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Minimax under Transportation Constrains : Applied Optimization - Vladimir Tsurkov

Minimax under Transportation Constrains

Applied Optimization

Hardcover

Published: December 2009
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This monograph is devoted to transportation problems with minimax criteria. The cost function of the classical transportation problem contains tariff coefficients. It is a common situation that the decision-maker does not know their values. In other situations, they do not have any meaning at all, and neither do nonlinear tariff objective functions. Instead of the classical cost function, a minimax cost function is introduced. In other words, a matrix with the minimal largest element is sought in the class of matrices with non-negative elements and given sums of row and column elements. The problem may also be interpreted as follows: suppose that the shipment time is proportional to the amount to be shipped. Then, the minimax gives the minimal time required to complete all shipments. An algorithm for finding the minimax and the corresponding matrix is developed. An extension to integer matrices is presented. Alternative minimax criteria are also considered. The solutions obtained are important for the theory of transportation polyhedrons. They determine the vertices of convex hulls of the sets of basis vector pairs and the corresponding matrices of solutions. Audience: The monograph is addressed to specialists in operations research, optimization, and transportation problems.

Preface
Transportation Models with Minimax Criteria and Preliminary Constructionsp. 1
Minimax Criteria and Solution Methods for Transportation Problemsp. 64
Integer Transportation Matricesp. 123
Extremal Vector Pairs and Matricesp. 169
Fundamental Polyhedronsp. 247
Indexp. 310
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792356097
ISBN-10: 0792356098
Series: Applied Optimization
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 310
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.39