Optimal programming of lot sizes, inventory and labor allocations

The economic lot size programming problem, as studied originally by A. S. Manne and later by B. P. Dzielinski, C. T. Baker and A. S. Manne, is the problem of making economic lot size, inventory and work force decisions in a multiproduction process. When several thousand distinct items are involved, the large number of equations that result from the linear programming formulation makes computation infeasible. Also, a large number of variables are involved because of inclusion of alternative set-up sequences for each item. In this paper, the application of the Dantzig and Wolfe decomposition principle and a method for creating alternative set-up sequences as they are needed by means of a computation of the Wagner and Whitin type is described as a method for overcoming the computational difficulty. A digital computer program has been developed using these methods. The results of some experiments where production was planned for a large number of distinct items are described.