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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (5): 743-758.doi: 10.3969/j.issn.1005-3085.2015.05.012

• • 上一篇    下一篇

基于效率最大化和极小极大相对差异的固定成本分配(英)

林瑞跃1,2   

  1. 1- 温州大学数学与信息科学学院，温州 325035
    2- 西安交通大学数学与统计学院，西安 710049
  • 收稿日期:2015-04-10 接受日期:2015-07-30 出版日期:2015-10-15 发布日期:2015-12-15
  • 基金资助:
    国家自然科学基金 (11301395; 11201344).

Fixed Cost Allocation Based on Efficiency Maximization and Min-max Relative Difference

LIN Rui-yue1,2   

  1. 1- School of Mathematics and Information Science, Wenzhou University, Wenzhou 325035
    2- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2015-04-10 Accepted:2015-07-30 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation of China (11301395; 11201344).

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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．

关键词: 数据包络分析, 固定成本分配, 效率最大化, 极大极小模型, 唯一性

Abstract:

In this paper, we apply the data envelopment analysis technique to propose a minimax 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.

Key words: data envelopment analysis, fixed cost allocation, efficiency maximization, minimax model, uniqueness

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