Journal of Productivity Analysis

, Volume 2, Issue 3, pp 197–237 | Cite as

A structure for classifying and characterizing efficiency and inefficiency in Data Envelopment Analysis

  • A. Charnes
  • W. W. Cooper
  • R. M. Thrall
Article

Abstract

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient.

Key words

Dual linear programs multicriterion efficiency analysis scale efficiency strong complementary slackness technical efficiency virtual multipliers 

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References

  1. Balinski, M.L. 1968. “Note on a Constructive Approach to Linear Programming.” In Mathematics of the Decision Sciences, Part 1. G.B. Dantzig and A.F. Veinott, Jr. (Ed.) Lectures in Applied Mathematics, Vol. II, Providence, RI: American Mathematical Society, pp. 38–64.Google Scholar
  2. Banker, R.D. 1984. “Estimating Most Productive Scale Size Using Data Envelopment Analysis.” European Journal of Operational Research, 17, pp. 35–44.Google Scholar
  3. Banker, R.D., A. Charnes, W.W. Cooper, J. Swarts, and D. Thomas. 1989. “An Introduction to Data Envelopment Analysis with Some of Its Models and Their Uses.” Research in Governmental and Nonprofit Accounting, 5, pp. 125–162.Google Scholar
  4. Banker, R.D. and R.M. Thrall. 1991. “Estimation of Returns to Scale Using Data Envelopment Analysis.” European Journal of Operational Research, (to appear in 1991).Google Scholar
  5. Banker, R.D., A. Charnes, and W.W. Cooper. 1984. “Models for Estimating Technical and Scale Efficiencies in Data Envelopment Analysis.” Management Science, 30, pp. 1078–1092.Google Scholar
  6. Banker, R.D., A. Charnes, W.W. Cooper, and A. Maindiratta. 1986. “A Comparison of DEA and Translog Estimates of Production Frontiers Using Simulated Observations from a Known Technology.” In A. Dogramaci and R. Fare, Applications of Modern Production Theory: Efficiency and Productivity, Boston: Kluwer.Google Scholar
  7. Bessent, A., W. Bessent, A. Charnes, W.W. Cooper, and N. Thorogood. 1983. “Evaluation of Educational Proposals by Means of DEA.” Educational Administration Quarterly, 19, pp. 82–87.Google Scholar
  8. Bowlin, W.F., A. Charnes and H.D. Sherman. 1985. “Data Envelopment Analysis and Regression Approaches to Efficiency Evaluation and Estimation.” Annals of Operations Research, pp. 113–138.Google Scholar
  9. Charnes, A. and W.W. Cooper. 1961. Management Models and Industrial Applications of Linear Programming. New York: Wiley & Sons.Google Scholar
  10. Charnes, A. and W.W. Cooper. 1985. “Preface to Topics in Data Envelopment Analysis.” Annals of Operations Research, 2, pp. 59–94.Google Scholar
  11. Charnes, A., W.W. Cooper, B. Golany, L. Seiford, and J. Stutz. 1985. “Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions.” Journal of Econometrics, 30, pp. 91–107.Google Scholar
  12. Charnes, A., W.W. Cooper, and E. Rhodes. 1978. “Management Science Relations for Evaluation and Management Accountability.” Journal of Enterprise Management, 2, pp. 143–153.Google Scholar
  13. Charnes, A., W.W. Cooper and E. Rhodes, 1978. “Measuring Efficiency of Decision Making Units.” European Journal of Operational Research, 2, pp. 429–444.Google Scholar
  14. Charnes, A., W.W. Cooper, and E. Rhodes. 1979. “Measuring Efficiency of Decision Making Units.” European Journal of Operational Research, 3, p. 339.Google Scholar
  15. Charnes, A., W.W. Cooper, S. Duffuaa, and M. Kress. 1980. “Complexity and Computability of Solutions to Linear Programming Systems.”. International Journal of Computer and Information Sciences, pp. 483–506.Google Scholar
  16. Charnes, A., W.W. Cooper, and A. Schinnar. 1982. “Transforms and Approximations in Cost and Production Function Theory.” Omega, 10, pp. 207–211.Google Scholar
  17. Charnes, A., W.W. Cooper and T. Sueyoshi. (1988). “A Goal Programming/Constrained Regression Review of the Bell System Breakup.” Managment Science, 34, pp. 1–26.Google Scholar
  18. Charnes, A., W.W. Cooper, and T. Sueyoshi. (To appear). “A Goal Programming/Constrained Regression Study of AT&T as a Natural Monopoly.” In (O.A. Davis, ed.), Cost/Benefit Analysis.Google Scholar
  19. Charnes, A., W.W. Cooper, and R.M. Thrall. (1986). “Identifying and Classfying Scale and Technical Efficiencies in Data Envelopment Analysis.” Operations Research Letters, 5, pp. 105–116.Google Scholar
  20. Charnes, A., W.W. Cooper, Q.L. Wei, and Z.M. Huang. 1989. “Cone Ratio Data Envelopment Analysis and Multi-Objective Programming.” International Journal of Systems Sciences, 20, pp. 1099–1118.Google Scholar
  21. Dantzig, G.G. 1963. Linear Programming and Extensions, Princeton: Princeton University Press.Google Scholar
  22. Spivey, W.A. and R.M. Thrall, 1970. Linear Optimization. New York: Holt, Rinehart & Winston.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • A. Charnes
    • 1
  • W. W. Cooper
    • 2
  • R. M. Thrall
    • 3
  1. 1.The University of Texas at AustinUSA
  2. 2.The University of Texas at AustinUSA
  3. 3.Rice UniversityUSA

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