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Aggregate directional distance formulation of DEA with integer variables

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Abstract

Conventional data envelopment analysis (DEA) models make the assumption of non-negativity and real values in the input and output of the systems that are under study. This paper combines these two interrelated ideas. One is the non-radial measurement of efficiency by establishing an aggregate directional distance formulation of the DEA model (ADDM). Another is the introduction of an integer directional distance function. Usually, directional distance formulations of DEA and ADDM projections of efficient targets for inefficient decision making units (DMUs) have non-integer values. In this paper directional distance function is modified and a mixed integer directional distance formulation of DEA is proposed. This model guarantees integer targets for inefficient DMUs and is applicable to measure efficiency even when input and output variables are negative integer values.

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Acknowledgments

Youchao Tan’s research is partially supported by National Natural Science Foundation of China, Grant no 71302005, humanities and social sciences Foundation of Ministry of Education in China, Grant no 14YJC630049.

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Authors and Affiliations

  1. School of Accounting, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Youchao Tan

  2. Directorate of Economics and Statistics, Government of Karnataka, Mangalore, 575 006, India

    Udaya Shetty

  3. Department of Engineering Systems and Management, Masdar Institute of Science and Technology, Abu Dhabi, UAE

    Ali Diabat

  4. Department of PG Studies and Research in Statistics, Mangalore University, Mangalagangotri, Mangalore, 574 199, India

    T. P. M. Pakkala

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  1. Youchao Tan
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  2. Udaya Shetty
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  4. T. P. M. Pakkala
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Correspondence to Udaya Shetty.

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Tan, Y., Shetty, U., Diabat, A. et al. Aggregate directional distance formulation of DEA with integer variables. Ann Oper Res 235, 741–756 (2015). https://doi.org/10.1007/s10479-015-1891-8

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  • DOI: https://doi.org/10.1007/s10479-015-1891-8

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