1 Introduction

The resource allocation problem has a great practical applied value. The difficulty of this problem is: how to evaluate the departments involved in the allocation, and how to determine their allocation weights. Recently, using DEA models to solve this problem has become a new research area. That is because DEA is a synthetic method measuring the relative efficiency of homogeneous production departments (referred to as decision making units, DMU) (see [1][4][5]). Moreover, the inputs and outputs weights vector obtained by DEA models is the Pareto solution for multiobjective programming, and it satisfies the Nash equilibrium condition as well(see [7]). In paper [8] and [9], they clearly define the extra resource allocation problem, and propose that the decision maker should take into account both the efficiency and the scale. Subsequently, paper [2] and [3] suggest the decision maker should consider the returns-to-scale also when dealing with this problem. Returns-to-scale (RTS) is a concept in economics, which reflects the potential production capacity when inputs are increased (see [4][5]).