Abstract: In this paper, the fixed cost allocation problem among the decision making units (DMU) with two stages is considered. First, the fixed cost is treated as an additional input to DMUs, and an additive two-stage DEA model is established. Then, some important theorems are proven:1. each DMU could find at least one allocation plan to make its total and each stage Pareto efficient; 2. there is at least one allocation plan for all DMUs and their stages to be Pareto efficient under a set of common weight; 3. the efficient fixed cost allocation set is provided. These theorems are also founded when it is expanded to the two-stage system with shared inputs. In order to obtain an equitable allocation, the satisfaction degree of each DMU's stage is defined. Through maximizing the minimal satisfaction degree, the final allocation plan is gotten. The numerical example shows that our approach is feasible and valid. Since the efficiency and fairness is considered together, the fixed cost allocation obtained from our approach is fair and valid. Our approach can give managers supports when they face cost allocation problems.

Key words: two-stage DEA, fixed cost allocation, satisfaction degree, Pareto efficient