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Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis

In: Data Envelopment Analysis

Author

Listed:
  • Timo Kuosmanen

    (Aalto University School of Business)

  • Abolfazl Keshvari

    (Aalto University School of Business)

  • Reza Kazemi Matin

    (Islamic Azad University)

Abstract

Standard axioms of free disposability, convexity and constant returns to scale employed in Data Envelopment Analysis (DEA) implicitly assume continuous, real-valued inputs and outputs. However, the implicit assumption of continuous data will never hold with exact precision in real world data. To address the discrete nature of data explicitly, various formulations of Integer DEA (IDEA) have been suggested. Unfortunately, the axiomatic foundations and the correct mathematical formulation of IDEA technology has caused considerable confusion in the literature. This chapter has three objectives. First, we re-examine the axiomatic foundations of IDEA, demonstrating that some IDEA formulations proposed in the literature fail to satisfy the axioms of free disposability of continuous inputs and outputs, and natural disposability of discrete inputs and outputs. Second, we critically examine alternative efficiency metrics available for IDEA. We complement the IDEA formulations for the radial input measure with the radial output measure and the directional distance function. We then critically discuss the additive efficiency metrics, demonstrating that the optimal slacks are not necessarily unique. Third, we consider estimation of the IDEA technology under stochastic noise, modeling inefficiency and noise as Poisson distributed random variables.

Suggested Citation

  • Timo Kuosmanen & Abolfazl Keshvari & Reza Kazemi Matin, 2015. "Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 4, pages 67-103, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7553-9_4
    DOI: 10.1007/978-1-4899-7553-9_4
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    Citations

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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. Topcu, Taylan G. & Triantis, Konstantinos & Roets, Bart, 2019. "Estimation of the workload boundary in socio-technical infrastructure management systems: The case of Belgian railroads," European Journal of Operational Research, Elsevier, vol. 278(1), pages 314-329.
    3. Ya Chen & Wade D. Cook & Juan Du & Hanhui Hu & Joe Zhu, 2017. "Bounded and discrete data and Likert scales in data envelopment analysis: application to regional energy efficiency in China," Annals of Operations Research, Springer, vol. 255(1), pages 347-366, August.
    4. 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.

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