contract is legal, given that the man- R ufacturer attempts to dictate the selling price to the retailer. To mal wholesale price in the dual-channel model. The wholesale avoid this problem, we take an approach similar to that of [51] price can have a significant impact on a retailer if his cash is to implement the price constraint without “forcing” the retailers limited prior to the start of the selling season. Therefore, the to participate. Specifically, we assume that the manufacturer of- revenue-sharing contract could be more attractive to the retailer than the GL sharing contract if the wholesale price is lower than fers a menu, with two options, to the retailer upfront. In the first ∗ I ∗ cR . option, the retailer orders QR at a wholesale price cR , as spec- I ified in Section IV-D, and sets retail price equal to pR .Atthe end of the selling season, the manufacturer shares the retailer’s VI. NUMERICAL STUDY AND OBSERVATIONS gain or loss according to the GL sharing contract. In the second option, the retailer can order any order quantity at the wholesale In this section, we conduct a series of numerical analyses ∗ to investigate the sensitivity of the equilibrium solution for the price cR and set any retail price. No GL sharing is offered in this option. As we will demonstrate in the following, the retailer dual-channel model to various key parameters, as well as to will earn more profits under the GL contract than without it. compare the performance of the dual-channel model to that Thus, the retailer will voluntarily choose to participate in the of the integrated system. Since we do not have closed-form GL sharing contract. solutions, we find the equilibrium solutions by solving the We next specify some additional notation. Π∗ is the retailer’s problems numerically. After reviewing the existing literature R on channel coordination and demand substitution with a lin- optimal expected profit without the contract, ΠR is the retailer’s I ear demand model (e.g., [8], [9], and [50]), we created a set expected profit under the contract, and ΠR is the retailer’s ex- pected profit if both parties use the optimal solutions for the of test problems by varying the key parameters, i.e., the firm’s ∗ own-price sensitivity (αi ∈{30, 40, 50, 60, 70, 80}), the firm’s integrated system. The manufacturer’s profits, ΠM , ΠM , and ∗ β ∈{0, 3, 6, 9, 12, 15} ΠI , are defined analogously. Also, note that T =Π . competitor-price sensitivity ( i ), and the M R v ∈{0.1, 0.3, 0.5, 0.7, 0.9} Theorem 10: A GL sharing contract (W ,W ,T) coordi- unit salvage value ( i ). For the ran- L G nates the decentralized dual-channel model. If ΠI >T, then dom component of demand i , we tested uniform distributions R B B ∈{50, 100, 150, 200, 250, 300} W >W . Otherwise, W >W . on [0, i]for i . The produc- G L L G c Thus, a GL sharing contract will always coordinate the sys- tion cost ( M ) is normalized at 1, while the base market demand δ tem. In the proof of the theorem, we indicate how to determine ( i) is fixed at 2000. values for the contract parameters WL and WG that will en- sure that the contract is Pareto-improving, i.e., that both the A. Analysis of Dual-Channel Model Equilibrium retailer and manufacturer will benefit from participating in the contract. The relative size of these gain and loss parameters We first discuss the behavior of the equilibrium prices, safety stocks, and profits. We note that the behavior of the equilibrium WG and WL will depend on the specific problem parameters. If, in expectation, the retailer does better under the integrated is similar across all uniform distributions tested, although the system than in the dual-channel system with no contract, i.e., if magnitude of the profits will differ [see Fig. 1(a)]. While we dis- ΠI >T =Π∗ , then the percentage of the retailer’s gain that cuss our general results, we have chosen to graphically display R R only selected results. 256 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 60, NO. 2, MAY 2013 (a) (b) Fig. 1. Graphical illustration of equilibrium behavior. (a) Retailer’s profits. (b) Manufacturer’s wholesale price. (a) (b) Fig. 2. Sensitivity analysis on dual-channel model. (a) Manufacturer’s profit. (b) Retailer’s profit. 1) Wholesale price: As shown in Fig. 1(b), the manufac- the online price was always less than the retail price. turer’s optimal wholesale price decreases as the firm’s More specifically, for our parameter values, we found that ∗ ∗ ∈ own-price sensitivity increases. However, when demand pO /pR [70%, 90%]. is very sensitive to the competitor’s price, the manufac- Our numerical results provide managerial insights into recent turer will set a higher wholesale price. Interestingly, the developments in manufacturer-owned online channels. Since the manufacturer lowers the wholesale price as the salvage manufacturer is the leader of the Stackelberg game, he optimally value increases. chooses the wholesale price to extract the retailer’s profits. As 2) Safety stock: As the savage value increases, the safety a result, although we consider only symmetric channels, we stock levels increase, as expected. Higher competitor-price observe that the manufacturer’s profits are significantly higher, sensitivity results in higher safety stock for the online i.e., about seven times (on average) larger, than the retailer’s channel but lower safety stock for the retailer. Interest- profits. ingly, while higher own-price sensitivity reduces the safety stock for the online channel, it increases the safety stock B. Performance of Supply-Chain Coordination for the retailer. 3) Profits: As depicted in Fig. 2, both channels’ optimal prof- One key question to be addressed in this research is the degree its behave as expected, and as predicted by the analysis of to which the proposed coordination contracts can improve the the deterministic model in Theorem 1. Specifically, as one system’s profits. To answer this question, we compare the dual- firm’s own-price sensitivity increases, its profits decrease. channel model with the integrated system for the 1080 problem However, the effect of a firm’s competitor-price sensitivity settings tested. As expected, the system profits for the integrated is exactly the opposite. Finally, as in a typical newsven- system are higher than for the dual-channel model for every dor model, a higher salvage value results in higher profits problem instance. The average percentage increase in profits [refer to Fig. 2(b)]. under the integrated system is 12.44%, ranging from 6.29% to 4) Prices: The impact of these parameters on the optimal 14.95%. Note that these increases can be interpreted as the value prices is identical to that for the optimal profits, and is of supply-chain coordination. as predicted by the analysis of the deterministic model in Further investigation reveals that the value of coordination Theorem 1, i.e., firm i’s price is decreasing in its own- increases with the own-price sensitivity and decreases with the price sensitivity and increasing in the competitor-price competitor-price sensitivity [see Fig. 3(b)]. These results can be sensitivity. Also, a higher salvage value leads to higher understood if we consider the behavior of total system profits in prices. In addition, as noted previously, we found that the dual-channel model, as illustrated in Fig. 3(a). Specifically, RYAN et al.: COORDINATING A SUPPLY CHAIN WITH A MANUFACTURER-OWNED ONLINE CHANNEL 257 (a) (b) Fig. 3. Performance of coordination contract. (a) Total profits in dual-channel model. (b) Percentage increase in total profits with coordination. as consumers become more sensitive to a firm’s own price, the safety stocks. Since the price for the online store is higher than ∗ I total system profits in the dual-channel model decrease. There- the system optimal price, i.e., pO >pO , the newsvendor criti- fore, there will be more room to improve performance through cal ratio is higher, and the safety stock held at the online store ∗ I supply-chain coordination. In contrast, as the competitor-price will be higher than the system optimal level, i.e., zO >zO .For ∗ I ∗ I sensitivity increases, and thus the two channels are viewed as the retailer, pR >pR will not necessarily imply that zR >zR closer substitutes, the total system profits in the dual-channel because the effect of vertical double marginalization leads to model increases and there is less room for improvement through lower safety stock at the retailer. From our numerical results, coordination. In summary, we conclude that coordination is most we find that the latter effect dominates, i.e., the retailer holds ∗ I critical for products which are highly price sensitive and for sys- less safety stock than system optimal level, i.e., zR we observe through our numerical analysis (the manufacturer’s ACKNOWLEDGMENT profits are seven times higher, on average, than the retailer’s). 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