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Global sub-increasing and global sub-decreasing returns to scale in free disposal hull technologies: Definition, characterization and calculation

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  • Mostafaee, Amin
  • Soleimani-damaneh, Majid

Abstract

Global Returns to Scale (GRS) is an important notion in performance analysis under Free Disposal Hull (FDH) technologies. Ray Average Productivity (RAP) function has a crucial role in interpreting the GRS. We define two new notions, called Global Sub-Increasing RTS (G-SIRS) and Global Sub-Decreasing RTS (G-SDRS), invoking the behaviour of the RAP function at its maximizers. These notions are useful from a managerial standpoint, because they help the decision maker to decide about contracting or expanding the operation of the units under consideration. After presenting a motivating example and defining G-SIRS and G-SDRS, some theorems are proved to characterize these new notions. A polynomial-time algorithm is sketched which is able to determine the GRS of the Decision Making Units (DMUs) under evaluation. The second part of the paper is devoted to calculating a stability interval for GRS. It is done through some theorems and a polynomial-time algorithm. The results of the paper are illustrated by numerical examples as well as empirical studies with real-world data. Computational experiments are reported as well.

Suggested Citation

  • Mostafaee, Amin & Soleimani-damaneh, Majid, 2020. "Global sub-increasing and global sub-decreasing returns to scale in free disposal hull technologies: Definition, characterization and calculation," European Journal of Operational Research, Elsevier, vol. 280(1), pages 230-241.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:1:p:230-241
    DOI: 10.1016/j.ejor.2019.07.005
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    Cited by:

    1. Geraldo Souza & Eliane Gonçalves Gomes & Eliseu Roberto Alves, 2022. "Two-part fractional regression model with conditional FDH responses: an application to Brazilian agriculture," Annals of Operations Research, Springer, vol. 314(2), pages 393-409, July.
    2. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    3. Xiaoqing Chen & Kristiaan Kerstens & Qingyuan Zhu, 2021. "Exploring Horizontal Mergers in Swedish District Courts Using Convex and Nonconvex Technologies: Usefulness of a Conservative Approach," Working Papers 2021-EQM-05, IESEG School of Management.

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