A Note on the Modigliani-Hohn Production Smoothing Model

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Abstract
Modigliani and Hohn [Modigliani, F., F. E. Hohn. 1955. Production planning over time. Econometrica 23 (1, January) 46–66.] have formulated a production planning and inventory control model that appears relevant to an important class of non-stochastic decision-making problems. It is the purpose of this note to suggest: (1) that the Modigliani Hohn problem may be studied in terms of linear programming as well as through the calculus model originally employed; (2) that by working through the stock-flow relationships, it is possible to effect certain conceptual and computational improvements over Edward Bowman's original method for converting this type of problem into the “transportation” form [Bowman, E. H. 1956. Production scheduling by the transportation method of linear programming. J. Oper. Res. Soc. America 4 (1, February) 100–103.]; and (3) that the linear programming version is especially suitable for tracing out the cost implications of stabilizing the work force at alternative levels. Like the “caterer problem” [Jacobs, W. 1954. The caterer problem. Naval Res. Logist. Quart. 1 (2, June) 154–165.] and the “warehousing problem” [Charnes, A., W. W. Cooper. 1955. Generalizations of the warehousing model. Oper. Res. Quart. 6 (4, December) 131–172.], this linear programming model represents another instance in which every basis is pure triangular and contains no elements but zero, +1, and −1.

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