Synopses & Reviews
The focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology. What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field. Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists.
Description
Includes bibliographical references (p. 455-467) and index.
Table of Contents
Preface.
Part I: Mathematical Programming. 1. Introduction.
2. Linear Progrmaming.
3. Integer Programming.
4. Nonlinear Programming.
Part II: Bilevel Programming. 5. Linear BLP: Continuous Variables.
6. Linear BLP: Discrete Variables.
7. Convex Bilevel Programming.
8. General Bilevel Programming.
9. Heuristics.
Part III: Applications. 10. Transportation Network Design.
11. Production Planning.
12. Determining Price Support Levels for Biofuel Crops. References. Index.