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

144 Scopus citations


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
Issue number1
StatePublished - Jan 1 1998

Bibliographical note

Funding Information:
Support for W. W. Cooper by the IC2 Institute of the University of Texas is gratefully acknowledged. Zhimin Huang’s research has been supported in part by 1995 Spring Provost Research Award of Adelphi University. The authors are also grateful to Dr. S. Thore at the IC2 Institute for his constructive comments and suggestions on an earlier version of this paper.

Copyright 2018 Elsevier B.V., All rights reserved.


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


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