A Theory of Supply Chains

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Springer Science & Business Media, Feb 13, 2003 - Business & Economics - 123 pages
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This work was stimulated by a comment made by a former student (Prof. Alan Erera of Georgia Tech) in connection with an inventory stabil ity game he was going to play in one of his logistics classes. This was the well-known "beer-game" that is often played in business schools to illus trate the "bullwhip" effect in supply chains. Al had said to me that he did not have to tell his students how to reorder replacement parts from the other members of the supply chain because he knew from experience that the order sizes the players would generate as the game progressed would become chaotic anyhow. Since I had not played the beer game, his asser tion was intriguing to me. Why would such an unstructured game always lead to the same undesirable effect? Did it have something to do with psy chology? What is it that players did to generate instabilities? I posed these to other people but could not get completely satisfactory an questions swers. Thus, the bullwhip mystery remained, at least in my mind. Since inventory chains are "conservative" systems analogous to a traffic stream, and since traffic flow models exhibit similar effects (the instability of automobile platoons and of certain numerical methods being two nota ble examples)' I suspected that traffic flow theory might shed some light on the puzzle.
 

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Contents

1 Introduction
1
12 Terminology and data representation
4
2 Algorithms Policies
9
22 Examples
14
23 Anticipative commitmentbased policies
17
24 Flexible commitment policies
20
25 Policies for queuing systems and traffic flow
21
3 Algorithmic Properties
25
522 The ACT family
67
linear case and J1T systems
73
nonlinear case
74
6 Cost Estimation and Optimization
79
61 Autonomous useroptimal operation with flexible commitments
80
Optimization
85
622 Flexible operation with systemoptimum bounds
87
7 Discussion
99

32 Steadystate properties
28
4 Stability and Monotonicity Requirements
35
42 Stability analysis
38
43 Interpretation and examples
42
44 Some additional properties of linear orderbased policies
49
Serial queues and push chains
52
The Act Method
55
52 Discretetime approximations of the KW target
63
72 Application issues
101
References
103
Stability via Control Theory
107
Kinematic Wave Theory Revisited
111
B2 The KW Theory Revisited
112
B3 Properties of the procedure
121
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