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Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

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  • Kazemi Matin, Reza
  • Kuosmanen, Timo

Abstract

Kuosmanen and Kazemi Matin [Theory of integer valued data envelopment analysis. European Journal of Operational Research 2009;192:658-67] developed an axiomatic foundation for a data envelopment analysis (DEA) model that assumes subsets of input and output variables to be integer valued. In this paper we extend and generalize the axiomatic foundation for the integer DEA under variable, non-decreasing and non-increasing returns to scale. These model variants are achieved by introducing new axioms of natural convexity and natural augmentability. We also develop mixed integer linear programming (MILP) formulations for computing efficiency scores in these environments. An empirical example illustrates the approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jomega:v:37:y:2009:i:5:p:988-995
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    1. 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.
    2. 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.
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    4. 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.
    5. 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.
    6. 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.
    7. V V Podinovski, 2004. "Bridging the gap between the constant and variable returns-to-scale models: selective proportionality in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 265-276, March.
    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. Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
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    Cited by:

    1. Zohreh Moghaddas & Alireza Amirteimoori & Reza Kazemi Matin, 2022. "Selective proportionality and integer-valued data in DEA: an application to performance evaluation of high schools," Operational Research, Springer, vol. 22(4), pages 3435-3459, September.
    2. Subhash C. Ray & Abhiman Das & Kankana Mukherjee, 2018. "Measures of Labor Use Efficiency from a Cost-Based Dual Representation of the Technology: A Study of Indian Bank Branches," Working papers 2018-17, University of Connecticut, Department of Economics.
    3. 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.
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    6. Youchao Tan & Udaya Shetty & Ali Diabat & T. Pakkala, 2015. "Aggregate directional distance formulation of DEA with integer variables," Annals of Operations Research, Springer, vol. 235(1), pages 741-756, December.
    7. Misiunas, Nicholas & Oztekin, Asil & Chen, Yao & Chandra, Kavitha, 2016. "DEANN: A healthcare analytic methodology of data envelopment analysis and artificial neural networks for the prediction of organ recipient functional status," Omega, Elsevier, vol. 58(C), pages 46-54.
    8. Shih-Heng Yu & Chia-Wei Hsu, 2020. "A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system," Annals of Operations Research, Springer, vol. 287(1), pages 515-535, April.
    9. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
    10. Majid Azadi & Mehdi Toloo & Fahimeh Ramezani & Reza Farzipoor Saen & Farookh Khadeer Hussain & Hajar Farnoudkia, 2024. "Evaluating efficiency of cloud service providers in era of digital technologies," Annals of Operations Research, Springer, vol. 342(2), pages 1049-1078, November.
    11. Kuosmanen, Timo & Zhou, Xun, 2021. "Shadow prices and marginal abatement costs: Convex quantile regression approach," European Journal of Operational Research, Elsevier, vol. 289(2), pages 666-675.
    12. See, Kok Fong & Ma, Zhanxin & Tian, Yuzhen, 2023. "Examining the efficiency of regional university technology transfer in China: A mixed-integer generalized data envelopment analysis framework," Technological Forecasting and Social Change, Elsevier, vol. 197(C).
    13. Lozano, Sebastián & Villa, Gabriel, 2016. "Data Envelopment Analysis of systems with multiple modes of functioning," MPRA Paper 76076, University Library of Munich, Germany.
    14. Mansour Zarrin, 2023. "A mixed-integer slacks-based measure data envelopment analysis for efficiency measuring of German university hospitals," Health Care Management Science, Springer, vol. 26(1), pages 138-160, March.
    15. Monireh Jahani Sayyad Noveiri & Sohrab Kordrostami & Alireza Amirteimoori, 2022. "Performance analysis of sustainable supply networks with bounded, discrete, and joint factors," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(1), pages 238-270, January.
    16. S. Lozano & G. Villa, 2019. "Data envelopment analysis of systems with multiple modes of functioning," Annals of Operations Research, Springer, vol. 278(1), pages 17-41, July.
    17. 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.
    18. 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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