DEA-based proportional-sharing fixed cost allocation considering bi-objective optimization

This paper proposes a new proportional-sharing approach for fixed cost allocation (FCA) among a group of decision-making units (DMUs) based on data envelopment analysis (DEA). We first prove the proportional invariance in DEA-based FCA. Then, we show that the all-efficient assumption in existing models usually leads to the use of unrealistic weights in efficiency analysis. To address this issue, we relax this assumption and adopt a weight constraint approach. Further, we illustrate that some DMUs would always be allocated with zero fixed cost if only the goal of efficiency maximizing is considered. Therefore, some weight constraints are added, and a new bi-objective model is proposed to allocate the fixed cost among the DMUs in order to simultaneously maximize the efficiencies of the DMUs and make the allocation as close as possible to the one generated according to the DMUs' operation sizes. A mono-objective nonlinear program, which can be solved using dichotomy and a linear program solver, is used to obtain a non-dominated or Pareto-optimal trade-off solution for the bi-objective model. With the use of our approach, neither unrealistic weights nor zero fixed cost appears in the result. Finally, the proposed approach is applied to a numerical example and a commercial bank case study.

Automated summary

This paper proposes a new proportional-sharing approach for fixed cost allocation (FCA) among a group of decision-making units (DMUs) based on data envelopment analysis (DEA). The paper relaxes the all-efficient assumption in existing models and adopts a weight constraint approach to address the issue of unrealistic weights in efficiency analysis. A new bi-objective model is proposed to simultaneously maximize the efficiencies of the DMUs and make the allocation as close as possible to the one generated according to the DMUs' operation sizes. The proposed approach is applied to a numerical example and a commercial bank case study.