1 / 65

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

tyrell
Download Presentation

Supply Chain Contracts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related