Multidimensional transportation problem
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This problem is usually a transportation problem with a third index that refers to a product type. Here there are i origins, j destinations and k types of products available at the origins and demanded at the destinations. The variables xijk represent the amount of the kth product shipped from the ith origin to the jth destination. The constraint set is a set of linear balance equations, with the usual linear cost objective function. It is also a special form of the multi-commodity network-flow problem. Unlike the transportation problem, its optimal solution may not be integer-valued even if the network data are given as integers. The problem can also be defined with more than three indices. Multicommodity network flows; Transportation problem.