Strategies for units incentivization: Assessing influence by maximizing loss/gain in centrally managed systems

In the context of centrally managed systems (CMSs), accurately determining the influence of units is crucial for effective incentive and compensation plans. Previous attempts to measure the impact of a specific DMU involved evaluating overall system efficiency after removing that DMU. However, challenges arise in accurately assessing post-removal system efficiency primarily because the aggregate unit fails to represent the transformed system adequately. The lack of modification to the remaining DMUs results in a disparity between the average of the remaining DMUs and the previous aggregate unit. Consequently, calculating the overall efficiency of the new system using the previous aggregate unit becomes imprecise and lacks meaningful insight. We develop a new incentivization method involving the redistribution of the DMU under evaluation among the remaining units to maintain the representativeness of the aggregate DMU before and after the removal of the DMU under evaluation. We propose two models to calculate the maximum loss and gain for each inefficient and efficient DMU during this redistribution, respectively. Our method also demonstrates robustness when assessing the contributions of efficient DMUs in the presence of nearby masked units. We provide adaptations for inefficient DMUs near efficient ones but significantly distant from other groups of inefficient units, ensuring precise scoring. Our approach is demonstrated using a real dataset.