Research On The Fixed Cost Allocation Based On DEA

The problem of allocating the fixed cost is regarded as a task of high frequency, great difficulty and remarkable importance in economic circles, or in social activities. Generally, in order to perfectly describe and analysis the fixed cost allocation problems, the analysts are inclined to select the related factors hand and foot But it may cause troubles to the traditional fixed cost allocation approaches which only consider one or two factors in solving the problem. While Data envelopment analysis (DEA) is a resultful tool, dealing with multiple factors to evaluate the relative efficiencies among Decision Making Units (DMUs). In the perspective of the efficiency evaluation of DMUs, this paper has studied the DEA-based fixed cost allocation problems.This paper involves six chapters, and the essence is described as follows.The first chapter firstly introduces the definition of the fixed cost, the traditional approach of allocating the fixed cost and its related application fields, as well as the basic knowledge of DEA. It is followed by reviewing the research status of the DEA-based fixed cost allocation, and pointing out the shortcomings of the traditional DEA-based approaches. Finally, this chapter describes the research content and significance of this paper in detail.When the fixed cost is treated as a new input, the second chapter firstly studies the efficiency evaluation of the individual DMU and the whole DMUs. And it proves that there is a set of fixed cost allocation plans which can make all DMUs and the whole DMUs efficient. Then, Based upon the fixed cost allocation plan set, and taking into consideration of reducing the gap between DMUs' allocated costs, this chapter proposes two kinds of cost allocation approaches. Both the numerical comparison and a case study of allocating the advertisement expense among automobile dealers show that the proposed cost allocation methods are more rational than traditional DEA approaches.Taking into consideration the competitive relationship between the DMUs, the third chapter combines DEA with non-cooperative game, and proposes maxmin, minmax and balanced cost allocation models based on the cost allocation plan set, Also, the three models' related algorithms have been proposed in this chapter. By the fixed cost allocations' comparison, this chapter describes that each proposed allocation model has its suitable environment. Taking into consideration the competitive and cooperative relationship between the DMUs, the fourth chapter combines DEA with cooperative game to solve the problem. Based on the DMUs' rationality assumption and the cost allocation plan set, this part defines the characteristic function of each coalition, and proposes six different cost allocation solutions to the cooperative game, which are (1) Nash bargaining game model; (2) least core model; (3) weak least core model; (4) proportional least core model; (5) Shapley value model; (6) Nucleolus model. Finally, the proposed approaches have been applied in allocating the expense of upgrading the electric trade system among branches in a commercial bank.When there are some other cost-measures, the fixed cost may not be treated as an extra independent factor rather than a complement of a single cost input. The fifth chapter studies the fixed cost allocation under this situation. First, this chapter studies the efficiency evaluation of each DMU under the situation. Then, it studies the effect on the DMU's DEA efficiency caused by the fixed cost, discovers that the DMU's DEA efficiency is non-increasing to the magnitude of the cost it affords. Based upon the conclusions, this chapter proposes a new fixed cost allocation model and its corresponding algorithm. Finally, a case study of allocating the advertisement expense shows the proposed method is feasible and rational.The last chapter summarizes all the work of this thesis, and gives some useful suggestions for future research.The major contributions of this thesis are briefly summarized as follows: (1) In measuring the efficiency of DMUs, this paper has considered whether the fixed cost can be treated as a new input to each DMU; (2) When the fixed cost can be treated as a new input, this paper has proven that all individual DMUs can be DEA efficient. Based upon this conclusion, this paper has proposed two extended cost allocation approaches. (3) Considering the competitive and cooperative relationship among DMUs, this paper integrates DEA with Game Theory, and proposes several fixed cost allocation approaches, corresponding to each kind of different backgrounds. (4) When the fixed cost can be treated as a new input, this paper has proven that the DMU's super CCR efficiency function is a non-increasing in the amount of the fixed cost DMU affords, then proposed a new approach of allocating the fixed cost.