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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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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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    Citations

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    Cited by:

    1. Chen, Yao & Djamasbi, Soussan & Du, Juan & Lim, Sungmook, 2013. "Integer-valued DEA super-efficiency based on directional distance function with an application of evaluating mood and its impact on performance," International Journal of Production Economics, Elsevier, vol. 146(2), pages 550-556.
    2. repec:spr:annopr:v:255:y:2017:i:1:d:10.1007_s10479-015-1827-3 is not listed on IDEAS
    3. repec:spr:annopr:v:250:y:2017:i:1:d:10.1007_s10479-015-1856-y is not listed on IDEAS
    4. Lozano, Sebastián & Villa, Gabriel, 2016. "Data Envelopment Analysis of systems with multiple modes of functioning," MPRA Paper 76076, University Library of Munich, Germany.
    5. Kazemi Matin, Reza & Kuosmanen, Timo, 2009. "Theory of integer-valued data envelopment analysis under alternative returns to scale axioms," Omega, Elsevier, vol. 37(5), pages 988-995, October.
    6. Subhash C. Ray & Abhiman Das & Kankana Mukherjee, 2017. "Labor-Cost Efficiency with Indivisible Outputs and Inputs: A Study of Indian Bank Branches," Working papers 2017-04, University of Connecticut, Department of Economics.
    7. Du, Juan & Chen, Chien-Ming & Chen, Yao & Cook, Wade D. & Zhu, Joe, 2012. "Additive super-efficiency in integer-valued data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 218(1), pages 186-192.
    8. Jie Wu & Qingyuan Zhu & Wade D Cook & Joe Zhu, 2016. "Best cooperative partner selection and input resource reallocation using DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1221-1237, September.
    9. Villa, G. & Lozano, S., 2016. "Assessing the scoring efficiency of a football match," European Journal of Operational Research, Elsevier, vol. 255(2), pages 559-569.

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