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Theory of integer-valued data envelopment analysis

  • Kuosmanen, Timo
  • Matin, Reza Kazemi

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.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 192 (2009)
Issue (Month): 2 (January)
Pages: 658-667

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Handle: RePEc:eee:ejores:v:192:y:2009:i:2:p:658-667
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  1. 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.
  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. John J. Rousseau & John H. Semple, 1993. "Notes: Categorical Outputs in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(3), pages 384-386, March.
  4. 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.
  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. 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.
  7. 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.
  8. 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.
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