The k-dimensional transportation pr

The k-dimensional transportation problem, with specified capacities at inter- mediate points, etc. can be solved with the formal version of the direct method, though in this case fractional solutions as well as negative solutions may be encountered. Fractional solution transformations are similar to negative solution transformations. This problem is the mathematical equivalent of the group assembly problem [7]. Earlier versions of solutions are available in the literature and B. A. Galler has prepared a machine program for problems with as many dimensions as 20 [9] and [17]. The direct generality of the formal method is seen from the fact the program in the k dimensions is also designed for the k = 2 dimensional problem under consideration in this paper.