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Minimax Under Transportation Constrains (Paperback, Softcover reprint of the original 1st ed. 1999)
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Minimax Under Transportation Constrains (Paperback, Softcover reprint of the original 1st ed. 1999)
Series: Applied Optimization, 27
Expected to ship within 10 - 15 working days
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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.
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