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Measuring individual efficiency and unit influence in centrally managed systems

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Abstract

A centrally managed system (CMS) typically comprises several decision making units (DMUs) that operate under a central DMU. The central DMU allocates the total available resources under its control among different DMUs to optimize the performance of the whole system. This distinguishing feature is at the heart of centralized resource allocation (CRA) methods and should be taken into account when assessing individual efficiency of each DMU in CMS. We introduce a slacks-based model for measuring individual efficiency of each DMU in CMS. As we will discuss, there are different possible CRA plans leading different projection points of DMUs on the frontier of the production possibility set (PPS). We will however show that all DMUs are projected on the same supporting hyperplane of the PPS under all CRA plans. We therefore have a common reference base, a subset of the ordinary efficient frontier, using which individual efficiency of each DMU can be measured in CMS. Having measured the individual efficiency of each DMU, we can categorize the DMUs into CRA-efficient and CRA-inefficient. To distinguish between CRA-efficient DMUs, we further introduce an influence index that measures the maximum effect of a specific CRA-efficient DMU on the construction of the projection points of the DMUs in CMS. We then propose a linear model to measure the influence of each CRA-efficient DMU. We can therefore provide a complete ranking of the DMUs in CMS. The proposed approach is demonstrated using a real data set.

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Notes

  1. See Charnes et al. (1986), Jahanshahloo et al. (2013), Davtalab Olyaie et al. (2014) and Davtalab-Olyaie et al. (2015) for more details about weak and strong frontiers.

  2. It should be noted that there may exist other projection points of \(\hbox {DMU}_{{A}}\) which correspond to other CRA plans.

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Acknowledgements

The authors would like to express their sincere thanks to the Editor, the AE who handled our submission and two referees for their constructive comments. The research of the third author is supported by the Natural Science and Engineering Research Council (NSERC) of Canada [NSERC RGPIN-2018-05618].

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Correspondence to Mostafa Davtalab-Olyaie.

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Davtalab-Olyaie, M., Mahmudi-Baram, H. & Asgharian, M. Measuring individual efficiency and unit influence in centrally managed systems. Ann Oper Res 321, 139–164 (2023). https://doi.org/10.1007/s10479-022-04676-6

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