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  • ISyE 8813 Logistics and transportation Systems ―Review‖ Paper Report Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations Authors: Cachon and Lariviere Publication: Management Science, 2005 Vol. 55, issue 1, pp 30-44 Submitted by: Divya Mangotra
  • [1] INTRODUCTION Each firm in a supply chain must execute a precise set of actions to achieve optimal supply chain performance. But the primary objective of each firm is its own profit. Thus, supply chain excellence requires the coordination of disparate incentives. There are several supply chain contracts such as Revenue Sharing, Wholesale Price, Buy-back, Quantity Discounts, Quantity Flexibility etc. This report attempts to study how different contracts perform in their attempt to coordinate the supply chain under different settings (models). 1. Supply Chain coordination under basic model The first (basic) model has a single supplier selling to a single retailer that faces the newsvendor problem. In this model the retailer orders a single product, with stochastic demand, from the supplier well in advance of a selling season. After receiving the retailer’s order, the supplier starts the production and delivers to the retailer at the start of the selling season. The retailer has no additional replenishment opportunity. Under the Fixed-Price Newsvendor problem, the retailer has to decide how much to stock depending on the contract the supplier offers. Price-Setting Newsvendor Problem is an extension to the newsvendor model. Now the retailer chooses his retail price in addition to his stocking quantity. It is shown that many of the contracts that coordinate the basic newsvendor model no longer coordinate in this setting. However, some contracts are robust to this change. Furthermore, those contracts coordinate the supply chain even though they place no restriction on the retailer’s pricing decision, which is important since in general suppliers are legally prohibited from dictating the prices their retailers may charge. The second extension to the newsvendor model expands the retailer’s action set by allowing the retailer to exert costly effort to increase demand. Like the retail price, the 2
  • retailer’s effort is non-contractible, i.e., the supplier cannot restrict the retailer to a limited set of effort levels. In this model there is a strong tension between the supplier and the retailer: since the cost of effort is borne exclusively by the retailer, the supplier always prefers the retailer to exert more effort. Nevertheless, coordinating contracts do exist for this setting. 2. Supply Chain Coordination under multiple competing retailers We analyze an extension of the basic model where the supplier sells to multiple competing retailers. 3. Supply Chain Coordination when demand is dependant on retail effort The retailer can often take actions that influence revenue, e.g., advertising, improve display of products, enhance ambience of the store and improve service quality. All of those activities are costly. As a result, a conflict exists between the supplier and the retailer. No matter what level of effort the retailer dedicates towards those activities, the supplier prefers that the retailer exert even more effort. Sharing the cost of effort is one solution to the effort coordination problem. In order for cost sharing to be an effective strategy, the supplier must be able to verify (without much hassle) that the retailer actually engaged in the costly activity, and the activity must directly benefit the supplier. There are also many situations in which cost sharing is not as effective. For example, a supplier probably will not pay for an ad that merely promotes the retailer’s brand image. In that case the ad enhances the demand for all of the retailer’s products, not just the supplier’s product. Retailer’s expected revenue = R ( q , e ) , where e is a measure of retailer’s effort The retailer incurs an effort cost g (e ) but no incremental cost, c r 0 3
  • [2] MOTIVATION: Success story of coordination (Blockbuster) Traditionally, retailers like Blockbuster purchased tapes from his supplier for $65 a copy and rented them for $3 a copy. Under this conventional sales agreement, a tape would start making profit only after 22 rentals. The demand for a tape would typically start high but quickly taper. Hence a retailer couldn’t justify purchase of enough tapes to cover the entire peak demand. The result was frequent stock outs of new-release videos and unhappy customers. In 1998, Blockbuster entered a Revenue Sharing contract with its supplier. Under the contract, supplier reduced the initial price per tape from $65 to $8 and rental revenue was shared. The retailer kept 45% of revenue, 45% went to the supplier and 10% went to Rentrak (Blockbuster’s distributor). Thus, Revenue sharing reaped huge benefits for Blockbuster. It was able to increase inventory of recent videos seven folds. The revenue sales went up and market share increased from 24% in 1997 to 40% in 2002. Revenue Sharing worked well in Video Industry fro two reasons. Firstly, Low administrative cost to attain visibility across the supply chain as all video stores have system of computers and bar codes to track each tape. Secondly, There is no impact of retail effort on demand, as customers do not decide on a tape after a lot of consultation. Thus, Video Rental Supply Chain is particularly suited for Revenue Sharing. [3] SUPPLY CHAIN COORDINATION UNDER DIFFERENT CONTRACTS Certain assumptions are followed throughout the analysis. They are Sales period as exogenously specified, only Retailer generates revenue in this supply chain, same revenue share is applied to all units, long-Run Revenue Impact of poor availability is not included in the model. 4
  • 3.1 REVENUE SHARING CONTRACT: Under the revenue sharing the downstream firms make royalty payments to upstream firms based on downstream sales revenue. This output payment is in addition to the direct input payments from downstream firms. Dana and Spier, (2001) discuss Revenue Sharing is an attractive instrument in vertically separated industries where there is intra band competition downstream, demand is stochastic and inventory in the downstream channel is decided before actual demand realization. The upstream channels want to soften the competition downstream and promote inventory holding. Whereas the traditional two- part tariff fails to meet the goals, Revenue Sharing aligns the incentives in such vertical supply chains. Video Rental Industry is an example of vertically separated supply chain. I. Single Supplier Single Retailer: Key Idea: ―Revenue sharing coordinates the supply chain under both price setting and fixed price newsvendor setup‖. Profit Functions: Retailer: r (q, p ) ( R (q, p ) vq ) (w c r )q Supplier: r (q, p ) (1 )( R ( q , p ) vq ) (c s w)q 1 Supply Chain: (q, p ) R (q, p ) (v c ) q where c cs cr Theorem 1. Consider the set of revenue sharing contracts with w c cr , and ( 0 ,1] . With those contracts, the firms’ profit functions are r (q, p ) (q, p ) and s (q, p ) (1 ) (q, p ) 1 Note that c s is unit production cost, c r is the retailer’s cost excluding payments to supplier and c is the channel (total) cost. 5
  • Furthermore, { q 0 , p 0 } is the retailer’s optimal quantity and price; i.e., those contracts coordinate the supply chain. Observations: 1. Revenue – Sharing contracts achieve supply chain coordination by making the retailer’s profit function an affine transformation2 of the supply chain’s profit function. 2. Coordination requires a wholesale price below the supplier’s cost of product c s w c cr (c s cr ) cr cs (1 )c r cs ( 0 ,1) So the supplier loses money in selling the product and only makes money by participating in the retailer’s revenue. 3. Revenue Sharing arbitrarily allocates the supply chain profit. The profit split chosen probably depends on the firms’ relative bargaining power. As retailer’s bargaining position becomes stronger, we can expect to increase. 4. The set of coordinating contracts is independent of the revenue function. It follows that a single revenue-sharing contract can coordinate the actions of multiple retailers with different revenue functions as long as each retailer’s revenue is independent of the other retail’s actions (do not compete) and they have the same marginal costs c r 5. Extreme value raises two- issues- (a) Retailer’s profit function become quite flat as 0 ; while q 0 remains optimal, deviation from q 0 imposes little penalty on the retailer. (b) c r / c : Wholesale price is negative. Since the retailer’s share of the channel cost is high, he is anyways in a low-margin business before the supplier takes a slice of revenue. If the supplier wants a larger portion of revenue, he has to subsidize the retailer’s acquisition of product. 2 Affine Transformation: An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances (e.g., the midpoint of a line segment remains the midpoint after transformation). 6
  • II. Multiple Retailers: Result: ―Revenue Sharing coordinates a supply chain with retailers competing in quantity (Fixed- price newsvendor model)‖. Theorem 2. The following revenue-sharing contracts coordinate the supply chain with multiple competing retailers and revenue functions R i ( q ) : note here R i ( q ) includes the salvage revenue 0 wi i (c i i ) c ri , 0 0 where i i (q ) , n i i (q ) R j (q ) , j i and 0 i (q ) 0 i 0 0 0 for i 1,..., n . i (q ) qi i The firms’ optimal profits are 0 0 0 0 i (q ) i ( i (q ) qi i ), n 0 0 0 0 0 0 s (q ) (1 i )( i (q ) qi i ) qi i , i 1 Observations: 1. Coordinating wholesale price is same as in the single retailer case with the addition of 0 i i term. This term represents the revenue externality imposed by retailer i on others at the optimal solution. 2. The retailers profit function is no longer an affine transformation of the supply chain’s profit for all q due to addition of a fixed term. 3. Range of each i exceeds one. So it can no longer be interpreted as retailer’s share of supply chain profit. 4. Retailer’s profit is increasing in while supplier’s profit is decreasing in . 7
  • Question: Why Revenue Sharing fails to coordinate in the Price Setting Newsvendor Model? At an optimal solution, we have 0 0 0 0 0 0 (q , p ) Ri (q , p ) n R j (q , p ) 0 pi pi j i pi but for 0, 0 0 0 0 i (q , p ) Ri (q , p ) i 0 pi pi Thus, Revenue Sharing stumbles when revenue is a function of both quantity and price, R i ( q , p ) III. Retail Effort: Revenue sharing fails! Retailer’s Profit: r (q, e) R (q, e) g (e) qw Integrated Supply Chain Profit: ( q , e ) R (q, e) g (e) qc Let { q 0 , e 0 } be an optimal solution. Then, we have 0 0 0 0 (q , e ) R (q , e ) ' 0 g (e ) 0 e e But for the retailer 0 0 0 0 r (q , e ) R (q , e ) ' 0 g (e ) 0 0 1 e e Thus, revenue sharing coordinates effort decision only when 1 , but then retailer’s quantity decision is coordinated for w cs , i.e., supplier makes zero profit. 8
  • IV. Multiple Suppliers Gerchak and Wang, 2004 study the supply chain with multiple suppliers and complementary products (products jointly purchased in each case). They argue that Revenue sharing contracts can’t coordinate the supply chain in the case of multiple suppliers. A new contract mechanism, namely, the Revenue-plus-surplus-subsidy contract is presented in the paper. Here in addition to a revenue share i from sales of final product, the retailer will pay supplier i s i per unit for its delivered components that are not sold—a surplus subsidy. The paper shows that revenue-plus-surplus-subsidy contract dominates the revenue-only contract and any other contract types that cannot achieve channel coordination. For example, due to the ―profit surplus‖ generated through coordination, the retailer can allocate to each supplier at least the same profit as when the channel is not coordinated and still leave itself with more. Also rational suppliers will actually deliver equal amounts, so unmated components will actually not occur. Such a subsidy, in effect, transfers some of the risk due to uncertain demand from the suppliers to the retailer. Also the performance of the system is independent of number of suppliers in the system. 3.2 WHOLESALE PRICE CONTRACT The supplier merely charges the retailer a fixed wholesale price w per unit ordered. I. Single Supplier Single Retailer Profit Functions: Retailer: r (q ) R (q ) qw ( q ) Supplier: r (q ) q (w(q ) c) Supply Chain: (q ) R (q ) cq Retailer’s optimal quantity is the unique solution to ' r (q ) R ' (q ) w(q ) 0 Supplier’s optimal quantity is the unique solution to ' ' s (q ) (w(q ) c) qw ( q ) 0 9
  • Supply Chain’s optimal quantity is the unique solution to ' (q ) R ' (q ) c 0 Let q s* be supplier’s optimal quantity. Then ' * * * ' * s (q s ) (w(q s ) c) q s w (q s ) 0 * * ' * ' * * " * i.e. (w(q s ) c) q s w (q s ) R (q s ) q s R (q s ) c 0 Since q s* R "' ( q s* ) 0, the supply chain performance is not optimal at q s* ; i.e., q s* < q 0 Also w (q ) decreasing in q and R ' ( q 0 ) c implies that under the Wholesale price contract: w ( q ) c as compared to revenue sharing contract where: w ( q ) c. Since R ' ( q ) is decreasing, q s* q 0 only when, w c . Thus, the wholesale price contract coordinates the supply chain only if the supplier uses marginal cost pricing. Since the supplier earns zero profit with marginal cost pricing, she prefers a higher wholesale price. Hence, the wholesale price contract is generally considered a non- coordinating contract still it is commonly observed in practice. This fact alone suggests the contract has redeeming qualities. For instance, the wholesale price contract is simple to administer. A supplier may prefer the wholesale price contract over a coordinating contract if the additional administrative burden associated with the coordinating contract exceeds the supplier’s potential profit increase. Key Idea: Revenue sharing may provide only a slight improvement over the wholesale price contract, which is administratively cheaper. The two performance measures applied to the wholesale price contract are the efficiency * * * (q s ) ( q s , w ( q s )) of the contract, 0 and the supplier’s profit share s * (q ) (q s ) From a supplier’s perspective wholesale price contract is attractive if both the performance measures are high. The curvature of the marginal revenue curve R ' ( q ) plays a vital role in determining the contract’s efficiency and profit share (for details refer appendix). 10
  • II. Multiple Retailers: The paper shows competition in the retail market has greater impact on the supply chain efficiency under the wholesale price contract as compared to revenue sharing. Thus, revenue sharing is less attractive to the supplier when several retailers compete in the market. This is true whenever the system requires significant administrative costs for each retailer added. III. Multiple Suppliers Gerchak and Wang, 2004 study the supply chain with multiple suppliers and complementary products (products jointly purchased in each case). Their studies show that the performance of a wholesale-price-based system degrades with the number of suppliers, and for certain cases appear to be inferior to the revenue sharing systems even for a small number of suppliers. IV. Multiple Period Problem Anupindi and Bassok (1999) studied an interesting extension to the simple model. Suppose the supplier sells to a retailer that faces an infinite succession of identical selling seasons. Inventory can be carried over to the next season but there is a holding cost on left over inventory at the end of a season. The retailer submits orders between seasons, which the supplier replenishes immediately. Within each season the retailer faces a newsvendor problem that makes the trade-off between lost sales and inventory holding costs. Hence, the retailer’s optimal inventory policy is to order up to a fixed level that is the solution to a newsvendor problem. But since inventory carries over from season to season, the supplier’s average sales per season equals the retailer’s average sales per season, i.e., the supplier’s profit function is ( w ( q ) c ) S ( q ) . The analysis of the supplier’s optimal wholesale price is more complex in this setting because the supplier’s profit is now proportional to the retailer’s sales, S (q ) ; rather than to his order quantity, q : Nevertheless, since S ( q ) ' q ; the supplier’s optimal wholesale price is lower S (q ) than in the single season model. Thus, the efficiency of the wholesale price contract is even better than in the single season model. 11
  • V. Market Variability Lariviere and Porteus, 2001 study price-only (wholesale price) contracts under market variability. They show that the manufacturer’s profit and sales quantity increase with market size, but the resulting wholesale price depends on how the market grows. The retailer’s price sensitivity falls and the wholesale price increases if variability increases less slowly than the mean (implying a lower coefficient of variation). If the market becomes more variable, the retailer becomes more price sensitive, and the wholesale price decreases. At lower levels of variability, the decentralized channel is more efficient and the share of realized profit the manufacturer captures is higher. Notably, the manufacturer’s profit usually rises much faster than the total supply-chain profit. The manufacturer’s early gains from falling variability come at the expense of the retailer; she finds exploiting decreased retailer price sensitivity more profitable than improving overall supply-chain performance. Their model neglects important factors such as supplier competition, retailer power, and retailer pricing policies that influence the setting of wholesale prices in practice. Thus, their analysis identifies an upper bound on the price one would observe in the market. It overestimates the wholesale price and underestimates channel efficiency. 3.3 BUY-BACK CONTRACT: With a buy-back contract the supplier charges the retailer w b per unit purchased, but pays the retailer b per unit remaining at the end of the season. I. Single Supplier Single Retailer Profit Functions: p R (q, p ) Retailer: r (q, p ) R (q, p ) (b v) q (c r wb )q p v p v b Supplier: s (q, p ) R (q, p ) (c s wb b)q p v Supply Chain: (q, p ) R (q, p ) (c v)q 12
  • Result: “Revenue Sharing is equivalent to Buybacks in the fixed price newsvendor case” Unlike Revenue Sharing; the coordinating buy-back parameters depend on the retail price. Theorem 3. In the newsvendor setting with a fixed retail price, for any coordinating revenue sharing contract, { , w} , there exits a unique buy-back contract, {b , w b } , that generates the same profit for each firm from any realization of demand: b (1 )( p v ), wb (1 )p c cr Proof: Refer to profit functions under revenue sharing. Equate the retailer (supplier) profit function for revenue sharing and buy-back to get [3a] ([3b]) Marvel and Peck (1995) show that Buy-Back contracts coordinate price-setting newsvendor only when supplier earns zero profit. Buybacks would coordinate price- setting model only if the supply was very flexible and willing to adjust the buyback and wholesale price in response to any price chosen by the retailer. Emmons and Gilbert (1998) showed that though buy-back contracts do not coordinate the system under a price-setting, they may still perform better than a wholesale price contract for b > 0. II. Retail Effort Profit Functions: ( v = salvage price) p R (q, e) Retailer: r (q, e) R (q, e) (b v) q ( g (e) wb )q p v p v Supply Chain: (q, e) R (q, e) ( g (e) cs v)q The optimal effort e 0 satisfies 0 0 (q, e ) R (q, e ) ' 0 g (e ) 0 e e 13
  • But for the retailer 0 0 0 0 r (q, e ) b R (q , e ) ' 0 (q, e ) (1 ) g (e ) b 0 e p v e e Thus, e 0 cannot be retailer’s optimal effort for b>0 but we need b>0 to coordinate retailer’s optimal quantity. Result: Buyback contracts cannot coordinate when demand depends on retail effort. Pasternack (1985) discusses the Buyback contracts in detail. The author studies two cases: Partial returns and Unlimited returns. Under partial returns, optimal contract parameter {b , w b } will both be function of the individual retailer demand. Hence these policies can’t be optimal in a multiple retailer scenario with different demand distributions. Under unlimited return, optimal contract parameters are independent of retailer’s demand distribution. The optimal parameters are defined in terms of supplier cost, retail sales price, salvage value and goodwill costs. Different optimal parameter pairs lead to different profit allocation between supplier and retailer. Padmanabhan and Png (1995) describe several motivations for return policies that are not included in the newsvendor model. A supplier may wish to offer a return policy to prevent the retailer from discounting left over items, thereby weakening the supplier’s brand image. Alternatively, a supplier may wish to accept returns to rebalance inventory among retailers. They also discuss several implementation issues with returns policies. In Padmanabhan and Png (1997) a supplier uses a buy-back contract to manipulate the competition between retailers. Anupindi and Bassok (1999) demonstrate buy-back contracts can coordinate a two-retailer supply chain in which consumer search among the retailers to find inventory. 14
  • Berstein and Federgruen (2005) studied a contract where buy-back rate and wholesale price are adjusted linearly in the retailer’s price. They call it Price-Discount contract3. Under this contract the supplier earns salvage revenue and c r 0 . Thus, Revenue sharing is equivalent to price discounts in the price-setting newsvendor case. For any revenue sharing contract there exists a unique price-discount contract that generates same profit for both firms irrespective of demand. Price-discount, like revenue sharing, is also costly to administer, as the retailer has to report its retail price and inventory status, which combined with demand quantity, yields sales revenue and salvage revenue. 3.4 QUANTITY FLEXIBILITY (QF) CONTRACT The retailer purchases q units for w per unit at the start of the season and may return up to q units at the end of the season for a full refund, [ 0 ,1) . Units not returned are salvaged for v per unit. There are several instances of Quantity Flexible contracts in industry. Sun Microsystems uses QF contracts in its purchase of various workstation components (cf. Farlow et al. 1995). Nippon Otis, a manufacturer of elevator equipment, implicitly uses such contracts with Tsuchiya, its supplier of parts and switches (cf. Lovejoy 1999). Quantity Flexibility contracts have also been used by Toyota Motor Corporation (Lovejoy 1999), IBM (Connors et al. 1995), Hewlett Packard, and Compaq (Faust 1996). I. Single Supplier Single Retailer Profit Functions: Retailer: r (q, p, w , ) R (q, p ) (c r w v)q (w v )( q (S (q, p ) S ((1 ) q , p ))) 3 Bernstein and Federgruen (2005) have the supplier earning the salvage revenue and c r 0 . Their ' ' coordinating contract is b ( p ) (p v) v and w ( p ) p (1 ) c , where 0 1. Let 1 in which case the retailer’s total revenue from each unit salvaged is the same with either contract. The wholesale prices are clearly the same given c r 0. 15
  • Fixed-Price Newsvendor model: For supply Chain Coordination, we want 0 0 r (q , p, w , ) (q , p ) , which holds for q q cs v w v 0 0 , where F (q ) is the distribution function of 1 F (q ) (1 ) F ((1 )q ) Retailer’s demand Result: QF contracts coordinates the supply chain and arbitrarily allocate profit. QF vs. Revenue Sharing 1. Unlike revenue sharing, the ration of retailer’s marginal profit to supply chain’s marginal profit is not constant for all q . This happens because the term S (q, p ) S ((1 ) q , p ) appears in the supply chain profit function. 2. The two contracts result in different division of profit for all realizations of demand. 3. Coordinating QF contracts depend on retailer’s demand distribution. Price-setting newsvendor model: For supply Chain coordination, we want 0 0 (q , p ) R (q , p ) 0 and p p 0 0 0 r (q , p, w , ) R (q , p ) q F ( x, p ) 0 dx 0 p p (1 )q p These two conditions are satisfied for 0 i.e. w cs . Result: The only coordinating contract has the supplier pricing at marginal cost and earning zero profit. II. Retail Effort Profit Function Retailer: r (q, p, w , ) R (q, p ) (c r w v)q (w v )( q (S (q, p ) S ((1 ) q , p ))) 16
  • The optimal effort e 0 satisfies 0 0 (q, e ) R (q, e ) 0 and e e 0 0 0 0 0 r (q, e , w , ) R (q, e ) q F ( x, e ) (q, e ) 0 dx 0 e e (1 )q e e Result: Quantity Flexibility contract cannot coordinate when demand depends on retail effort. III. Further discussion on QF contracts Tsay (1999) extensively studied QF contracts. The author showed that the QF contract, by itself, does not guarantee efficiency. There is a discussion of certain conditions under which this arrangement will generate efficiency gains that can be shared by the two parties. There is indeed a tradeoff between flexibility and unit price, with the customer willingly paying more for increased flexibility. The paper illustrates how this might unfold, including identifying arrangements that either party could propose with confidence that the other would accept. In their analysis they establish, even when the statistics of market demand are common knowledge, there is still a need to properly structure the supply relationship to share the consequences of uncertainty in that demand. Incentives and information are distinct causes of inefficiency and should be managed as such. However their results demonstrate efficiency only under shared beliefs, the issue of coordination under information asymmetry remains unresolved. Note: Other contracts are discussed in appendix due to space constraint. [4] DISCUSSIONS  Why most of the literature talks about coordination under newsvendor setup? The newsvendor model, though not complex, is sufficiently rich to study three main questions in supply chain coordination. 17
  • First, which contracts coordinate the supply chain? A contract is said to coordinate the supply chain if the set of supply chain optimal actions is Nash equilibrium, i.e., no firm has a profitable unilateral deviation from the set of supply chain optimal actions. Ideally, the optimal actions should also be a unique Nash equilibrium; otherwise the firms may ―coordinate‖ on a sub-optimal set of actions. Second, which contracts have sufficient flexibility (by adjusting parameters) to allow for any division of the supply chain’s profit among the firms? If a coordinating contract can allocate revenues arbitrarily, then there always exists a contract that Pareto dominates a noncoordinating contract, i.e., each firm’s profit is no worse of and at least one firm is strictly better of with the coordinating contract. Third, which contracts are worth adopting? Although coordination and flexible revenue allocation are desirable features, contracts with these properties tend to have administrative costs. So the contract designer may actually prefer to offer a simple contract even if that contract does not optimize the supply chain’s performance. A simple contract is particularly desirable if the contract’s efficiency is high (the ratio of supply chain profit with the contract to the supply chain’s optimal profit) and if the contract designer captures a big share of supply chain profit.  There is need to address the open question-Does there exist a simple legal contract with common terms that coordinates the heterogeneous competing retailers.  Limitations of the Paper: 1. The paper only addresses the newsvendor model with single opportunity before the selling season. In practice this may not be the case always. Hence, Newsvendor problem with two replenishment opportunities is an interesting setup to explore. 18
  • 2. Under the price-setting newsvendor model, the paper assumes a very simple structure i.e., the retailer chooses the price only once when he chooses order quantity. In a realistic model the retailer would be able to adjust his price throughout the season, possibly for a fee for each adjustment. Such a dynamic pricing strategy would allow the retailer to adjust his price to reflect demand conditions: e.g., if demand were less than expected the retailer could accelerate price discounts. This dynamic pricing problem is quite complex even when supply chain coordination is not considered. Hence, to obtain initial insights, assume the retailer sets his price at the same time as his stocking decision and the price is fixed throughout the season. 3. There is a substantial literature on the multiple supplier systems. This paper doesn’t address that case. It would be interesting to see how different contracts perform in the case of multiple suppliers. 4. The paper discusses all models under simple assumptions like no long run impact of poor availability. This assumption us certainly debatable. 19
  • Appendix (Other Contracts) 3.5 QUANTITY DISCOUNT CONTRACT Quantity discount is a common practice is industry (refer appendix for examples). The supplier charges the retailer w (q ) per unit purchased where w (q ) is a decreasing function. Profit Functions: Retailer: r (q, p ) R (q, p ) vq (c r w ( q )) q Supplier: s (q, p ) (w(q ) c s )q Supply Chain: (q, p ) R (q, p ) vq cq Result: Quantity Discount Coordinates the Supply Chain under both price setting and fixed price newsvendor model. I. Single Supplier Single Retailer Theorem 4 (Price Setting Newsvendor model): Let o R (q, p ) w(q ) (1 ) c (1 )v cr [3a] q 0 0 for ( 0 ,1] . { q , p } maximizes the retailers profit and 0 o r (q, p ) (q, p ) [3b] Proof: Simply substitute w (q ) in r ( q , p ) to get [3b]. As retailer keeps as the revenue, retailer’s optimal price for any given q equals supply chain optimal price. Thus, o 0 { q , p } is optimal as q 0 is optimal given p 0 (This clearly holds from [3b] for all 0 ). 20
  • Observations: Retailer’s expected profit is proportional to the supply chain’s expected profit. Fixed-Price Newsvendor model- for a fixed price p 0 , the quantity discount coordinates supply chain but it differs from Revenue Sharing in some aspects.  Under Revenue sharing, Retailer’s expected profit is proportional to the supply chain’s expected profit even if he sets a non-optimal price. This is not the case with Quantity Discounts.  In the Quantity Discount, retailer pays a portion of the supply chain’s expected revenue whereas in revenue sharing, retailer shares a portion of the realized revenue. Thus, with a quantity discount supplier earns the same profit independent of the realization of demand but with revenue sharing supplier has to bear some demand risk  Since w (q ) is a function of R ( q , p ) , a single quantity discount schedule can coordinate multiple independent retailers with identical revenue functions. Shin and Benton, 2004 studied the effectiveness of quantity discounts as an inventory coordination mechanism under different environmental conditions. Their work showed that certain environmental factors significantly impact the effectiveness of QDIC (Quantity discount based inventory coordination) policies. The analytical results revealed that the supply chain system’s inventory performance is mainly affected by the inventory cost structure of the buyer and supplier. The supplier’s profit improvement is mainly affected by the buyer’s economic order frequencies (BOFR), and the buyer’s inventory cost performance is mainly influenced by the choice of inventory coordination policies and the magnitude of demand variation. Due to the strong influence of certain environmental factors, it seems essential for supply chain participants to analyze the environmental factors in order to obtain the full benefits of a certain QDIC policy. 21
  • 3.6 SALES REBATE CONTRACT The supplier charges the retailer a per-unit wholesale price w but gives the retailer a rebate r > 0 per unit sold above a fixed threshold t, and the retailer continues to salvage leftover units for v per unit Result: Sales rebate contract coordinate the supply chain under fixed-price newsvendor model. Retailer’s profit function: r (q, p, w s , r , t ) R (q, p ) vq (c r w s )q r ( S (t , p ) S ( q , p )) Retailer’s Marginal profit: R (q, p ) (c r ws v ), q t r (q, p, w s , r , t ) q q R (q, p ) (1 r) (c r ws v ), q t q Observations: 1. Sales-rebate acts like revenue sharing for q t as one contract parameter, r, modifies retailer’s marginal revenue and second parameter, w s , modifies retailer’s marginal cost. 2. For q t, sales rebate doesn’t modify retailers’ marginal revenue whereas revenue sharing does. 3. The retailer’s profit function may not be unimodal like the supply chain profit because of the inclusion of absolute threshold. 4. The supplier will earn positive profit only when q 0 t Result: Sales Rebate fails to coordinate under price-setting newsvendor For optimality, we want 22
  • 0 0 (q , p ) R (q , p ) 0 p p 0 0 0 q 0 r (q , p, w s , r , t ) R (q , p ) F (q , p ) r 0 p p t p 0 This is possible only when t q , i.e., w s c s in order to coordinate quantity which means supplier earns zero profit. 3.7 TWO-PART TARIFF With a two-part tariff the supplier charges a per unit wholesale price, w 2 , and a fixed fee, F. Coordination is achieved with marginal cost pricing, w 2 cs , because then the retailer’s profit is (q, p ) F . The fixed fee serves to allocate profit between the supplier and the retailer. Two-part tariffs achieve the same results as a revenue-sharing contract in the single-retailer model. 3.8 FRANCHISE CONTRACT A franchise contract combines revenue sharing with a two-part tariff: The supplier charges a fixed fee, a per-unit wholesale price, and a revenue share per transaction, which is usually called a royalty rate. As a result, a franchise contract enjoys the capabilities of both revenue sharing and two-part tariffs. Interpretation of R ( q , p ) : Define S ( q , p ) Expected unit Sales Then, Expected Sales Revenue = pS ( q , p ) Expected Salvage Revenue = v(q- S ( q , p ) ) Total Revenue = (p-v) S ( q , p ) + vq Interpretation of R ( q , p ) 23
  • Appendix: (marginal Revenue curve analysis) The curvature of the marginal revenue curve R ' ( q ) plays an important role in determining the contract’s efficiency and profit share . This follows from the expression for optimal wholesale price w ( q s* ) c * " q s R (q s ) * . This is shown in Figure above. At the optimal solution; R ' ( q s* ) c * " * q s R (q s ) Thus, in the optimal solution * " * q s R (q s ) , height of the triangle label a 2 , equals the height of the rectangle labeled a 3 (The triangle a 2 is formed by the tangent of the marginal revenue curve at q s* ). The supplier’s profit equals the area of the rectangle a 3 , q s* ( w ( q s* ) c ) . The triangle a 2 is an approximation for the retailer’s profit. It underestimates the retailer’s earnings if R ' ( q ) is convex and it overestimates the retailer’s profit if R ' ( q ) is concave. Because the area of the triangle is half of the area of the rectangle, the supplier’s profit share is less (more) than two-thirds if the marginal revenue is convex (concave). Turning to system efficiency, the loss in supply chain profit is 0 q ' (R (z) c ) dz * qs The corresponding region is labeled a 4 in the diagram. An approximation for this loss is the triangle formed by dropping the tangent to R ' ( q s* ) from q s* down to where it crosses 24
  • the horizontal at c. This happens at 2 q s* . The area of the resulting triangle is again equal to half of the supplier’s profit. It is less than the area of a 4 if R ' ( q ) is convex, but greater if R ' ( q ) is concave. It is straightforward to see that this also implies 0 0 * q q qs when marginal revenue is concave (convex). Consequently, 2 2 coordinating the system increases total profit by more (less) than 50% of the supplier’s profit if marginal revenue is convex (concave). It increases by exactly 50% of the supplier’s profit if marginal revenue is linear. 25
  • References Cachon,P. 2001. Supply Chain Coordination with Contracts, Handbooks of operations research and Management Science Dana, J. and K. Spier. 1999. Revenue sharing and vertical control in the video rental market. The Journal of industrial Economics. 59(3). 223-245 Tsay, A. 1999. Quantity-Flexibility contract and supplier-customer incentives. Management Science. 45(10). 1339-58. Pasternack, B. 1985. Optimal pricing and returns policies for perishable commodities. Marketing Science. 4(2). 166-76. Lariviere, M. and E. Porteus. 2001. Selling to the newsvendor: An Analysis of Price - Only Contratcts. Management Science. 3(4). 293-305. Gerchak, Y and Y. Wang, 2004. Revenue-Sharing vs.Wholesale-Price Contracts in Assembly Systems with Random Demand, Production and operations Management. 13(1), 23-33 Anupindi, R. and Y. Bassok. 1999. Centralization of stocks: retailers vs. manufacturer. Management Science. 45(2). 178-91. Shin, H. and W.C. Benton. 2004. Quantity Discount-Based Inventory Coordination: Effectiveness and Critical Environmental Factors, Production and operations Management. 13(1). 63-76. 26