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Supply Chain Contracts

Supply Chain Contracts. Gabriela Contreras Wendy O’Donnell April 8, 2005. Outline. Introducing Contracts Example: ski jackets Buy-back Revenue-sharing Quantity-flexibility Newsvendor Problem Wholesale Buy-back Revenue-sharing Quantity-flexibility

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Supply Chain Contracts

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  1. Supply Chain Contracts Gabriela Contreras Wendy O’Donnell April 8, 2005

  2. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems and open questions

  3. A contract provides the parameters within which a retailer places orders and the supplier fulfills them.

  4. Example: Music store • Supplier’s cost c=$1.00/unit • Supplier’s revenue w=$4.00/unit • Retail price p=$10.00/unit • Retailer’s service level CSL*=0.5

  5. Question What is the highest service level both the supplier and retailer can hope to achieve?

  6. Example: Music store (continued) • Supplier’s cost c=$1.00/unit • Supplier’s revenue w=$4.00/unit • Retail price p=$10.00/unit • Supplier & retailer’s service level CSL*=0.9

  7. Characteristics of an Effective Contract: • Replacement of traditional strategies • No room for improvement • Risk sharing • Flexibility • Ease of implementation

  8. Why? Sharing risk increase in order quantity increases supply chain profit

  9. Types of Contracts: • Wholesale price contracts • Buyback contracts • Revenue-sharing contracts • Quantity flexibility contracts

  10. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems & open questions

  11. Example: Ski Jacket Supplier • Supplier cost c = $10/unit • Supplier revenue w = $100/unit • Retail price p = $200/unit • Assume: • Demand is normal(m=1000,s=300) • No salvage value

  12. Formulas for General Case • E[retailer profit] = • E[supplier profit] = q(w-c) • E[supply chain profit] = E[retailer profit] + E[supplier profit]

  13. Results: Optimal order quantity for retailer = 1,000 Retail profit = $76,063 Supplier profit = $90,000 Total supply chain profit = $166,063 Loss on unsold jackets: • For retailer = $100/unit • For supply chain = $10/unit

  14. Optimal Quantities for Supply Chain: • When we use cost = $10/unit, supply chain makes $190/unit • Optimal order quantity for retailer = 1,493 • Supply chain profit = $183,812 • Difference in supply chain profits = $17,749

  15. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  16. Buy-Back Contracts Supplier agrees to buy back all unsold goods for agreed upon price $b/unit

  17. Change in Formulas: • E[retailer profit] = • E[supplier profit] = q(w-c) 3. E[overstock] = + bE[overstock] – bE[overstock]

  18. Expected Results from Buy-back Contracts for Ski Example

  19. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  20. Revenue-sharing Contracts Seller agrees to reduce the wholesale price and shares a fraction f of the revenue

  21. Change in formulas • E[supplier profit]= (w-c)q+fp(q-E[overstock]) • E[retailer profit]= (1-f)p(q-E[overstock])+vE[overstock]-wq

  22. Expected results from revenue-sharing contracts for ski example

  23. “Go Away Happy” “Guaranteed to be There”

  24. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  25. Quantity-flexibility Contracts • Retailer can change order quantity after observing demand • Supplier agrees to a full refund of dq units

  26. Quantity-flexibility Contract for Ski Example

  27. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  28. Contracts and the Newsvendor Problem • One supplier, one retailer • Game description: Y Accept Contract? Q N Production End Product Delivery Demand Recognition Transfer payments

  29. Assumptions • Risk neutral • Full information • Forced compliance

  30. Profit Equations pr = pS(q) – T ps = T – cq P(q) = pS(q) – cq = pr +ps p= price per unit sold S(q)= expected sales c= production cost Proof:

  31. Transfer Payment What the retailer pays the supplier after demand is recognized T = wq w = what the supplier charges the retailer per unit purchased

  32. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  33. Newsvendor Problem Wholesale Price Contract Decide on q, w

  34. Let w be what the supplier charges the retailer per unit purchased Tw(q,w)=wq

  35. Retailer’s profit function pr= pS(q)-T

  36. Supplier’s Profit Function ps= (w-c)q

  37. Results: • Commonly used • Does not coordinate the supply chain • Simpler to administer

  38. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  39. Buy-back Contracts • Decide on q,w,b • Transfer payment T = wq – bI(q) = wq – b(q – S(q))

  40. Claim A contract coordinates retailer’s and supplier’s action when each firm’s profit with the contract equals a constant fraction of the supply chain profit. i.e. a Nash equilibrium is a profit sharing contract

  41. Buy-back contracts coordinate if w & b are chosen such that:

  42. Recall: pr = pS(q) – T pr = pS(q) – wq – b(q – S(q)) = (p – b)S(q) – (w – b)q = lP(q)

  43. Recall: ps = T - cq ps = – cq wq – b(q – S(q)) = bS(q) + (w – b)q – cq = (1 - l)P(q)

  44. Results Since q0 maximizes p(q), q0 is the optimal quantity for both pr and ps And both players receive a fraction of the supply chain profit

  45. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

  46. Newsvendor Problem Revenue-Sharing Contracts Decide on q, w, f

  47. Transfer Payment Tr= wq + pS(q) (1-f)

  48. Retailer’s Profit pr= pS(q)- T • For l Є (0,1], let fp= lp w= lc pr= lP(q) f

  49. Similar to Buy-Back From Previous Slide: pr(q,wr,f)=lP(q) Recall from Buy-Back: pr(q,wr,b)=lP(q)

  50. Outline • Introducing Contracts • Example: ski jackets • Buy-back • Revenue-sharing • Quantity-flexibility • Newsvendor Problem • Wholesale • Buy-back • Revenue-sharing • Quantity-flexibility • Results for other problems

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