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A Model for Optimizing Production by Reference to Cost Surrogates

A. Charnes
W. W. Cooper
B. Mellon

Abstract

Cost structures of the kind usually posited in the economic theory of the firm do not seem to be readily ascertainable by an examination of business records. A somewhat different approach to the problem of optimizing business costs is therefore essayed in this article. The objective is to develop a means whereby general qualitative properties of economic theorems on cost behavior may be used to provide quantitative answers as a guide to business conduct. It is assumed that total costs are unknown but have the general form theoretically ascribed to total cost functions when output occurs beyond the inflection point (or point of minimum marginal cost) on the total cost function. Certain easily ascertained variables (direct manhours) are then used as surrogates in place of the unknown total costs in order to determine optimal production patterns over a finite time horizon, in which sales are assumed to be known or given. The model includes multi-product and factor considerations but not inventory carrying costs, liquidity considerations, etc. In short, it is a production model intended for application to production problems.