1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with...
-
Upload
neil-french -
Category
Documents
-
view
229 -
download
0
Transcript of 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with...
![Page 1: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/1.jpg)
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
![Page 2: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/2.jpg)
2
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
)()(
0
,
0
iiii
ii
ii
dppd
hhh
hc
000 ,, hcK
rii
si KKK
)( id
T0 wTi , pi (or di)
![Page 3: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/3.jpg)
3
Notation
![Page 4: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/4.jpg)
4
Notation
![Page 5: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/5.jpg)
5
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)?
![Page 6: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/6.jpg)
6
Decentralized Decision Model
![Page 7: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/7.jpg)
7
Decentralized Decision: Stackelberg Game
Retailer i’s problem
The supplier’s problem
di (w)
Ti (w)
(12)
![Page 8: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/8.jpg)
8
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,…)
![Page 9: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/9.jpg)
9
Centralized Decision Model
![Page 10: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/10.jpg)
10
Centralized Solution
Fangruo Chen; Awi Federgruen; Yu-Sheng Zheng. OR, 2001, 49/6, 839-853
(1)
(1)(…,-2,-1,0,1,2,…)
![Page 11: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/11.jpg)
11
Order-Quantity Discount
![Page 12: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/12.jpg)
12
Proof
![Page 13: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/13.jpg)
13
Proof
![Page 14: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/14.jpg)
14
Proof
![Page 15: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/15.jpg)
15
Order-Quantity Discount:Demand rates are exogenously given
![Page 16: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/16.jpg)
16
Proof
![Page 17: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/17.jpg)
17
Proof: Incremental Order-Quantity Discount
![Page 18: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/18.jpg)
18
Proof
![Page 19: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/19.jpg)
19
Proof: All-Unit Order-Quantity Discount
![Page 20: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/20.jpg)
20
Proof
![Page 21: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/21.jpg)
21
Proof
![Page 22: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/22.jpg)
22
Proof
![Page 23: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/23.jpg)
23
Note
![Page 24: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/24.jpg)
24
Coordination Mechanisms (1)
![Page 25: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/25.jpg)
25
Coordination Mechanisms (2)Pay to the supplier: retailer i
![Page 26: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/26.jpg)
26
Coordination Mechanisms (3)
![Page 27: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/27.jpg)
27
Coordination Mechanisms (4)
![Page 28: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/28.jpg)
28
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.
![Page 29: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/29.jpg)
29
Proof: Retailers’ Problem
![Page 30: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/30.jpg)
30
Proof: Retailers’ Problem
![Page 31: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/31.jpg)
31
Proof: Supplier’s ProblemAverage payment from retailers to supplier
Average cost of the supplier
Profit function of the supplier
![Page 32: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/32.jpg)
32
Proof: Supplier’s Problem
![Page 33: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/33.jpg)
33
When a new retailer comes …
![Page 34: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/34.jpg)
34
When a new retailer comes …
Proof. (Omitted)
![Page 35: 1 Inventory Management (Deterministic Model) Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers Prof. Dr. Jinxing.](https://reader036.fdocuments.net/reader036/viewer/2022062301/56649eeb5503460f94bfc19b/html5/thumbnails/35.jpg)
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