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.
