Abstract
Finding the closest most productive scale size (MPSS) unit is an important issue in the data envelopment analysis (DEA) literature. The closest MPSS unit to the decision-making unit (DMU) under evaluation may be one of the existing (actually) observed MPSS units in the production technology. Also, finding the closest (actually) observed MPSS unit to the DMU under evaluation causes this DMU can easily achieve the optimal size for improving its performance because, in this case, the closest MPSS unit is only selected from the (actually) observed MPSS units. Hence, the manager (or decision-maker) of the DMU is more interested in considering the closest (actually) observed MPSS unit as a more accessible reference unit for his/her DMU than the closest non-observed MPSS unit. Hitherto several DEA-based models have been presented to determine the closest MPSS unit for the DMU under evaluation. However, the closest unit obtained from these models may not be MPSS, and also, this unit may not be one of the existing (actually) observed MPSS units in the technology. These problems indicate the drawbacks of these models. Hence, this research contributes to DEA by proposing three linear DEA-based models to tackle these drawbacks. Identifying the closest (actually) observed MPSS unit to the DMU under evaluation can be also used as a criterion for ranking the (actually) observed MPSS units as reference units for this DMU in the technology. This study also clarifies the managerial and economic implications of identifying the closest (observed) MPSS unit. Moreover, three numerical examples are given to illustrate the drawbacks of the previous models. Finally, a numerical illustration and an empirical application are provided to highlight the use of the proposed models.
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Notes
“The symbol \(\varepsilon > 0\) refers a ʻnon-Archimedean’ element which is smaller than any positive real number and, to avoid having to specify \(\varepsilon\) explicitly DEA computer codes (Arnold et al. 1997) generally utilize a two-stage process in which the sum of the slacks (as parenthesized in (5)) is maximized while fixing \(\theta^{ * }\) at its optimal value, ((Banker et al. 1996), p. 477)”.
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The authors thank Prof. Guido Voigt, the Editor-in-Chief of OR Spectrum, and three anonymous referees for valuable comments and constructive suggestions that helped us to significantly improve the manuscript.
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RE and MK contributed to conceptualization, methodology, supervision, visualization, resources, and data curation and provided software; RE, MK, AG, and EE were involved in formal analysis and investigation; and MK contributed to writing—original draft preparation, and writing—reviewing and editing.
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Esfandiar, E., Eslami, R., Khoveyni, M. et al. Identifying the closest most productive scale size unit in data envelopment analysis. OR Spectrum 45, 623–660 (2023). https://doi.org/10.1007/s00291-022-00692-x
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DOI: https://doi.org/10.1007/s00291-022-00692-x