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Measuring individual efficiency and unit influence in centrally managed systems

Author

Listed:
  • Mostafa Davtalab-Olyaie

    (University of Kashan)

  • Hadis Mahmudi-Baram

    (University of Kashan)

  • Masoud Asgharian

    (McGill University)

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.

Suggested Citation

  • Mostafa Davtalab-Olyaie & Hadis Mahmudi-Baram & Masoud Asgharian, 2023. "Measuring individual efficiency and unit influence in centrally managed systems," Annals of Operations Research, Springer, vol. 321(1), pages 139-164, February.
    • Handle: RePEc:spr:annopr:v:321:y:2023:i:1:d:10.1007_s10479-022-04676-6
    DOI: 10.1007/s10479-022-04676-6
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