A Theory of Supply Chains

by Carlos F. Daganzo

Overview

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.

Product Details

ISBN-13:	9783540002888
Publisher:	Springer Berlin Heidelberg
Publication date:	04/10/2003
Series:	Lecture Notes in Economics and Mathematical Systems , #526
Edition description:	2003
Pages:	125
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1. Introduction.- 1.1 The problem.- 1.2 Terminology and data representation.- 2. Algorithms I Policies.- 2.1 The canonical form: order-based and inventory-based policies.- 2.2 Examples.- 2.3 Anticipative (commitment-based) policies.- 2.4 Flexible commitment policies.- 2.5 Policies for queuing systems and traffic flow.- 3. Algorithmic Properties.- 3.1 Properness.- 3.2 Steady-state properties.- 4. Stability and Monotonicity Requirements.- 4.1 Types of stability.- 4.2 Stability analysis.- 4.3 Interpretation and examples.- 4.4 Some additional properties of linear, order-based policies.- 4.5 Duality: Serial queues and “push chains”.- 5. Strongly Stable Policies: The Act Method.- 5.1 The kinematic wave target.- 5.2 Discrete-time approximations of the KW target.- 6. Cost Estimation and Optimization.- 6.1 Autonomous user-optimal operation with flexible commitments.- 6.2 Coordinated “system-optimum” operation: Optimization.- 7. Discussion.- 7.1 Extensions: Multi-commodity networks.- 7.2 Application issues.- References.- Appendix A: Stability via Control Theory.- Appendix B: Kinematic Wave Theory Revisited.- B.1 Preliminaries.- B.2 The KW Theory Revisited.- B.3 Properties of the procedure.