Report

ISyE 8813Logistics 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

[email protected]

[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

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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 = , where is a measure of retailer’s effort

The retailer incurs an effort cost but no incremental cost,

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[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.

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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:

Supplier:

Supply Chain: where 1

Theorem 1. Consider the set of revenue sharing contracts with

and . With those contracts, the firms’ profit functions are

and

1 Note that is unit production cost, is the retailer’s cost excluding payments to supplier and is the channel (total) cost.

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Furthermore, 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

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

5. Extreme value raises two- issues-

(a) Retailer’s profit function become quite flat as ; while remains

optimal, deviation from imposes little penalty on the retailer.

(b) : 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.

II. Multiple Retailers:

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).

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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 : note here includes the salvage revenue

where

and

The firms’ optimal profits are

Observations:

1. Coordinating wholesale price is same as in the single retailer case with the addition of

term. This term represents the revenue externality imposed by retailer 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 due to addition of a fixed term.

3. Range of each 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 .

Question: Why Revenue Sharing fails to coordinate in the Price Setting Newsvendor

Model?

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At an optimal solution, we have

but for ,

Thus, Revenue Sharing stumbles when revenue is a function of both quantity and price,

III. Retail Effort: Revenue sharing fails!

Retailer’s Profit:

Integrated Supply Chain Profit:

Let be an optimal solution. Then, we have

But for the retailer

Thus, revenue sharing coordinates effort decision only when , but then retailer’s

quantity decision is coordinated for , i.e., supplier makes zero profit.

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

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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 from sales of

final product, the retailer will pay supplier 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 per unit ordered.

I. Single Supplier Single Retailer

Profit Functions:

Retailer:

Supplier:

Supply Chain:

Retailer’s optimal quantity is the unique solution to

Supplier’s optimal quantity is the unique solution to

Supply Chain’s optimal quantity is the unique solution to

Let be supplier’s optimal quantity. Then

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i.e.

Since the supply chain performance is not

optimal at ; i.e., <

Also decreasing in and implies that under the Wholesale price

contract: as compared to revenue sharing contract where: .

Since is decreasing, only when, . 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

of the contract, and the supplier’s profit share

From a supplier’s perspective wholesale price contract is attractive if both the

performance measures are high. The curvature of the marginal revenue curve plays

a vital role in determining the contract’s efficiency and profit share (for details refer

appendix).

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,

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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 . 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, ; rather than to his order quantity, :

Nevertheless, since ; the supplier’s optimal wholesale price is lower

than in the single season model. Thus, the efficiency of the wholesale price contract is

even better than in the single season model.

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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 per unit purchased, but pays

the retailer per unit remaining at the end of the season.

I. Single Supplier Single Retailer

Profit Functions:

Retailer:

Supplier:

Supply Chain:

Result: “Revenue Sharing is equivalent to Buybacks in the fixed price newsvendor case”

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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, , there exits a unique buy-back contract, ,

that generates the same profit for each firm from any realization of demand:

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: ( = salvage price)

Retailer:

Supply Chain:

The optimal effort satisfies

But for the retailer

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Thus, 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 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.

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 . Thus, Revenue

3 Bernstein and Federgruen (2005) have the supplier earning the salvage revenue and . Their

coordinating contract is and , where .

Let 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 .

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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 units for per unit at the start of the season and may return up

to units at the end of the season for a full refund, . Units not returned are

salvaged for 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:

Fixed-Price Newsvendor model: For supply Chain Coordination, we want

, which holds for

, where is the distribution function of

Retailer’s demand

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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 . This happens because the term

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

and

These two conditions are satisfied for i.e. .

Result: The only coordinating contract has the supplier pricing at marginal cost and

earning zero profit.

II. Retail Effort

Profit Function Retailer:

The optimal effort satisfies

and

Result: Quantity Flexibility contract cannot coordinate when demand depends on retail

effort.

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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.

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

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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.

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.

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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.

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 per unit purchased where is a decreasing function.

Profit Functions:

Retailer:

Supplier:

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Supply Chain:

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

[3a]

for . maximizes the retailers profit and

[3b]

Proof: Simply substitute in to get [3b]. As retailer keeps as the revenue,

retailer’s optimal price for any given q equals supply chain optimal price. Thus, is

optimal as is optimal given (This clearly holds from [3b] for all ).

Observations: Retailer’s expected profit is proportional to the supply chain’s expected

profit.

Fixed-Price Newsvendor model- for a fixed price 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.

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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 is a function of , 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.

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:

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Retailer’s Marginal profit:

Observations:

1. Sales-rebate acts like revenue sharing for as one contract parameter, r, modifies

retailer’s marginal revenue and second parameter, , modifies retailer’s marginal

cost.

2. For , 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

Result: Sales Rebate fails to coordinate under price-setting newsvendor

For optimality, we want

This is possible only when , i.e., in order to coordinate quantity which means

supplier earns zero profit.

3.7 TWO-PART TARIFF

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With a two-part tariff the supplier charges a per unit wholesale price, , and a fixed fee,

F. Coordination is achieved with marginal cost pricing, , because then the

retailer’s profit is . 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 :Define Expected unit SalesThen, Expected Sales Revenue = Expected Salvage Revenue = v(q- )Total Revenue = (p-v) + vq

Interpretation of

Appendix: (marginal Revenue curve analysis)

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The curvature of the marginal revenue curve plays an important role in determining

the contract’s efficiency and profit share . This follows from the expression for optimal

wholesale price . This is shown in Figure above. At the optimal solution;

Thus, in the optimal solution

, height of the triangle label , equals the

height of the rectangle labeled (The triangle is formed by the tangent of the

marginal revenue curve at ). The supplier’s profit equals the area of the rectangle ,

. The triangle is an approximation for the retailer’s profit. It

underestimates the retailer’s earnings if is convex and it overestimates the

retailer’s profit if 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

The corresponding region is labeled in the diagram. An approximation for this loss is

the triangle formed by dropping the tangent to from down to where it crosses the

horizontal at c. This happens at 2 . The area of the resulting triangle is again equal to

half of the supplier’s profit. It is less than the area of if is convex, but greater if

is concave. It is straightforward to see that this also implies

when marginal revenue is concave (convex). Consequently, 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.

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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.

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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 -

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Gerchak, Y and Y. Wang, 2004. Revenue-Sharing vs.Wholesale-Price Contracts in

Assembly Systems with Random Demand, Production and operations Management.

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Anupindi, R. and Y. Bassok. 1999. Centralization of stocks: retailers vs. manufacturer.

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