Relaxation Methods for Pure and Mixed Integer Programming Problems (Classic Reprint) - Softcover

G. A. Gorry

Softcover

ISBN 10: 1332278612 ISBN 13: 9781332278619

Publisher: Forgotten Books, 2020

Synopsis

Excerpt from Relaxation Methods for Pure and Mixed Integer Programming Problems

Computational experience with a group theoretic integer programming (ip) algorithm has been unusually promising; see reference 6. A major irawback, however, of this method in the past has been the size of the finite abelian groups encountered during the computation of certain 1? Problems. In this paper, we show how the difficulty can be overcome by the application of some rather simple number theoretic procedures. Although these procedures cannot be guaranteed to reduce the size of the induced groups, computational experience to date has shown them to be efficacious in practically all cases. The central idea is that a given IP problem can be usefully transformed by dividing all the coefficients of an inequality by a rational divisor greater than 1, and then taking integer parts. Such a transformation of the problem, called a relaxation, has the property that all feasible solutions to the original IP problem are feasible in the transformed or relaxed problem. The idea for this particular relaxation method in IP is originally due to Wolsey The term relaxation is also used by Geoffrion in [3] to describe mathematical programming methods conceived in the same spirit as the ones here.

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About the Author

Jeremy Shapiro is a professor emeritus in the Sloan School of Management at MIT. For nine years he served as the co-director of MIT's Operations Research Center. Previously, he was employed by Procter and Gamble, Hughes Aircraft Company, and the Port of New York Authority. He received his B.M.E. and M.I.E. degrees from Cornell University and a Ph.D. degree in Operations Research from Stanford University. Dr. Shapiro has published over 60 papers in the areas of operations research, mathematical programming, logistics, supply chain management, finance, and marketing. He is also president of SLIM Technologies, LLC, a Boston-based firm specializing in the implementation and application of modeling systems for supply chain management and other business problems. His outside interests include reading, traveling, biking and playing tennis. He is married to Martha J. Heigham and has three children, Alexander, Lara, and Nicholas.

LAURENCE A. WOLSEY is Professor of Applied Mathematics at the Center for Operations Research and Econometrics (CORE) at l'UniversitA(c) Catholique de Louvain at Louvain-la-Neuve, Belgium. He is the author, with George Nemhauser, of Integer and Combinatorial Optimization (Wiley).

Edition details

• Publisher: Forgotten Books
• Publication date: 2020
• ISBN 10: 1332278612
• ISBN 13: 9781332278619
• Binding: Paperback
• Language: English
• Number of pages: 53