Fixed cost allocation in two-stage system: A data-driven approach from the perspective of fairness concern

Abstract

Fixed cost allocation is the common issue for decision maker in real case, especially in the two-stage system such as banks, insurance companies, schools and other enterprises. Due to the complexity of two-stage system, fixed cost allocation in two-stage system between two stages is always worthy of investigation. Numerous studies have emerged to address the issue on the basis of data envelopment analysis (DEA). However, fairness concern is frequently ignored in those studies. Fairness concern is regarded as one of the most important factors guiding human behaviour in daily life. This paper studies how fairness concern impacts allocating fixed cost between two stages among all decision making units (DMUs). On the basis of cooperation and conflict between two stages, we investigate the fixed cost allocation under non-cooperative mode and cooperative mode respectively, and minimize the maximal fairness concern disutility by proposing max–min model. Further, we give some theorems to illustrate our proposed models and give algorithms for models to obtain the unique allocation plan under different modes. Lastly, a numerical example is presented, and we apply our approaches to address fixed cost allocation issue of a commercial bank which has 27 branches. Results shows that our proposed approaches can obtain an equitable allocation plan as much as possible compared with previous studies.