Management Science

Abstract: Context-dependent data envelopment analysis (DEA) based on cross-efficiency evaluation has been proposed to present more meaningful measures of attractiveness and progress scores, cross-attractiveness, and cross-progress scores, by considering the distance between the decision-making unit (DMU) under evaluation and the entire evaluation context overall. Using an illustrative example, we show that the state of the art existing method does not guarantee to produce a non-dominated cross- attractiveness (cross-progress) scores vector. This raises concerns about the reliability and universal acceptance of the derived scores. Thus, we investigate the Pareto optimality of these peer evaluation scores and introduce a concept of optimality in line with the dominance notion. We subsequently propose a multi-objective model designed to produce all non-dominated cross-attractiveness (cross-progress) score vectors. We introduce two perspectives – a common base and an individualized approach. The common base method determines the same vector of weights for all units in the evaluation context to produce non-dominated scores. In contrast, the individualized based approach empowers each DMU within the evaluation context to assess the attractiveness (progress) score of DMUs under evaluation at a specific level based on their own distinct criteria. This methodology is aligned with the inherent desire of the DMUs within the evaluation context to have the most substantial impact on the evaluation of cross-attractiveness (cross-progress) for the DMUs under the assessment at a specific level. We illustrate our proposed methods with a real-world examples to yield non-dominated cross-attractiveness (cross-progress) scores.

Abstract: 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 maxi- mum 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.