A general framework and an individual dominance realization model for efficient fixed cost allocation based on DEA

Abstract

Data Envelopment Analysis (DEA) has become a powerful tool for addressing fixed cost allocation (FCA) problems. Among the numerous DEA-based FCA studies, a significant category seeks to make all Decision-making Units (DMUs) efficient under a set of common weights after cost allocation, falling under the common-weights FCA framework. However, the classical DEA efficiency evaluation mechanism does not require all DMUs to be evaluated based on a set of common weights. Instead, a DMU is considered efficient if it can choose its favorable weights to achieve an efficiency score of one while ensuring that the efficiencies of other DMUs do not exceed one. Motivated by this, we develop a novel and general efficient FCA framework that allocates the total fixed cost by allowing each DMU to select its preferred weights to be efficient. We prove that the FCA possible set under the traditional common-weights framework is a subset of that under this new framework. Then, an Assurance Region (AR) constraint on fixed costs is introduced to avoid extreme allocation schemes. Moreover, an individual dominance realization strategy and a FCA model based on it are proposed within this framework, aimed at minimizing each DMU’s cross-efficiencies from the perspective of all other DMUs while ensuring its self-assessed efficiency remains at one. Additionally, an algorithm is introduced to guarantee the uniqueness of the FCA scheme. A numerical example and a case study from the Shanghai Automotive Industry Corporation are used to validate the effectiveness of this approach and compare it with other classic methods.