Ebook: Practical Bilevel Optimization: Algorithms and Applications

The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problern in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential 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.

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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.

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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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Introduction....Pages 3-16
Linear Programming....Pages 17-75
Integer Programming....Pages 76-136
Nonlinear Programming....Pages 137-192
Front Matter....Pages 193-193
Linear Bilevel Programming: Continuous Variables....Pages 195-231
Linear Bilevel Programming: Discrete Variables....Pages 232-268
Convex Bilevel Programming....Pages 269-300
General Bilevel Programming....Pages 301-360
Heuristics....Pages 361-388
Front Matter....Pages 389-389
Transportation Network Design....Pages 391-413
Production Planning with Inexact Customer Demand....Pages 414-427
Determining Price Support Levels for Biofuel Crops....Pages 428-454
Back Matter....Pages 455-476

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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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Introduction....Pages 3-16
Linear Programming....Pages 17-75
Integer Programming....Pages 76-136
Nonlinear Programming....Pages 137-192
Front Matter....Pages 193-193
Linear Bilevel Programming: Continuous Variables....Pages 195-231
Linear Bilevel Programming: Discrete Variables....Pages 232-268
Convex Bilevel Programming....Pages 269-300
General Bilevel Programming....Pages 301-360
Heuristics....Pages 361-388
Front Matter....Pages 389-389
Transportation Network Design....Pages 391-413
Production Planning with Inexact Customer Demand....Pages 414-427
Determining Price Support Levels for Biofuel Crops....Pages 428-454
Back Matter....Pages 455-476
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