SOLUTION OF A MULTI-PRODUCT MANUFACTURING AND DISTRIBUTION PROBLEM

An actual multi-product production and distribution problem is described and an optimizating algorithm is developed. The problem, which is an example of a multi-commodity capacitated trans-shipment problem, is solved by the technique suggested by L. R. Ford and D. R. Fulkerson. Due to the size of the problem and computational constraints, the usefulness of this technique is improved by incorporating the Generalized Upper Bound algorithm of G. B. Dantzig and R. M. Van Slyke. The modified technique requires manipulation of a relatively small matrix whose order is N by N where N is the number of capacitated links in the network. The traditional node-arc formulation solved by linear programming, the original arc-chain technique and the modified arc-chain algorithm are each compared in terms of computer storage requirements and solution times, resulting in considerable time efficiencies, of the order of fifty to one, for the modified Ford-Fulkerson method.