Minimax Under Transportation Constrains

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.

שנה

2013

שפה

English

הוצאה

Springer London, Limited

מהדורות

4

עמודים

310

ISBN

9781461540601

מקור הנתונים: Wikidata