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An Approach to single parameter process design

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This paper presents an approach to the analysis of single parameter process design problems such as the problem of set-up reduction formulated by Van Beek (1984), Porteus (1985), and Van Beek and Van Putten (1987). The problems considered typically entail minimizing the sum of a convex and a concave function, and are therefore potentially difficult to solve. The approach consists of transforming such problems into equivalent affine problems involving the tradeoff between fixed and variable costs. The transformation enables the derivation of necessary and sufficient conditions for the quasi-convexity and the quasi-concavity of the original problem. Various structural properties and solution methods are discussed, including an algorithm for the finite case. The use of the approach is illustrated by a number of applications

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