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A Bi-Extremal Principle for Frontier Estimation and Efficiency Evaluations

Author

Listed:
  • R. D. Banker

    (Carnegie-Mellon University)

  • A. Charnes

    (University of Texas at Austin)

  • W. W. Cooper

    (University of Texas at Austin)

  • A. P. Schinnar

    (University of Pennsylvania)

Abstract

A new approach is supplied for locating efficiency frontiers and evaluating the efficiency of Decision Making Units (DMU's). This is accomplished from observational data by means of an envelopment procedure called DEA (Data Envelopment Analysis) originally developed by Charnes, Cooper and Rhodes (Charnes, A., W. W. Cooper, E. Rhodes, 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (6). See also, Short communication. Eur. J. Oper. Res. 3 (1979) 339.) in connection with their ratio formulation for relative efficiency measurement. The current variant employs a bi-extremal principle which, though nonlinear, is subsequently shown to be reducible to a finite sequence of linear programming problems. The development is illustrated by means of multiple output functions which are piecewise of Cobb-Douglas or general log linear type and which also allow for increasing, decreasing and constant returns to scale. More than one production function for the DMU's is also allowed. The reduction of the bi-extremal principle to linear programming equivalence is also accomplished for much more general classes of functions. A numerical example illustrates some of these ideas and also provides a springboard for a new theorem which relates these efficiency measures to ones which were supplied earlier in the Charnes, Cooper and Rhodes's work (Charnes, A., W. W. Cooper, E. Rhodes, 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (6). See also, Short communication. Eur. J. Oper. Res. 3 (1979) 339.).

Suggested Citation

  • R. D. Banker & A. Charnes & W. W. Cooper & A. P. Schinnar, 1981. "A Bi-Extremal Principle for Frontier Estimation and Efficiency Evaluations," Management Science, INFORMS, vol. 27(12), pages 1370-1382, December.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:12:p:1370-1382
    DOI: 10.1287/mnsc.27.12.1370
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    Cited by:

    1. Mehdiloozad, Mahmood & Sahoo, Biresh K. & Roshdi, Israfil, 2014. "A generalized multiplicative directional distance function for efficiency measurement in DEA," European Journal of Operational Research, Elsevier, vol. 232(3), pages 679-688.
    2. Farzaneh Asadi & Sohrab Kordrostami & Alireza Amirteimoori & Morteza Bazrafshan, 2023. "Inverse data envelopment analysis without convexity: double frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 335-354, June.
    3. M. Zarepisheh & E. Khorram & G. Jahanshahloo, 2010. "Returns to scale in multiplicative models in data envelopment analysis," Annals of Operations Research, Springer, vol. 173(1), pages 195-206, January.
    4. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    5. Pina, Vicente & Torres, Lourdes, 2001. "Analysis of the efficiency of local government services delivery. An application to urban public transport," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(10), pages 929-944, December.
    6. Tao, Xiangyang & An, Qingxian & Goh, Mark, 2024. "Plant capacity utilization with piecewise Cobb-Douglas technology: Definition and interpretation," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1034-1043.
    7. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.

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