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Theory of integer-valued data envelopment analysis

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  • Kuosmanen, Timo
  • Matin, Reza Kazemi

Abstract

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of "natural disposability" and "natural divisibility". We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.

Suggested Citation

  • Kuosmanen, Timo & Matin, Reza Kazemi, 2009. "Theory of integer-valued data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 192(2), pages 658-667, January.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:2:p:658-667
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    References listed on IDEAS

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    1. John J. Rousseau & John H. Semple, 1993. "Notes: Categorical Outputs in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(3), pages 384-386, March.
    2. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    3. Wagner A. Kamakura, 1988. "Note---A Note on "The Use of Categorical Variables in Data Envelopment Analysis"," Management Science, INFORMS, vol. 34(10), pages 1273-1276, October.
    4. Sebastián Lozano & Gabriel Villa, 2007. "Integer Dea Models," Springer Books, in: Joe Zhu & Wade D. Cook (ed.), Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, chapter 0, pages 271-289, Springer.
    5. Cherchye, Laurens & Kuosmanen, Timo & Post, Thierry, 2001. "Alternative treatments of congestion in DEA: A rejoinder to Cooper, Gu, and Li," European Journal of Operational Research, Elsevier, vol. 132(1), pages 75-80, July.
    6. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    7. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    8. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    9. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    10. Wade D. Cook & Joe Zhu, 2007. "Data Irregularities And Structural Complexities In Dea," Springer Books, in: Joe Zhu & Wade D. Cook (ed.), Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, chapter 0, pages 1-11, Springer.
    11. Rajiv D. Banker & Richard C. Morey, 1986. "The Use of Categorical Variables in Data Envelopment Analysis," Management Science, INFORMS, vol. 32(12), pages 1613-1627, December.
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