Supply Chain Coordination with Contracts

A Typical Supply Chain

A Paradigm Shift From optimization within an organization to optimization for a SC. Design incentive structures (contracts) to coordinate various parties of the SC to achieve system optimization.

Why Coordination? Each player (company) in the SC has different, and often time, conflicting objectives. These individual objectives are usually not in line with that of the SC. An incentive structure (contract) is needed to align the optimization action of each individual player for the interest of the SC (Contract Design) Make the pie bigger then divide!

Popular SC Systems Studied in Literature: Two levels: a supplier and a retailer (or multiple retailers). Product: seasonal or stable (newsvendor v.s. EOQ) Demand: deterministic or stochastic insensitive or sensitive to retail price Objective Function: risk neutral or risk averse. Other variations: information asymmetry, multiple replenishment opportunities, competing retailers, …

Contract Design and Evaluation For a given SC structure, which contracts coordinate the SC? How does the contract allocate profit among players of the SC? Efficiency v.s. administrative cost for a given contract.

Newsvendor Problem News paper demand unknown but distribution known with cdf F. Underage cost (Price-Cost): Cu Overage cost (Cost - Salvage): Co How much to order to maximize the expected profit?

Newsvendor Solution At the best order quantity, marginal underage = marginal overage => [1- F(Q)] ͯ Cu = F(Q) ͯ Co => F(Q) = Cu / (Cu + Co) (1) If F is a Normal distribution with mean μ and std σ , => Q = μ + σ ͯ z, where z is the z-value based on (1). Marginal underage cost for Qth product = marginal overage cost of Qth product.

Performance Measures Expected lost sales (for Normal dist.): = σ ͯ [Normdist(z,0,1,0)-z ͯ (1-Normsdist(z,0,1,1)] Expected sales: = Exp demand – Exp lost sales Expected leftover inv: = Q – Exp sales Expected profit: = (Price-Cost)*Exp sales – (Cost-Salvage)*Exp inv Normdist(x,mean,std, cum or density) Normsdist(x) = cum distribution of standard normal

A Sunglass Supply Chain Sunglass designer and manufacturer (called supplier): Manufacturing cost: $35 Whole sale price: $75 Sunglass retailer: Retail price: $115 End-of-season price: $25 Estimated demand: Normal ( =250, =125) Should the retailer order more or fewer glasses than average?

Best Decision for Retailer Underage cost Cu : $115 - $75 = $40 Overage cost Co : $75 - $25 = $50 Cu / (Cu + Co) = 40 / (40 + 50) = 44.4% z = -0.1397 Q = 250 + (-0.1397)*125 = 233 Expected sale = 191 Expected leftover Inventory = 42 Expected profit = $40*191-$50*42 =$5,540

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

What’s Best for the System? Underage cost Cu : $115 - $35 = $80 Overage cost Co : $35 - $25 = $10 Cu / (Cu + Co) = 80 / (80 + 10) = 88.9% z = 1.2206 Q = 250 + 1.2206 *125 = 403 Expected sale = 243 Expected leftover = 160 Expected system profit = $17,840 =>19% profit increase! Double marginalization. Retailer is more conservative than the system since his profit margin is smaller than the system.

How to Improve System Performance Retailer needs to order more! Option 1: Reduce whole sale price What happened? We need a win-win (not win-lose) mechanism Option 2: How about buy back contract? Specified by a whole sale price and a buy back price.

Option 1: Reduce whole sale price What happened? If the supplier reduce the whole sale price from $75 to $65, what happens? Best Decision for Retailer Underage cost Cu : $115 - $65 = $50 Overage cost Co : $65 - $25 = $40 Cu / (Cu + Co) = 50 / (50 + 40) = 55.55%

Option 1: Reduce whole sale price z = 0.1397 Q = 250 + (0.1397)*125 = 267 Expected sale = 208 Expected leftover Inventory = 59 Expected profit = $50*208-$40*59 =$8,040 Supplier’s profit = 267*($65-$35) = $8,010 System profit = $5,540+$9,320 = $16,050.

Option 1: Reduce whole sale price Conclusion: System total profit will increase but the supplier’s profit will decrease. Supplier will not reduce selling price to retailer. NO COORDINATION. In fact, at whole sale price of $85.5, the supplier’s profit maximized.

Option 2: How about buy back contract? Assume that the supplier offers to buy back unsold items back at the price of $40 each, what happens? Retailer: Underage cost Cu : $115 - $75 = $40 Overage cost Co : $75 - $30 = $45 Cu / (Cu + Co) = 40 / (40 + 45) =0.4707 z = -0.0738

Option 2: How about buy back contract? Q = 250 + (-0.0738)*125 = 241 Expected sale = 195 Expected leftover = 45 Expected profit = $5,775 Supplier: Suppliers profit = 241*($75-$35) - 45*($30-$25)=$9,415 System profit = $5,775+$9,415=$15,190 All better off.

Retailer’s Profit with BB Price at $65 Underage cost Cu : $115 - $75 = $40 Overage cost Co : $75 - $65 = $10 Cu / (Cu + Co) = 40 / (40 + 10) = 80% z = 0.8416 Q = 250 + 0.8416*125 = 355 Expected sale = 236 Expected leftover = 119 Expected profit = $8,250

Supplier’s and System Profit with BB Price at $65 Suppliers profit = 355*($75-$35) - 119*($65-$25)=$9,440 System profit = $8,250 + $9,440=$17,690 System profit is higher Both supplier and retailer are also better off (Win-Win). How to improve system profit further?

Optimal Whole Sale and BB Price Need to make sure retailer’s Q is optimal for the system. System Q is determined by (Price-Cost)/(Price-Cost + Cost-Salvage) Retailer’s Q is determined by (Price-Whole)/(Price-Whole + Whole-BuyBack) Two ratios should equal to each other

Optimal Whole Sale and BB Price Optimal Buy Back Price = Price – (Price-Whole Sale Price)* (Price-Salvage)/(Price-Cost) Profit calculations

Optimal Whole Sale and BB Price If the whole sale price is $75, the optimal BB price must be $70. Retailer Underage cost Cu : $115 - $75 = $40 Overage cost Co : $75 - $70 = $5 Cu / (Cu + Co) = 40 / (40 + 5) = 0.8889 z = 1.2206 Q = 250 + 1.2206*125 = 403 Expected profit =$8,920

Optimal Whole Sale and BB Price Supplier Expected Profit =$8,920 Total Expected Profit = $17,840 Are they happy? Not for supplier

Observation To keep the Cu / (Cu + Co) = 0.8889, when whole sale price (as well as BB price) increases, the supplier’s profit increases When whole sale price is $85.5 and BB price is $81.81, Retailer’s expected profit is $6,565.5 Supplier’s profit is $11,261.50 Both are better off

Observation When whole sale price is $90.13 and the BB price is $87.02, The retailer’s profit is $5,540 (same as before) Therefore the whole sale price cannot be over $90.13!

Observations on Optimal Buy Back Contract Optimal whole sale and buy back price pairs are not unique. All lead to optimal system profit. All profit allocations are possible. => Buy Back contract is flexible! Zero sum game, but based on the largest pie possible. => Achieve supply chain coordination. When does retailer makes more profit?

Other Advantages of Buy Back Contract Preserve brand name Prevent strategic shoppers Re-distribute inventories Alleviate fears from product upgrade Encourage supplier to promote its products

Disadvantages of Buy Back Contract Cost of return and salvage Irrational retailer Dampen retailer’s incentive to sell

Quantity Discount Contract Supplier offers lower price for larger orders Increase underage cost and decrease overage cost => larger Q

Options Contract Retailer buy capacity option form supplier pre-season Retailer exercise the option as season starts Encourages supplier to build up capacity pre-season for uncertain market

Revenue Sharing Retailer pays lower whole sale price Supplier shares revenue generated by retailer => both share risk of demand uncertainty => Q increases Successfully used by Blockbuster

Quantity Flexibility Contract Retailer order pre-season. Retailer is obligated to buy at least a % and has an option of buying up to b% of pre-season order when season starts. Risk sharing to courage supplier build sufficient capacity pre-season.

Price Protection Retailer will be compensated by the price differences as product price drops. Encourage retailer to order sufficient (hopefully close to system optimal) quantity.