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Supply Chain Contracts Zhentong Lu SOE and IAR, SUFE April 27, 2017

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Page 1: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain Contracts

Zhentong Lu

SOE and IAR, SUFE

April 27, 2017

Page 2: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain/B2B Contracts

I based on “Pricing in Business-to-Business Contracts: SharingRisk, Prot and Information,” by Murat Kaya and Ozalp Ozer,The Oxford Handbook of Pricing Management

I question: how pricing terms in business-to-business (B2B)contracts can be used to align incentives, and share risks,profits and information between the members of a supplychain

I specifically, we shall discuss how pricing terms in B2Bcontracts can be used to share inventory risk, which comesfrom the possible mismatch between the inventory/productionlevel and uncertain demand

I manufacture vs retailer (facing uncertainty demand): how B2Bcontracts affect the retailer’s product availability level and onher product pricing policy

1 / 18

Page 3: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain/B2B Contracts

I based on “Pricing in Business-to-Business Contracts: SharingRisk, Prot and Information,” by Murat Kaya and Ozalp Ozer,The Oxford Handbook of Pricing Management

I question: how pricing terms in business-to-business (B2B)contracts can be used to align incentives, and share risks,profits and information between the members of a supplychain

I specifically, we shall discuss how pricing terms in B2Bcontracts can be used to share inventory risk, which comesfrom the possible mismatch between the inventory/productionlevel and uncertain demand

I manufacture vs retailer (facing uncertainty demand): how B2Bcontracts affect the retailer’s product availability level and onher product pricing policy

1 / 18

Page 4: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain/B2B Contracts

I based on “Pricing in Business-to-Business Contracts: SharingRisk, Prot and Information,” by Murat Kaya and Ozalp Ozer,The Oxford Handbook of Pricing Management

I question: how pricing terms in business-to-business (B2B)contracts can be used to align incentives, and share risks,profits and information between the members of a supplychain

I specifically, we shall discuss how pricing terms in B2Bcontracts can be used to share inventory risk, which comesfrom the possible mismatch between the inventory/productionlevel and uncertain demand

I manufacture vs retailer (facing uncertainty demand): how B2Bcontracts affect the retailer’s product availability level and onher product pricing policy

1 / 18

Page 5: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Newsvendor as Integrated Firm

I a newsvendor owns both the printing (manufacturing) facilityand the distribution operations, i.e., the supply chain for thenewspaper is vertically integrated

I maximize expected profit

ΠI (Q) = pE [min (Q, d)] + v {Q − E [min (Q, d)]} − cQ

= (p − v)E [min (Q, d)]− (c − v)Q

I optimal production/stocking quantity

Q I = F−1

(p − c

p − v

)where F is the CDF of demand

2 / 18

Page 6: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Newsvendor as Integrated Firm

I a newsvendor owns both the printing (manufacturing) facilityand the distribution operations, i.e., the supply chain for thenewspaper is vertically integrated

I maximize expected profit

ΠI (Q) = pE [min (Q, d)] + v {Q − E [min (Q, d)]} − cQ

= (p − v)E [min (Q, d)]− (c − v)Q

I optimal production/stocking quantity

Q I = F−1

(p − c

p − v

)where F is the CDF of demand

2 / 18

Page 7: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Newsvendor as Integrated Firm

I a newsvendor owns both the printing (manufacturing) facilityand the distribution operations, i.e., the supply chain for thenewspaper is vertically integrated

I maximize expected profit

ΠI (Q) = pE [min (Q, d)] + v {Q − E [min (Q, d)]} − cQ

= (p − v)E [min (Q, d)]− (c − v)Q

I optimal production/stocking quantity

Q I = F−1

(p − c

p − v

)where F is the CDF of demand

2 / 18

Page 8: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract

I now, consider the case that the newsvendor disintegrates thefirm, outsources manufacturing and establishes a supply chainby agreeing on a wholesale price contract to buy the printedpapers from the manufacturer

I the newsvendor (retailer) decides the stocking quantity Q, themanufacturer produces Q and satisfies the retailer’s orderprior to the sales season

I information, including the cost and demand parameters, iscommon to both firms, i.e., there is no private information

3 / 18

Page 9: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract

I now, consider the case that the newsvendor disintegrates thefirm, outsources manufacturing and establishes a supply chainby agreeing on a wholesale price contract to buy the printedpapers from the manufacturer

I the newsvendor (retailer) decides the stocking quantity Q, themanufacturer produces Q and satisfies the retailer’s orderprior to the sales season

I information, including the cost and demand parameters, iscommon to both firms, i.e., there is no private information

3 / 18

Page 10: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract

I now, consider the case that the newsvendor disintegrates thefirm, outsources manufacturing and establishes a supply chainby agreeing on a wholesale price contract to buy the printedpapers from the manufacturer

I the newsvendor (retailer) decides the stocking quantity Q, themanufacturer produces Q and satisfies the retailer’s orderprior to the sales season

I information, including the cost and demand parameters, iscommon to both firms, i.e., there is no private information

3 / 18

Page 11: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract (Cont’d)I manufacturer’s profit

Πwm (Q) = (w − c)Q

I manufacturer’s profit is certain once the retailer submits herorder Q

I retailer’s expected profit

Πwr (Q) = (p − v)E [min (Q,D)]− (w − v)Q

I optimal stocking/order quantity is

Qw = F−1

(p − w

p − v

)I supply chain’s total profit

Πwtotal = Πw

m (Q)− Πwr (Q)

= (p − v)E [min (Q, d)]− (c − v)Q

= ΠI (Q)

4 / 18

Page 12: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract (Cont’d)I manufacturer’s profit

Πwm (Q) = (w − c)Q

I manufacturer’s profit is certain once the retailer submits herorder Q

I retailer’s expected profit

Πwr (Q) = (p − v)E [min (Q,D)]− (w − v)Q

I optimal stocking/order quantity is

Qw = F−1

(p − w

p − v

)

I supply chain’s total profit

Πwtotal = Πw

m (Q)− Πwr (Q)

= (p − v)E [min (Q, d)]− (c − v)Q

= ΠI (Q)

4 / 18

Page 13: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract (Cont’d)I manufacturer’s profit

Πwm (Q) = (w − c)Q

I manufacturer’s profit is certain once the retailer submits herorder Q

I retailer’s expected profit

Πwr (Q) = (p − v)E [min (Q,D)]− (w − v)Q

I optimal stocking/order quantity is

Qw = F−1

(p − w

p − v

)I supply chain’s total profit

Πwtotal = Πw

m (Q)− Πwr (Q)

= (p − v)E [min (Q, d)]− (c − v)Q

= ΠI (Q)

4 / 18

Page 14: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract (Cont’d)

I retailer prefers c and manufacture wants w∗, so the actualwhole sale price is between c and w∗, which may bedetermined by some bargaining process

5 / 18

Page 15: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Wholesale Price Contract (Cont’d)

I retailer prefers c and manufacture wants w∗, so the actualwhole sale price is between c and w∗, which may bedetermined by some bargaining process

5 / 18

Page 16: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Double Marginalization

I the retailer orders a quantity less than the integrated firm’soptimal quantity, i.e.,

Q I > Qw

because c < w (of course, the above inequality becomesequality if c = w)

I implication: the retailer is more likely to run out of stock

I why does the retailer order and stock less than the integratedfirm? the reason is that the retailer’s profit margin (p − w) islower than that of the integrated firm’s (p − c), while facing ahigher cost of excess inventory (w − v > c − v)

I this is parallel to “double marginalization” in the standard“monopoly-monopoly” vertical model

6 / 18

Page 17: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Double Marginalization

I the retailer orders a quantity less than the integrated firm’soptimal quantity, i.e.,

Q I > Qw

because c < w (of course, the above inequality becomesequality if c = w)

I implication: the retailer is more likely to run out of stock

I why does the retailer order and stock less than the integratedfirm? the reason is that the retailer’s profit margin (p − w) islower than that of the integrated firm’s (p − c), while facing ahigher cost of excess inventory (w − v > c − v)

I this is parallel to “double marginalization” in the standard“monopoly-monopoly” vertical model

6 / 18

Page 18: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain Inefficiency

I supply chain inefficiency ΠI(Q I

)− Πw

total (Qw ): how muchmoney the manufacturer and the retailer leave on the table

I with a proper B2B contract mechanism, the firms can sharethis extra money and achieve an improvement over what theyearn under the existing wholesale price agreement

7 / 18

Page 19: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Supply Chain Inefficiency

I supply chain inefficiency ΠI(Q I

)− Πw

total (Qw ): how muchmoney the manufacturer and the retailer leave on the table

I with a proper B2B contract mechanism, the firms can sharethis extra money and achieve an improvement over what theyearn under the existing wholesale price agreement

7 / 18

Page 20: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Improper Risk Sharing

I note: lower case π’s denote the payoffs as a function ofdemand realization d

I improper risk sharing: the retailer’s upside potential (downsiderisk) is lower (higher) than the integrated firm’s

8 / 18

Page 21: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Improper Risk Sharing

I note: lower case π’s denote the payoffs as a function ofdemand realization d

I improper risk sharing: the retailer’s upside potential (downsiderisk) is lower (higher) than the integrated firm’s

8 / 18

Page 22: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Coordination and Efficiency

I disintegrated supply chain achieves coordination if theexpected total supply chain profit under the contract is equalto the integrated firm’s optimal expected profit

I we could measure a B2B contract’s efficiency by the ratio ofthe total supply chain expected profit under the contract tothe integrated firm’s optimal expected profit, i.e.,(Πr + Πm)/ ΠI

I channel efficiency (or, contract efficiency) does not indicatehow the total profit is shared, e.g., a wholesale price contractwith w close to c would be very efficient but it leaves almostno profit to the manufacturer

9 / 18

Page 23: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Coordination and Efficiency

I disintegrated supply chain achieves coordination if theexpected total supply chain profit under the contract is equalto the integrated firm’s optimal expected profit

I we could measure a B2B contract’s efficiency by the ratio ofthe total supply chain expected profit under the contract tothe integrated firm’s optimal expected profit, i.e.,(Πr + Πm)/ ΠI

I channel efficiency (or, contract efficiency) does not indicatehow the total profit is shared, e.g., a wholesale price contractwith w close to c would be very efficient but it leaves almostno profit to the manufacturer

9 / 18

Page 24: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Coordination and Efficiency

I disintegrated supply chain achieves coordination if theexpected total supply chain profit under the contract is equalto the integrated firm’s optimal expected profit

I we could measure a B2B contract’s efficiency by the ratio ofthe total supply chain expected profit under the contract tothe integrated firm’s optimal expected profit, i.e.,(Πr + Πm)/ ΠI

I channel efficiency (or, contract efficiency) does not indicatehow the total profit is shared, e.g., a wholesale price contractwith w close to c would be very efficient but it leaves almostno profit to the manufacturer

9 / 18

Page 25: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract

I buyback contract (w , b): the retailer pays the manufacturer awholesale price w per unit prior to the selling season; at theend of the season she returns any leftover units to themanufacturer and receives b per unit; the manufacturer cansalvage the returned units at v per unit

I with a buyback contract, the retailer’s overage cost is w − band her underage cost is p − w , so the retailer’s optimal orderis

Qb = F−1

(p − w

p − b

)> F−1

(p − w

p − v

)= Qw

I how to design a contract so that Q I = F−1(p−cp−v

)could be

achieved?

10 / 18

Page 26: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract

I buyback contract (w , b): the retailer pays the manufacturer awholesale price w per unit prior to the selling season; at theend of the season she returns any leftover units to themanufacturer and receives b per unit; the manufacturer cansalvage the returned units at v per unit

I with a buyback contract, the retailer’s overage cost is w − band her underage cost is p − w , so the retailer’s optimal orderis

Qb = F−1

(p − w

p − b

)> F−1

(p − w

p − v

)= Qw

I how to design a contract so that Q I = F−1(p−cp−v

)could be

achieved?

10 / 18

Page 27: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract

I buyback contract (w , b): the retailer pays the manufacturer awholesale price w per unit prior to the selling season; at theend of the season she returns any leftover units to themanufacturer and receives b per unit; the manufacturer cansalvage the returned units at v per unit

I with a buyback contract, the retailer’s overage cost is w − band her underage cost is p − w , so the retailer’s optimal orderis

Qb = F−1

(p − w

p − b

)> F−1

(p − w

p − v

)= Qw

I how to design a contract so that Q I = F−1(p−cp−v

)could be

achieved?

10 / 18

Page 28: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I the contract parameters (w , b) can be set such that theretailer’s critical ratio is equal to the integrated firm’s criticalratio, i.e.,

p − w

p − b=

p − c

p − v

I rearranging the terms, we obtain the relationship betweenprice parameters w and b of a coordinating buyback contract

b =p (w + v − c)− vw

p − c(1)

I the coordination relation is independent of the demanddistribution: this allows a coordinating contract to be designedwithout market demand information

I any (w , b) pair satisfies the above equation help achievechannel coordination

11 / 18

Page 29: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I the contract parameters (w , b) can be set such that theretailer’s critical ratio is equal to the integrated firm’s criticalratio, i.e.,

p − w

p − b=

p − c

p − v

I rearranging the terms, we obtain the relationship betweenprice parameters w and b of a coordinating buyback contract

b =p (w + v − c)− vw

p − c(1)

I the coordination relation is independent of the demanddistribution: this allows a coordinating contract to be designedwithout market demand information

I any (w , b) pair satisfies the above equation help achievechannel coordination

11 / 18

Page 30: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I interpret the buyback contract via expected profits

Πbr (Q) = pE [min (Q,D)] + bE [Q −min (Q,D)]− wQ

= (p − b)E [min (Q,D)]− (w − b)Q

Πbtotal (Q) = (p − v)E [min (Q, d)]− (c − v)Q

I profit sharing: if the contract parameter w and b satisfy

p − b = θ (p − v) and w − b = θ (c − v)

for some θ, then we have Πbr (Q) = θΠb

total (Q)I the retailer’s optimal stocking quantity coincides with the

supply chain optimal stocking quantity so the supply chain iscoordinated

I the two equations are identical to (1) and imply θ = p−wp−c ,

which is a rule of profit sharingI higher buyback price - lower inventory risk - higher whole sale

price - lower share of profit

12 / 18

Page 31: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I interpret the buyback contract via expected profits

Πbr (Q) = pE [min (Q,D)] + bE [Q −min (Q,D)]− wQ

= (p − b)E [min (Q,D)]− (w − b)Q

Πbtotal (Q) = (p − v)E [min (Q, d)]− (c − v)Q

I profit sharing: if the contract parameter w and b satisfy

p − b = θ (p − v) and w − b = θ (c − v)

for some θ, then we have Πbr (Q) = θΠb

total (Q)I the retailer’s optimal stocking quantity coincides with the

supply chain optimal stocking quantity so the supply chain iscoordinated

I the two equations are identical to (1) and imply θ = p−wp−c ,

which is a rule of profit sharingI higher buyback price - lower inventory risk - higher whole sale

price - lower share of profit

12 / 18

Page 32: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I compare the payoffs between a wholesale price contract (darkcolor) and a coordinating buyback contract (light color): thebuyback contract enables the retailer to share her downsiderisk with the manufacturer

13 / 18

Page 33: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I buyback contracts are very popular in the book publishingindustry: around 30-35% of new hardcover books are returnedto their publishers

I to minimize transportation costs, a bookstore often ships backnot the book itself, but only its cover to prove that the bookwas not sold

I a manufacture can also use a buyback contract toI signal the retailer high demand potential for the productI buy back unsold units with the purpose of redistributing them

to the retailers that need additional unitsI prevent them from being sold at deep discounts, which would

damage his brand image

14 / 18

Page 34: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

The Buyback Contract (Cont’d)

I buyback contracts are very popular in the book publishingindustry: around 30-35% of new hardcover books are returnedto their publishers

I to minimize transportation costs, a bookstore often ships backnot the book itself, but only its cover to prove that the bookwas not sold

I a manufacture can also use a buyback contract toI signal the retailer high demand potential for the productI buy back unsold units with the purpose of redistributing them

to the retailers that need additional unitsI prevent them from being sold at deep discounts, which would

damage his brand image

14 / 18

Page 35: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Contracting on Quantity Sales

I consider a contract (w , f )I the retailer pays to the manufacturer w per unit ordered and

sells the product at price p per unitI for each unit sold, the retailer keeps fp and transfers (1− f ) p

to the manufacturer

I depending on the value of f , there are two possible casesI when 0 < f < 1, the retailer shares (1− f ) percent of her

sales revenue with the manufacturer: this is interpreted as arevenue sharing contract

I when f > 1, the manufacturer pays (f − 1) p for each unit soldto the retailer: this is interpreted as a rebate contract

15 / 18

Page 36: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Contracting on Quantity Sales

I consider a contract (w , f )I the retailer pays to the manufacturer w per unit ordered and

sells the product at price p per unitI for each unit sold, the retailer keeps fp and transfers (1− f ) p

to the manufacturer

I depending on the value of f , there are two possible casesI when 0 < f < 1, the retailer shares (1− f ) percent of her

sales revenue with the manufacturer: this is interpreted as arevenue sharing contract

I when f > 1, the manufacturer pays (f − 1) p for each unit soldto the retailer: this is interpreted as a rebate contract

15 / 18

Page 37: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Revenue Sharing and Rebate ContractI with a revenue sharing or rebate contract, the retailer’s

underage cost is fp − w and overage cost is w − v , so theretailer’s optimal stocking quantity satisfies

Qrc = F−1

(fp − w

fp − v

)

I the supply chain can be coordinated if the retailer’s criticalratio is equal to the integrated firm’s critical ratio, i.e.,fp−wfp−v = p−c

p−v , which implies

f =w (p − v)− v (p − c)

p (c − v)

I risk and profit sharing property of (w , f rc)

Πrcr (Q) = (fp − c)E [min (Q,D)]− (w − v)Q

=

(w − v

c − v

){(p − v)E [min (Q,D)]− (c − v)Q}

=

(w − v

c − v

)Πrc

total (Q)

16 / 18

Page 38: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Revenue Sharing and Rebate ContractI with a revenue sharing or rebate contract, the retailer’s

underage cost is fp − w and overage cost is w − v , so theretailer’s optimal stocking quantity satisfies

Qrc = F−1

(fp − w

fp − v

)I the supply chain can be coordinated if the retailer’s critical

ratio is equal to the integrated firm’s critical ratio, i.e.,fp−wfp−v = p−c

p−v , which implies

f =w (p − v)− v (p − c)

p (c − v)

I risk and profit sharing property of (w , f rc)

Πrcr (Q) = (fp − c)E [min (Q,D)]− (w − v)Q

=

(w − v

c − v

){(p − v)E [min (Q,D)]− (c − v)Q}

=

(w − v

c − v

)Πrc

total (Q)

16 / 18

Page 39: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Revenue Sharing and Rebate ContractI with a revenue sharing or rebate contract, the retailer’s

underage cost is fp − w and overage cost is w − v , so theretailer’s optimal stocking quantity satisfies

Qrc = F−1

(fp − w

fp − v

)I the supply chain can be coordinated if the retailer’s critical

ratio is equal to the integrated firm’s critical ratio, i.e.,fp−wfp−v = p−c

p−v , which implies

f =w (p − v)− v (p − c)

p (c − v)

I risk and profit sharing property of (w , f rc)

Πrcr (Q) = (fp − c)E [min (Q,D)]− (w − v)Q

=

(w − v

c − v

){(p − v)E [min (Q,D)]− (c − v)Q}

=

(w − v

c − v

)Πrc

total (Q)

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Page 40: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Revenue Sharing and Rebate Contract

I compare the payoffs between a wholesale price contract (darkcolor) and a coordinating revenue sharing/rebate contract(light color)

I revenue sharing: reduce retailer’s downside risk (overage cost)I rebate: increase the retailer’s upside risk (shortage cost)

17 / 18

Page 41: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Other B2B Contracts

I B2B contracts help a manufacturer and a retailer achievechannel coordination by reallocating the risk of inventoryexcess and shortage, i.e., align the retailer’s (decision maker’s)objective with that of the integrated rm’s (central decisionmaker’s).

I in general, most B2B contracts can be categorized underthree groups

I reduce the risk of excess inventory (downside risk): buyback,revenue sharing, etc.

I decrease the risk of shortage (upside risk): rebate, etc.I flexibility to target both risks simultaneously: reduce the

wholesale price, e.g., quantity discount, which simultaneouslyincreases the cost of underage and decreases the cost ofoverage for the retailer

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Page 42: Supply Chain Contracts - Zhentong Lu Chain/B2B Contracts I based on \Pricing in Business-to-Business Contracts: Sharing Risk, Prot and Information," by Murat Kaya and Ozalp Ozer, The

Other B2B Contracts

I B2B contracts help a manufacturer and a retailer achievechannel coordination by reallocating the risk of inventoryexcess and shortage, i.e., align the retailer’s (decision maker’s)objective with that of the integrated rm’s (central decisionmaker’s).

I in general, most B2B contracts can be categorized underthree groups

I reduce the risk of excess inventory (downside risk): buyback,revenue sharing, etc.

I decrease the risk of shortage (upside risk): rebate, etc.I flexibility to target both risks simultaneously: reduce the

wholesale price, e.g., quantity discount, which simultaneouslyincreases the cost of underage and decreases the cost ofoverage for the retailer

18 / 18