Usually a transportation problem with a third index that refers to a product type available at the origins and demanded at the destinations. The variables x_ijk represent the amount of the kth product type 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 multicommodity 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.