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Deterministic Models for Production of Services with Stochastic Technology
Joseph Lipscomb
David Zalkind
Abstract
Production problems in which profit is to be maximized subject to constraints onresources and outputs are frequently modeled as linear programs. While in practice the technology coefficients are often treated as constants, they are frequently better regarded as random variables. Stochastic programming models, first developed in the 1950's, recognized that explicit representation of randomness in factors of production is sometimes necessary to derive program solutions [3]. In 1970 Resh [12] noted that a certain class of implied chance-constrained models with zero-order decision rules were utilizing inappropriately conservative constraints. We have extended his results from integer to continuous decision variables and present experimental evidence from dental services production that substantial undercalculation of "optimal" output does occur when Resh's model variant is not used. We show that solutions for continuous variable models can be closely approximated by linear programming models derived by Resh in an integer case.
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