Incentivization in centrally managed systems: Inconsistencies resolution

In centrally managed systems (CMSs), the need for incentivization systems at the local management level is crucial to optimize overall performance. Three alternative incentive systems have emerged within the centralized resource allocation (CRA) framework, aiming to measure the contribution of decision-making units (DMUs) in CMSs. However, we identify inconsistencies within these approaches and present them through illustrative examples. First, existing methods may struggle to effectively distinguish between CRA-efficient and CRA-inefficient DMUs, potentially resulting in inappropriate penalties or rewards for some the DMUs. Second, they may encounter difficulty in differentiating among CRA-efficient DMUs, especially when dealing with non-extreme DMUs or masked data within the dataset. Third, these methods may lack precision in measuring the impact of non-extreme CRA-efficient DMUs on overall performance. To address these limitations, we first highlight certain misconceptions related to individual efficiency within CMSs in the existing literature. Subsequently, we establish a fundamental characterization of individual efficient DMUs by outlining necessary and sufficient conditions for categorizing a DMU as CRA-efficient. For the second and third limitations, we adopt an endogenous perspective to quantify the influence of each CRA-efficient DMU. This involves calculating the maximum potential contribution of the DMU under evaluation in constructing the projection points of other DMUs. Furthermore, we propose a new method to handle masked data well in differentiating among CRA-efficient DMUs. We show the validity and applicability of our approaches using a real dataset.