CHANCE-CONSTRAINED PROGRAMMING FORMULATIONS FOR STOCHASTIC CHARACTERIZATIONS OF EFFICIENCY AND DOMINANCE IN DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is exten ded to stochastic inputs and outputs via probabilistic input-output ve ctor comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Progr amming formulations in DEA, the emphasis here is on ''joint chance con straints.'' An assumption of arbitrary but known probability distribut ions leads to the P-Model of chance constrained programming, A necessa ry condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chanc e constrained programming and multivariate normal distributions take t he form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available determin istic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elem ents are present.