supply chain coordination with contracts. a typical supply chain

Supply Chain Coordination Supply Chain Coordination with Contractswith Contracts

A Typical Supply ChainA Typical Supply Chain

A Paradigm ShiftA Paradigm Shift

From optimization within an From optimization within an organization to optimization for a organization to optimization for a SC.SC.

Design incentive structures Design incentive structures (contracts) to coordinate various (contracts) to coordinate various parties of the SC to achieve system parties of the SC to achieve system optimization.optimization.

Why Coordination?Why Coordination?

Each player (company) in the SC has Each player (company) in the SC has different, and often time, conflicting different, and often time, conflicting objectives. objectives.

These individual objectives are usually not These individual objectives are usually not in line with that of the SC.in line with that of the SC.

An incentive structure (contract) is needed An incentive structure (contract) is needed to align the optimization action of each to align the optimization action of each individual player for the interest of the SC individual player for the interest of the SC (Contract Design)(Contract Design)

Make the pie bigger then divide!Make the pie bigger then divide!

Popular SC Systems Studied Popular SC Systems Studied in Literature:in Literature:

Two levels: a supplier and a retailer (or multiple Two levels: a supplier and a retailer (or multiple retailers).retailers).

Product: seasonal or stable (newsvendor v.s. Product: seasonal or stable (newsvendor v.s. EOQ)EOQ)

Demand:Demand: deterministic or stochasticdeterministic or stochastic insensitive or sensitive to retail price insensitive or sensitive to retail price

Objective Function: risk neutral or risk averse.Objective Function: risk neutral or risk averse. Other variations: information asymmetry, multiple Other variations: information asymmetry, multiple

replenishment opportunities, competing retailers, replenishment opportunities, competing retailers, ……

Contract Design and EvaluationContract Design and Evaluation

For a given SC structure, which For a given SC structure, which contracts coordinate the SC? contracts coordinate the SC?

How does the contract allocate profit How does the contract allocate profit among players of the SC?among players of the SC?

Efficiency v.s. administrative cost for a Efficiency v.s. administrative cost for a given contract.given contract.

Newsvendor ProblemNewsvendor Problem

News paper demand unknown but News paper demand unknown but distribution known with cdf F.distribution known with cdf F.

Underage cost (Price-Cost): Underage cost (Price-Cost): CCuu

Overage cost (Cost - Salvage): Overage cost (Cost - Salvage): CCoo

How much to order to maximize the How much to order to maximize the expected profit? expected profit?

Newsvendor SolutionNewsvendor Solution

At the best order quantity, At the best order quantity, marginal underage = marginal overagemarginal underage = marginal overage=> [1- F(=> [1- F(QQ)] : )] : CCuu = F( = F(QQ) : ) : CCoo => F(=> F(QQ) = ) = CCuu / ( / (CCuu + + CCoo)) (1)(1)

If F is a Normal distribution with mean If F is a Normal distribution with mean μμ and std and std σσ , , => => QQ = = μμ + + σ σ : z, : z,where z is the z-value based on (1).where z is the z-value based on (1).

Performance MeasuresPerformance Measures

Expected lost sales (for Normal dist.): Expected lost sales (for Normal dist.): = = σσ : [Normdist(z,0,1,0)-z : (1-Normsdist(z,0,1,1)] : [Normdist(z,0,1,0)-z : (1-Normsdist(z,0,1,1)]

Expected sales:Expected sales:= Exp demand – Exp lost sales= Exp demand – Exp lost sales

Expected leftover inv:Expected leftover inv:= Q – Exp sales= Q – Exp sales

Expected profit:Expected profit:= (Price-Cost)*Exp sales = (Price-Cost)*Exp sales

– – (Cost-Salvage)*Exp inv(Cost-Salvage)*Exp inv

A Sunglass Supply ChainA Sunglass Supply Chain

Sunglass designer and manufacturer Sunglass designer and manufacturer (called supplier): (called supplier):

Manufacturing cost: $35Manufacturing cost: $35 Whole sale price: $75Whole sale price: $75

Sunglass retailer:Sunglass retailer: Retail price: $115Retail price: $115 End-of-season price: $25End-of-season price: $25

Estimated demand: Estimated demand: Normal ( =250, =125)Normal ( =250, =125)

Best Decision for RetailerBest Decision for Retailer

Underage cost CUnderage cost Cuu : $115 - $75 = $40 : $115 - $75 = $40 Overage cost COverage cost Coo : $75 - $25 = $50 : $75 - $25 = $50 CCuu / (C / (Cuu + C + Coo) = 40 / (40 + 50) = 44.4%) = 40 / (40 + 50) = 44.4% z = -0.1397z = -0.1397 Q = 250 + (-0.1397)*125 = 233Q = 250 + (-0.1397)*125 = 233 Expected sale = 191Expected sale = 191 Expected leftover Inventory = 42Expected leftover Inventory = 42 Expected profit = $40*191-$50*42 =$5,540Expected profit = $40*191-$50*42 =$5,540

SupplierSupplier and System Profitand System Profit

Supplier’s profit = 233*($75-$35) = $9,320Supplier’s profit = 233*($75-$35) = $9,320 System profit = $5,540+$9,320 = $14,860.System profit = $5,540+$9,320 = $14,860. Retailer takes all riskRetailer takes all risk Supplier assumes no riskSupplier assumes no risk Can we do better for the supply chain Can we do better for the supply chain

(system)?(system)?

What’s Best for the System?What’s Best for the System?

Underage cost CUnderage cost Cuu : $115 - $35 = $80 : $115 - $35 = $80 Overage cost COverage cost Coo : $35 - $25 = $10 : $35 - $25 = $10 CCuu / (C / (Cuu + C + Coo) = 80 / (80 + 10) = 88.9%) = 80 / (80 + 10) = 88.9% z = 1.2206z = 1.2206 Q = 250 + 1.2206 *125 = 403Q = 250 + 1.2206 *125 = 403 Expected sale = 243Expected sale = 243 Expected leftover = 160Expected leftover = 160 Expected system profit = $17,840 Expected system profit = $17,840

=>19% profit increase!=>19% profit increase!

How to Improve System How to Improve System PerformancePerformance

Retailer needs to order more!Retailer needs to order more! Option 1: Reduce whole sale priceOption 1: Reduce whole sale price What happened?What happened? We need a win-win (not win-lose) We need a win-win (not win-lose)

mechanism mechanism Option 2: How about buy back contract?Option 2: How about buy back contract? Specified by a whole sale price and a buy Specified by a whole sale price and a buy

back price.back price.

Option 1: Reduce whole sale Option 1: Reduce whole sale priceprice

What happened?What happened?

If the supplier reduce the whole sale price If the supplier reduce the whole sale price from $75 to $65, what happens?from $75 to $65, what happens?

Best Decision for RetailerBest Decision for Retailer Underage cost CUnderage cost Cuu : $115 - $65 = $50 : $115 - $65 = $50 Overage cost COverage cost Coo : $65 - $25 = $40 : $65 - $25 = $40 CCuu / (C / (Cuu + C + Coo) = 50 / (50 + 40) = 55.55%) = 50 / (50 + 40) = 55.55%


z = 0.1397z = 0.1397 Q = 250 + (0.1397)*125 = 267Q = 250 + (0.1397)*125 = 267 Expected sale = 208Expected sale = 208 Expected leftover Inventory = 59Expected leftover Inventory = 59 Expected profit = $50*208-$40*59 =$8,040Expected profit = $50*208-$40*59 =$8,040 Supplier’s profit = 267*($65-$35) = $8,010Supplier’s profit = 267*($65-$35) = $8,010 System profit = $5,540+$9,320 = $16,050.System profit = $5,540+$9,320 = $16,050.


Conclusion: System total profit will Conclusion: System total profit will increase but the supplier’s profit will increase but the supplier’s profit will decrease.decrease.

Supplier will not reduce selling price to Supplier will not reduce selling price to retailer. NO COORDINATION.retailer. NO COORDINATION.

In fact, at whole sale price of $85.5, the In fact, at whole sale price of $85.5, the supplier’s profit maximized.supplier’s profit maximized.

Option 2: How about buy back Option 2: How about buy back contract?contract?

Assume that the supplier offers to buy Assume that the supplier offers to buy back unsold items back at the price of $40 back unsold items back at the price of $40 each, what happens?each, what happens?

Retailer:Retailer: Underage cost CUnderage cost Cuu : $115 - $75 = $40 : $115 - $75 = $40 Overage cost COverage cost Coo : $75 - $30 = $45 : $75 - $30 = $45 CCuu / (C / (Cuu + C + Coo) = 40 / (40 + 45) =0.4707) = 40 / (40 + 45) =0.4707 z = -0.0738z = -0.0738

Option 2: How about buy back Option 2: How about buy back contract?contract?

Q = 250 + (-0.0738)*125 = 241Q = 250 + (-0.0738)*125 = 241 Expected sale = 195Expected sale = 195 Expected leftover = 45Expected leftover = 45 Expected profit = $5,775Expected profit = $5,775

Supplier:Supplier: Suppliers profit Suppliers profit

= 241*($75-$35) - 45*($30-$25)=$9,415= 241*($75-$35) - 45*($30-$25)=$9,415 System profit = $5,775+$9,415=$15,190System profit = $5,775+$9,415=$15,190All better off.All better off.

Retailer’s Profit with Retailer’s Profit with BB Price at $65BB Price at $65

Underage cost CUnderage cost Cuu : $115 - $75 = $40 : $115 - $75 = $40 Overage cost COverage cost Coo : $75 - $65 = $10 : $75 - $65 = $10 CCuu / (C / (Cuu + C + Coo) = 40 / (40 + 10) = 80%) = 40 / (40 + 10) = 80% z = 0.8416z = 0.8416 Q = 250 + 0.8416*125 = 355Q = 250 + 0.8416*125 = 355 Expected sale = 236Expected sale = 236 Expected leftover = 119Expected leftover = 119 Expected profit = $8,250Expected profit = $8,250

Supplier’s and System Profit with Supplier’s and System Profit with BB Price at $65BB Price at $65

Suppliers profit Suppliers profit

= 355*($75-$35) - 119*($65-$25)=$9,440= 355*($75-$35) - 119*($65-$25)=$9,440 System profit = $8,250 + $9,440=$17,690System profit = $8,250 + $9,440=$17,690 System profit is higherSystem profit is higher Both supplier and retailer are also better Both supplier and retailer are also better

off (Win-Win).off (Win-Win). How to improve system profit further?How to improve system profit further?

Optimal Whole Sale and BB PriceOptimal Whole Sale and BB Price

Need to make sure retailer’s Q is optimal Need to make sure retailer’s Q is optimal for the system.for the system.

System Q is determined by System Q is determined by

(Price-Cost)/(Price-Cost + Cost-Salvage)(Price-Cost)/(Price-Cost + Cost-Salvage) Retailer’s Q is determined byRetailer’s Q is determined by

(Price-Whole)/(Price-Whole + Whole-(Price-Whole)/(Price-Whole + Whole-BuyBack)BuyBack)

Two ratios should equal to each otherTwo ratios should equal to each other


Optimal Buy Back Price =Optimal Buy Back Price =

Price – (Price-Whole Sale Price)*Price – (Price-Whole Sale Price)*

(Price-Salvage)/(Price-Cost)(Price-Salvage)/(Price-Cost) Profit calculationsProfit calculations


If the whole sale price is $75, the optimal BB If the whole sale price is $75, the optimal BB price must be $70.price must be $70.

RetailerRetailer Underage cost CUnderage cost Cuu : $115 - $75 = $40 : $115 - $75 = $40 Overage cost COverage cost Coo : $75 - $70 = $5 : $75 - $70 = $5 CCuu / (C / (Cuu + C + Coo) = 40 / (40 + 5) = 0.8889) = 40 / (40 + 5) = 0.8889 z = 1.2206z = 1.2206 Q = 250 + 1.2206*125 = 403Q = 250 + 1.2206*125 = 403 Expected profit =$8,920Expected profit =$8,920


SupplierSupplier Expected Profit =$8,920Expected Profit =$8,920 Total Expected Profit = $17,840Total Expected Profit = $17,840

Are they happy?Are they happy? Not for supplierNot for supplier

ObservationObservation

To keep the To keep the CCuu / (C / (Cuu + C + Coo) = 0.8889, when ) = 0.8889, when whole sale price (as well as BB price) whole sale price (as well as BB price) increases, the supplier’s profit increasesincreases, the supplier’s profit increases

When whole sale price is $85.5 and BB When whole sale price is $85.5 and BB price is $81.81,price is $81.81,

Retailer’s expected profit is $6,565.5Retailer’s expected profit is $6,565.5 Supplier’s profit is $11,261.50Supplier’s profit is $11,261.50 Both are better offBoth are better off

ObservationObservation

When whole sale price is $90.13 and the When whole sale price is $90.13 and the BB price is $87.02, BB price is $87.02,

The retailer’s profit is $5,540 (same as The retailer’s profit is $5,540 (same as before)before)

Therefore the whole sale price cannot be Therefore the whole sale price cannot be over $90.13!over $90.13!

Observations on Observations on Optimal Buy Back ContractOptimal Buy Back Contract

Optimal whole sale and buy back price Optimal whole sale and buy back price pairs are not unique. All lead to optimal pairs are not unique. All lead to optimal system profit.system profit.

All profit allocations are possible. All profit allocations are possible. => Buy Back contract is flexible!=> Buy Back contract is flexible!

Zero sum game, but based on the largest Zero sum game, but based on the largest pie possible.pie possible.=> Achieve supply chain coordination.=> Achieve supply chain coordination.

Other Advantages of Buy Back Other Advantages of Buy Back ContractContract

Preserve brand namePreserve brand name Prevent strategic shoppersPrevent strategic shoppers Re-distribute inventoriesRe-distribute inventories Alleviate fears from product upgradeAlleviate fears from product upgrade Encourage supplier to promote its Encourage supplier to promote its

productsproducts

Disadvantages of Buy Back Disadvantages of Buy Back ContractContract

Cost of return and salvageCost of return and salvage Irrational retailerIrrational retailer Dampen retailer’s incentive to sellDampen retailer’s incentive to sell

Quantity Discount ContractQuantity Discount Contract

Supplier offers lower price for larger ordersSupplier offers lower price for larger orders Increase underage cost and decrease Increase underage cost and decrease

overage costoverage cost

=> larger Q => larger Q

Options ContractOptions Contract

Retailer buy capacity option form supplier Retailer buy capacity option form supplier pre-seasonpre-season

Retailer exercise the option as season Retailer exercise the option as season startsstarts

Encourages supplier to build up capacity Encourages supplier to build up capacity pre-season for uncertain marketpre-season for uncertain market

Revenue SharingRevenue Sharing

Retailer pays lower whole sale priceRetailer pays lower whole sale price Supplier shares revenue generated by Supplier shares revenue generated by

retailerretailer

=> both share risk of demand uncertainty=> both share risk of demand uncertainty

=> Q increases=> Q increases Successfully used by BlockbusterSuccessfully used by Blockbuster

Quantity Flexibility ContractQuantity Flexibility Contract

Retailer order pre-season.Retailer order pre-season. Retailer is obligated to buy at least a % Retailer is obligated to buy at least a %

and has an option of buying up to b% of and has an option of buying up to b% of pre-season order when season starts.pre-season order when season starts.

Risk sharing to courage supplier build Risk sharing to courage supplier build sufficient capacity pre-season.sufficient capacity pre-season.

Price ProtectionPrice Protection

Retailer will be compensated by the price Retailer will be compensated by the price differences as product price drops.differences as product price drops.

Encourage retailer to order sufficient Encourage retailer to order sufficient (hopefully close to system optimal) (hopefully close to system optimal) quantity.quantity.

supply chain coordination with contracts. a typical supply chain

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