Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

William W. Cooper, Zhimin Huang, Vedran Lelas, Susan X. Li, Ole B. Olesen

Research output: Contribution to journalArticlepeer-review

113 Scopus citations

Abstract

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on "joint chance constraints." An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary 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 chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.

Original languageEnglish (US)
Pages (from-to)53-79
Number of pages27
JournalJournal of Productivity Analysis
Volume9
Issue number1
DOIs
StatePublished - Jan 1 1998

Keywords

  • Almost 100% confidence chance constraints
  • Stochastic DEA
  • Stochastic efficiency
  • Stochastic efficiency dominance

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