Equitable revenue allocation in DEA under a common set of weights: a unified optimization approach

Abstract

Data Envelopment Analysis (DEA) can be used to allocate common revenue. This paper proposes a common revenue allocation approach based on a common set of weights (CSW). The proposed approach is governed by two principles: efficiency ratio (ER) invariance and common weight ratio (CWR) invariance. Specifically, a centralized decision-making unit (DMU) model is first developed to determine a CSW. By imposing lower-bound restrictions on virtual weights, the proposed model effectively eliminates the common issue of zero weights in traditional DEA. Subsequently, a secondary objective function model is introduced to resolve CSW non-uniqueness. Research findings confirm that the framework strictly preserves both ER and CWR invariance. Furthermore, empirical evidence demonstrates a wider allocation span across DMUs and the complete elimination of zero-revenue outcomes. These results effectively overcome the incentive compression and punitive zero-allocations of traditional models. Consequently, the method ensures high incentive power and managerial acceptability. Ultimately, the main contribution of this study is an equitable framework that bridges the gap between theoretical evaluation and practical decision-making.