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Supply Chain Coordination with Contracts

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?.

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Supply Chain Coordination with Contracts

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  1. Supply Chain Coordination with Contracts

  2. A Typical Supply Chain

  3. 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.

  4. 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!

  5. 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, …

  6. 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.

  7. 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?

  8. 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).

  9. 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

  10. 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)

  11. 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

  12. Supplierand 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)?

  13. 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!

  14. 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.

  15. 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%

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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

  21. 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?

  22. 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

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

  24. 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

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

  26. 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

  27. 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!

  28. 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.

  29. 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

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

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

  32. 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

  33. 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

  34. 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.

  35. 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.

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