基于效率最大化和极小极大相对差异的固定成本分配

摘要

本文基于两个假设：所有决策单元(DMU)在分配之后达到在共同权重下强CCR有效；最小化分配成本和相应的规模分配成本之间的最大相对差异，利用数据包络分析技术提出了一个极小极大模型来求解固定成本分配问题。在纯投入和纯产出情况下，导出了该极小极大模型的解析解；并在一般情况下，提出了该极小极大模型的相应算法，该算法能够生成一组唯一的固定成本分配解且具有良好的计算有效性。与其它基于类似假设的分配方法相比，新方法能够根据DMU的投入和产出分配成本，从而避免成本间的不恰当差距。数值例子显示了新方法的有效性和优势。%In this paper, we apply the data envelopment analysis technique to propose a mini-max model for the fixed cost allocation problem under two assumptions: all decision making units (DMUs) become strong CCR-efficient under common weights after the fixed cost allocation; the maximum relative difference between allocated costs and the corresponding scale sharing costs is minimized. In the pure input case and the pure output case, we deduce the analytical solution of the minimax model; in the general case, we propose an algorithm for the minimax model, which always produces a unique fixed cost allocation solution with good computational efficiency. Compared with other allocation methods based on the similar assumption, the new approach can avoid inappropriate gaps among costs with the help of appropriately allocating costs among DMUs according to their individual inputs and outputs. Numerical analysis shows the validity and superiorities of the new approach.