A dynamic-programming model is developed for the determination of optimal manpower schedules in a large aircraft plant. The basic model consists of a cost equation representing the weekly costs of obtaining, utilizing, and disposing of various categories of personnel. Losses in efficiency in weeks following transfers among jobs or hiring of new men are included. The optimum schedule is that which minimizes the sum of the weekly costs over an arbitrary scheduling period for a given forecast demand. Computation of the minimum-cost schedule is accomplished by use of dynamic programming. This formulation of the problem (a) leads directly to the optimum solution, (b) is independent of the functional form of the cost equation, (c) can utilize tabular data directly without the necessity of curve-fitting, (d) permits ready adjustment for changes in process parameters and demand forecasts, and (e) is readily programmed for computer solution, but, if need be, it can be earned out manually with some simple computational aids. The procedure is illustrated for a hypothetical demand curve and a representative cost equation.
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Bishop et al. (1958) studied this question.
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