- V. I. Tsurkov , A. A. Mironov
Сборник тезисов рабочей группы инаугурации Межд. инст. сист. исслед. Слиппери Рок, США, 1995 , 01.1995 , p. 74, language: английский
Аннотация
- The minimax is studied in many fields. For example in game theory, it is
the inevitable minimal loss. The minimax is used in this paper for the
transportation problems. The expenditure for the transports of a homogeneous
product from the production points to the consumption ones is minimized in
the classical transportation problem. Suppose that the transport time is
proportional to the product quantity. If the product goes bad (agriculture) then
it is necessary to minimize the maximal transport time. We obtain the
following problem: to find the matrix with the fixed sums of the lines and
columns where its maximal element would be minimal. The condition for the
set of the transportation problem matrixes is offered when this set contains
matrixes where their elements are not more than a fixed value. The identity is
designed which determines properties of all matrixes of the transportation
problem with bounded elements. Above condition and identity give the matrix
when its maximal element is minimal as well as calculate the minimax value.
The necessary and sufficient conditions of the uniqueness of the minimax
matrix are obtained. The case of the integer solution is investigated in detail.
The approach is enlarged for the many indexes transportation problems too.
Ключевые слова
- minimax, optimization, integer programming, transportation problem
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