DEA Based Fixed Cost Allocation:Individual Rationality And Overall Fairness

Fixed Cost Allocation(FCA)is the problem of determining how the total fixed cost incurred by a public platform should be equitably distributed among multiple DMUs.In this paper,we will study fixed cost allocation based on the DEA from the perspective: individual rationality and overall fairness.First of all,we propose an allocation method based on the Pareto optimal cross-efficiency model.First,the individual rationality principle is proposed when individual DMUs give their preferred cost allocation scheme.Second,the lower bound principle and the overall pareto optimality principle are proposed from the perspective of overall fairness when considering the determination of the final cost allocation scheme.A multi-objective fixed cost allocation model is constructed in this paper,and the corresponding algorithm is proposed to ensure the linear solution of the model and the uniqueness of the solution.Finally,we apply the proposed model to a numerical case and a truck case to illustrate the feasibility and superiority of the method proposed in this paper.Second,this paper constructs a fixed cost allocation model considering complex competing relationships among DMUs.First,the K-means clustering method is used to find out the cooperation intention between DMUs.Then this paper further combines the principle of individual rationality of DMUs and proposes the constraints that individual DMUs should satisfy when giving their preferred cost allocation results.Then,from the perspective of overall fairness,maxing the post-allocation efficiency score and ensuring the uniqueness of the solution are considered in the model for determining the final allocation results.Finally,the proposed method is applied to a numerical example and a commercial bank example to illustrate the approach of this paper.The main innovations of this paper are summarized as follows:(1)The principles of individual rationality and overall fairness of DMUs in the process of cost allocation are specified for the first time,and a mathematical expression for the specification of the corresponding principles is given.(2)A cost allocation model considering individual rationality and overall fairness is proposed,which helps to improve the acceptance of our allocation scheme by DMUs.(3)A new game feedback mechanism is proposed,and a fixed cost allocation model considering the hybrid game relationship is established.(4)On the basis of ensuring individual rationality and overall fairness,the proposed cost allocation method has better robustness.