Derivation of a Linear Decision Rule for Production and Employment

Abstract

An application of linear decision rules to production and employment scheduling was described in the last issue of this journal [Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October).]. The hypothetical performance of these rules represented a significant improvement over the actual company performance as measured by independent cost estimates and other managerial measures of efficiency. The quadratic cost function which was used should be applicable to production and employment scheduling decisions in many other situations. Also the general approach of approximating decision criteria with quadratic functions and obtaining linear decision rules can usefully be extended to many decision problems. In the present paper we will demonstrate (a) how optimal (i.e., minimum expected cost) decision rules may be derived for a quadratic cost function involving inventory, overtime, and employment costs, and (b) how the numerical coefficients of the rules may be computed for any set of cost parameters.