Annals of Operations Research

, Volume 66, Issue 4, pp 279–295 | Cite as

Chapter 13 Satisficing DEA models under chance constraints

  • W. W. Cooper
  • Zhimin Huang
  • Susan X. Li
Part IV Statistical And Stochastic Characterizations

Abstract

DEA (Data Envelopment Analysis) models and concepts are formulated here in terms of the “P-Models” of Chance Constrained Programming, which are then modified to contact the “satisficing concepts” of H.A. Simon. Satisficing is thereby added as a third category to the efficiency/inefficiency dichotomies that have heretofore prevailed in DEA. Formulations include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. Attention is also devoted to situations in which variations in inputs and outputs are related through a common random variable. Extensions include new developments in goal programming with deterministic equivalents for the corresponding satisficing models under chance constraints.

Keywords

Efficiency satisficing data envelopment analysis stochastic efficiency 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Banker, R.D., Maximum likelihood, consistency and DEA: Statistical foundations, Management Science 39, 1993, 1265–1273.Google Scholar
  2. Banker, R.D., Stochastic data envelopment analysis, Working Paper, Carnegie-Mellon University School of Urban and Public Affairs, Pittsburgh, PA, 1986.Google Scholar
  3. Banker, R.D. and W.W. Cooper, Validation and generalization of DEA and its uses, TOP 2, 1994, 249–296.MathSciNetGoogle Scholar
  4. Banker, R.D., A. Charnes and W.W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30, 1984, 1078–1092.Google Scholar
  5. Banker, R.D., A. Charnes, W.W. Cooper, J. Swarts and D.A. Thomas, An introduction to data envelopment analysis with some of its models and their uses, Research in Governmental and Nonprofit Accounting 5, 1989, 125–163.Google Scholar
  6. Charnes, A. and W.W. Cooper, Deterministic equivalents for optimizing and satisficing under chance constraints, Operations Research 11, 1963, 18–39.Google Scholar
  7. Charnes, A. and W.W. Cooper,Management Models and Industrial Applications of Linear Programming, Wiley, New York, 1961Google Scholar
  8. Charnes, A. and W.W. Cooper, Goal programming and multiple objective optimizations, European Journal of Operational Research 1, 1977, 39–54.Google Scholar
  9. Charnes, A. and W.W. Cooper, Preface to topics in data envelopment analysis, Annals of Operations Research 2, 1985, 59–94.CrossRefGoogle Scholar
  10. Charnes, A. and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics Quarterly 9, 1962, 181–185.Google Scholar
  11. Charnes, A., W.W. Cooper, J.K. DeVoe and D.B. Learner, Demon, Mark II: An extremal equation approach to new product marketing, Management Science 14, 1968, 513–524.Google Scholar
  12. Charnes, A., W.W. Cooper and J. Hsu, A chance constrained programming approach to multiple-objective sample designs in auditing, Working Paper, University of Texas Graduate School of Business, Austin, TX, 1986.Google Scholar
  13. Charnes, A., W.W. Cooper and E. Rhodes, Evaluating program and managerial efficiency: An application of data envelopment analysis to program follow through, Management Science 27, 1981, 668–697.Google Scholar
  14. Charnes, A., W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2, 1978, 429–444.CrossRefGoogle Scholar
  15. Charnes, A., W.W. Cooper and G.H. Symonds, Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil, Management Science 4, 1958, 235–236.Google Scholar
  16. Cooper, W.W., Z.M. Huang and S.X. Li, Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA, Journal of Productivity Analysis (submitted, 1996).Google Scholar
  17. Cooper, W.W. and Y. Ijiri (eds.),Kohler's Dictionary for Accountants, 6th ed., Prentice-Hall, Englewood Cliffs, NJ, 1983.Google Scholar
  18. Desai, A.A. and A.P. Schinnar, Stochastic data envelopment analysis, Working Paper, The Ohio State University, 1987.Google Scholar
  19. Jagannathan, R., Use of sample information in stochastic recourse and chance constrained programming, Management Science 31, 1985, 96–108.Google Scholar
  20. Kahane, Y., Determination of the product mix and the business policy of an insurance company — a portfolio approach, Management Science 23, 1977, 1060–1069.Google Scholar
  21. Land, K.C., C.A.K. Lovell and S. Thore, Chance-constrained data envelopment analysis, Managerial and Decision Economics 14, 1993, 541–554.Google Scholar
  22. Land, K., C.A.K. Lovell and S. Thore, Productive efficiency under capitalism and state socialism: An empirical inquiry using chance-constrained data envelopment analysis, Technological Forecasting and Social Change 46, 1994, 139–152.CrossRefGoogle Scholar
  23. Land, K., C.A.K. Lovell and S. Thore, Productive efficiency under capitalism and state socialism: The chance-constrained programming approach,Public Finance in a World of Transition, Proceedings of the 47th Congress of the International Institute of Public Finance, P. Pestieau, ed., 1992, supplement to Public Finance/Finances Publique 47, 1992, 109–121.Google Scholar
  24. Leibenstein, H.,Beyond Economic Man, Harvard University Press, Cambridge, 1976.Google Scholar
  25. Rhodes, E., Data envelopment analysis and related approaches for measuring the efficiency of decision making units with an spplication to program follow through in U.S. public school education, Ph.D. Thesis, Carnegie Mellon University School of Urban and Public Affairs, Pittsburgh, PA, 1978. Also available from Michigan University Microfilms, Inc., Ann Arbor.Google Scholar
  26. Seiford, L.M. and R.M. Thrall, Recent developments in DEA: The mathematical programming approach to frontier analysis, Journal of Econometrics 46, 1990, 7–38.CrossRefGoogle Scholar
  27. Sengupta, J.K., Data envelopment analysis for efficiency measurement in the stochastic case, Computers and Operations Research 14, 1987, 117–129.CrossRefGoogle Scholar
  28. Sengupta, J.K., Data envelopment with maximum correlation, International Journal of Systems Science 20, 1989, 2085–2093.Google Scholar
  29. Sengupta, J.K., Efficiency measurement in stochastic input-output systems, International Journal of Systems Science 13, 1982, 273–287.Google Scholar
  30. Sengupta, J.K., Robust efficiency measures in a stochastic efficiency, International Journal of Systems Science 19, 1988, 779–791.Google Scholar
  31. Sharpe, W.F., A simplified model for portfolio analysis, Management Science 9, 1963, 277–293.Google Scholar
  32. Simon, H.A.,Models of Man, Wiley, New York, 1957.Google Scholar
  33. Stedry, A.C.,Budget Control and Cost Behavior, Prentice-Hall, Englewood Cliffs, NJ, 1960.Google Scholar
  34. Stigler, G.J., The Xistence of X-efficiency, American Economic Review 66, 1976, 213–216.Google Scholar
  35. Wagner, H.M.,Principles of Operations Research, Prentice-Hall, Englewood Cliffs, NJ, 1969.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • W. W. Cooper
    • 1
  • Zhimin Huang
    • 2
  • Susan X. Li
    • 2
  1. 1.Graduate School of BusinessThe University of Texas at AustinAustinUSA
  2. 2.Schools of Business and BankingAdelphi University, Garden CityLong IslandUSA

Personalised recommendations