Fixed cost allocation based on data envelopment analysis from inequality aversion perspectives

Abstract

In many real-world cases, fixed cost allocation frequently occurs in constructing the common platform of an organization: all divisions related to the platform must share the platform's fixed cost. Addressing the fixed cost allocation issue has become a vital topic, and numerous approaches have been used, including data envelopment analysis (DEA). However, inequality aversion, one vital concept of fairness concern, is frequently ignored in the previous publications. This paper is devoted to guaranteeing fairness for all decision-making units (DMUs) in allocation solutions from DEA. Firstly, we discuss how inequality impacts DMUs by proposing the concept of “fairness concern disutility” and using various parameters to reflect the negative impact of an unfair allocation plan on DMUs. Secondly, we discuss fixed cost allocation from three perspectives: optimistic, pessimistic, and mixed. Moreover, we give algorithms to obtain a unique, optimal solution and propose theorems to better understand our model. Lastly, we use a numerical example to illustrate the proposed models and theorems before applying our approach to address a fixed allocation issue in a commercial bank. Our analysis results show that the proposed approaches can guarantee fairness in fixed cost allocation.