Single-Facility Location Problems With Barriers

by Klamroth, Kathrin

• ISBN13: 9780387954981
• ISBN10: 0387954988
• Format: Hardcover
• Copyright: 2002-12-01
• Publisher: Springer Verlag

Summary

Growing transportation costs and tight delivery schedules mean that good located decisions are more crucial than ever in the success or failure of industrial and puplic projects. The development of realistic location models is an essential phase in every locational decision process. Especially when dealing with geometric representations of continuous (planar) location model problems, the goegraphical reality must be incorporated.This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems.Besides their relevance in the application of location theoretic results, location problems with barriers are also very interesting from a mathematical point of view. The nonconvexity of distance measures in the presence of barriers leads to nonconvex optimization problems. Most of the classical methods in continuous location theory rely heaily on the convexity of the objective function and will thus fail in this context. On the other hand, general methods in global optimization capable of treating nonconvex problems ignore the geometric charateristics of the location problems considered.Theoretic as well as algorithmic approaches are utilized to overcome the described difficulties for the solution of location problems with barriers. Depending on the barrier shapes, the underlying distance measure, and type of objective function, different concepts are conceived to handle the nonconvexity of the problem. This book will appeal to those working in operations research and management science and mathematicians interested in optimization theory and its applications.

Table of Contents

Preface
Introduction and General Results	p. 1
Measuring Distances	p. 3
Shortest Paths in the Presence of Barriers	p. 15
Location Problems with Barriers: Basic Concepts and Literature Review	p. 39
Bounds for Location Problems with Barriers	p. 49
Solution Methods for Specially Shaped Barriers	p. 55
Planar Location Problems with Polyhedral Barriers	p. 57
Location Problems with a Circular Barrier	p. 85
Weber Problems with a Line Barrier	p. 101
Solution Methods for Special Distance and Objective Functions	p. 119
Weber Problems with Block Norms	p. 121
Center Problems with the Manhattan Metric	p. 135
Multicriteria Location Problems with Polyhedral Barriers	p. 153
Application	p. 171
Location with Barriers Put to Work in Practice	p. 173
References	p. 183
Index	p. 199
Table of Contents provided by Blackwell. All Rights Reserved.