1 / 35

Prof. Dr. Jinxing Xie Department of Mathematical Sciences

Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers. Prof. Dr. Jinxing Xie Department of Mathematical Sciences Tsinghua University, Beijing 100084, China http://faculty.math.tsinghua.edu.cn/~jxie

branxton
Download Presentation

Prof. Dr. Jinxing Xie Department of Mathematical Sciences

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. Inventory Management (Deterministic Model)Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing Xie Department of Mathematical Sciences Tsinghua University, Beijing 100084, China http://faculty.math.tsinghua.edu.cn/~jxie Email: jxie@ math.tsinghua.edu.cn Voice: (86-10)62787812 Fax: (86-10)62785847 Office: Rm. 1202, New Science Building

  2. Background: Supply Chain Structure • Fangruo Chen, Awi Federgruen, Y.S. Zheng. Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers, MS 2001, 47/5, 693-708 Ti, pi (or di) T0 w

  3. Notation

  4. Notation

  5. Problems: Coordination Mechanism Centralized Decision  Decentralized Decision Can order-quantity discount scheme coordinate the supply chain (the distribution system)? Definition. A contract (scheme, mechanism) is said to coordinate the supply chain if the set of supply chain optimal actions is a Nash equilibrium, i.e., no firm has a profitable unilateral deviation from the set of supply chain optimal actions.

  6. Decentralized Decision Model

  7. Decentralized Decision: Stackelberg Game Retailer i’s problem di (w) Ti (w) (12) The supplier’s problem

  8. (1) (…,-2,-1,0,1,2,…) Decentralized Decision: Algorithm Fangruo Chen; Awi Federgruen; Yu-Sheng Zheng. NEAR-OPTIMAL PRICING AND REPLENISHMENT STRATEGIES FOR A RETAIL / DISTRIBUTION SYSTEM.OR, 2001, 49/6, 839-853.

  9. Centralized Decision Model

  10. (1) (1) (…,-2,-1,0,1,2,…) Centralized Solution Fangruo Chen; Awi Federgruen; Yu-Sheng Zheng. OR, 2001, 49/6, 839-853

  11. Order-Quantity Discount

  12. Proof

  13. Proof

  14. Proof

  15. Order-Quantity Discount:Demand rates are exogenously given

  16. Proof

  17. Proof: Incremental Order-Quantity Discount

  18. Proof

  19. Proof: All-Unit Order-Quantity Discount

  20. Proof

  21. Proof

  22. Proof

  23. Note

  24. Coordination Mechanisms (1)

  25. Pay to the supplier: retailer i Coordination Mechanisms (2)

  26. Coordination Mechanisms (3)

  27. Coordination Mechanisms (4)

  28. Property of the Contract • Notes • The scheme is by no means unique. • If {Kis } are retailer-specific, the pricing scheme fails to be uniform across all retailers.

  29. Proof: Retailers’ Problem

  30. Proof: Retailers’ Problem

  31. Proof: Supplier’s Problem Average payment from retailers to supplier Average cost of the supplier Profit function of the supplier

  32. Proof: Supplier’s Problem

  33. When a new retailer comes …

  34. When a new retailer comes … Proof. (Omitted)

  35. Review of this lecture • Distribution system • centralized vs. decentralized control • order-quantity discount scheme • coordination mechanism • Any other simpler coordination mechanisms? • How about other system? • general system • information asymmetry

More Related