Minimax Under Transportation Constrains

• Anatoli Mironov
Book

Part of the Applied Optimization book series (APOP, volume 27)

1. Front Matter
Pages i-x
Pages 1-63
Pages 64-122
Pages 123-168
Pages 169-246
Pages 247-309
7. Back Matter
Pages 310-310

Introduction

Transportation problems belong to the domains mathematical program­ ming and operations research. Transportation models are widely applied in various fields. Numerous concrete problems (for example, assignment and distribution problems, maximum-flow problem, etc. ) are formulated as trans­ portation problems. Some efficient methods have been developed for solving transportation problems of various types. This monograph is devoted to transportation problems with minimax cri­ teria. The classical (linear) transportation problem was posed several decades ago. In this problem, supply and demand points are given, and it is required to minimize the transportation cost. This statement paved the way for numerous extensions and generalizations. In contrast to the original statement of the problem, we consider a min­ imax rather than a minimum criterion. In particular, a matrix with the minimal largest element is sought in the class of nonnegative matrices with given sums of row and column elements. In this case, the idea behind the minimax criterion can be interpreted as follows. Suppose that the shipment time from a supply point to a demand point is proportional to the amount to be shipped. Then, the minimax is the minimal time required to transport the total amount. It is a common situation that the decision maker does not know the tariff coefficients. In other situations, they do not have any meaning at all, and neither do nonlinear tariff objective functions. In such cases, the minimax interpretation leads to an effective solution.

Keywords

Matrix algorithms operations research optimization vertices

Authors and affiliations

• 1
• Anatoli Mironov
• 1
1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4615-4060-1
• Copyright Information Springer-Verlag US 1999
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4613-6818-2
• Online ISBN 978-1-4615-4060-1
• Series Print ISSN 1384-6485
• Buy this book on publisher's site