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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
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Background: Supply Chain Structure Fangruo Chen, Awi Federgruen, Y.S. Zheng. Coord
ination Mechanisms for a Distribution System with One Supplier and Multiple Retailers, MS 2001, 47/5, 693-708
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Notation
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Notation
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Problems: Coordination Mechanism
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.
Centralized Decision Decentralized Decision
Can order-quantity discount scheme coordinate the supply chain (the distribution system)?
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Decentralized Decision Model
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Decentralized Decision: Stackelberg Game
Retailer i’s problem
The supplier’s problem
di (w)
Ti (w)
(12)
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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.
(1)(…,-2,-1,0,1,2,…)
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Centralized Decision Model
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Centralized Solution
Fangruo Chen; Awi Federgruen; Yu-Sheng Zheng. OR, 2001, 49/6, 839-853
(1)
(1)(…,-2,-1,0,1,2,…)
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Order-Quantity Discount
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Proof
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Proof
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Proof
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Order-Quantity Discount:Demand rates are exogenously given
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Proof
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Proof: Incremental Order-Quantity Discount
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Proof
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Proof: All-Unit Order-Quantity Discount
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Proof
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Proof
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Proof
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Note
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Coordination Mechanisms (1)
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Coordination Mechanisms (2)Pay to the supplier: retailer i
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Coordination Mechanisms (3)
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Coordination Mechanisms (4)
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Property of the Contract
Notes
• The scheme is by no means unique.
• If {Kis } are retailer-specific, the pricing scheme f
ails to be uniform across all retailers.
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Proof: Retailers’ Problem
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Proof: Retailers’ Problem
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Proof: Supplier’s ProblemAverage payment from retailers to supplier
Average cost of the supplier
Profit function of the supplier
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Proof: Supplier’s Problem
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When a new retailer comes …
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When a new retailer comes …
Proof. (Omitted)
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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