Optimal Programming of Lot Sizes, Inventories and Labor Allocations---A Comment

In a recent article in this journal, B. P. Dzielinski and R. E. Gomory [Dzielinski, B. P., R. E. Gomory. 1965. Optimal programming of lot sizes, inventory and labor allocations. Management Sci.119, July 874--890.] discussed the use of the Dantzig-Wolfe decomposition principle to accomplish a reduction in the large number of constraints appearing in the linear programming tableau. A comment is included on the maximum number of fractional solutions, i.e. the solutions specifying that items are to be manufactured according to two or more production plan sequences. The interpretation of such solutions in terms of the physical situation requires special attention and treatment on the part of the analyst.