基于公共权重的区间DEA效率评价及其排序方法研究

doi:10.15960/j.cnki.issn.1007-6093.2021.04.005

摘要/Abstract

摘要：

针对传统区间数据包络分析方法，在确定每一个决策单元区间效率的上界和下界时，存在的评价尺度不一致且计算复杂等问题，本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型，并给出了一种考虑决策者偏好信息的可能度排序方法，用以解决区间效率的全排序问题。最后，以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。

关键词: 数据包络分析, 区间效率, 公共权重, 可能度, 决策者偏好

Abstract:

In order to solve the inconsistency of the evaluation scale in efficiency evaluation in interval data envelopment analysis, this paper proposes a common weight interval DEA model based on the target by maximizing the sum of the upper bound efficiency and the lower bound efficiency of all decision-making units (DMUs). Thus, our approach not only makes the interval efficiency of all DMUs being comparable, but also ensures that the upper bound efficiency and the lower bound efficiency are evaluated in the same scale. To rank the interval efficiencies completely a new approach which is based on the defined possibility degree formula in considering of the decision makers' interval preference is proposed. Finally, an example of measuring the industrial efficiencies in 11 coastal provinces of China is investigated to illustrate the effectiveness and the usefulness of our approaches.

Key words: data envelopment analysis, interval efficiency, common weights, possibility degree, decision maker's preference

中图分类号:

O221

蓝以信, 温槟檐, 王应明. 基于公共权重的区间DEA效率评价及其排序方法研究[J]. 运筹学学报, 2021, 25(4): 58-68.

Yixin LAN, Bingyan WEN, Yingming WANG. A common-weights interval DEA approach for efficiency evaluation and its ranking method[J]. Operations Research Transactions, 2021, 25(4): 58-68.

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地区	从业人员数/万人	资产总计/亿元	工业产值/亿元	工业SO₂排放量/万t
天津	[133.12, 136.82]	[10 351.21, 12 617.69]	[12 302.63, 12 845.13]	[17.30, 21.00]
河北	[316.85, 319.94]	[17 261.75, 20 662.67]	[22 408.10, 23 434.08]	[104.30, 115.90]
辽宁	[366.23, 386.62]	[22 040.91, 25 333.81]	[24 105.81, 27 543.97]	[91.9, 100.10]
上海	[284.12, 304.01]	[22 750.35, 24 595.29]	[23 847.88, 24 800.47]	[23.90, 29.80]
江苏	[1 026.16, 1 104.06]	[48 321.94, 53 600.08]	[66 537.70, 71 970.22]	[101.20, 107.40]
浙江	[787.64, 814.55]	[35 550.76, 39 752.79]	[39 717.51, 39 969.91]	[67.70, 71.60]
福建	[379.47, 380.06]	[11 694.91, 13 344.47]	[14 838.96, 16 316.29]	[39.90, 40.90]
山东	[912.70, 926.60]	[39 224.51, 46 052.69]	[60 731.24, 70 148.15]	[136.60, 146.60]
广东	[1 436.02, 1 493.38]	[45 750.15, 50 321.88]	[63 547.23, 66 292.14]	[101.30, 109.70]
广西	[114.60, 122.88]	[5 981.12, 6 840.57]	[5 759.32, 6 542.47]	[83.50, 87.00]
海南	[12.00, 12.96]	[1 207.77, 1 291.39]	[1 052.92, 1 089.60]	[2.10, 2.10]

地区	本文方法的区间效率		Kao^[15]方法的区间效率
地区	效率下界	效率上界	效率下界	效率上界
天津	0.708 5	0.898 0	1.000 0	1.000 0
河北	0.487 8	0.584 8	0.786 5	1.000 0
辽宁	0.508 6	0.650 8	0.696 0	1.000 0
上海	0.755 6	0.872 5	1.000 0	1.000 0
江苏	0.845 1	1.000 0	0.905 6	1.000 0
浙江	0.700 8	0.774 8	0.725 4	0.931 3
福建	0.650 0	0.778 2	0.654 7	1.000 0
山东	0.767 5	1.000 0	0.905 5	1.000 0
广东	0.827 8	0.943 2	0.837 5	1.000 0
广西	0.225 2	0.273 2	0.557 8	0.852 5
海南	0.597 0	0.649 0	0.865 3	1.000 0

地区	$ \alpha = 0 $	$ \alpha = 0.1 $	$ \alpha = 0.2 $	$ \alpha = 0.3 $	$ \alpha = 0.4 $	$ \alpha = 0.5 $	$ \alpha = 0.6 $	$ \alpha = 0.7 $	$ \alpha = 0.8 $	$ \alpha = 0.9 $	$ \alpha = 1 $
天津	6	6	5	5	5	5	5	4	4	4	4
河北	10	10	10	10	10	10	10	10	10	10	10
辽宁	9	9	9	9	9	9	9	9	9	8	8
上海	3	4	4	4	4	4	4	5	5	5	5
江苏	1	1	1	1	1	1	1	1	1	1	1
浙江	5	5	6	6	6	6	6	6	7	7	7
福建	7	7	7	7	7	7	7	7	6	6	6
山东	4	3	3	3	3	3	2	2	2	2	2
广东	2	2	2	2	2	2	3	3	3	3	3
广西	11	11	11	11	11	11	11	11	11	11	11
海南	8	8	8	8	8	8	8	8	8	9	9

对比地区	$ \alpha = 0 $	$ \alpha = 0.1 $	$ \alpha = 0.2 $	$ \alpha = 0.3 $	$ \alpha = 0.4 $	$ \alpha = 0.5 $	$ \alpha = 0.6 $	$ \alpha = 0.7 $	$ \alpha = 0.8 $	$ \alpha = 0.9 $	$ \alpha = 1 $
天津/上海	0.251 5	0.289 8	0.328 1	0.366 4	0.404 7	0.443 0	0.481 3	0.519 6	0.557 9	0.596 3	0.634 6
天津/浙江	0.539 0	0.597 6	0.656 2	0.714 8	0.773 3	0.831 9	0.890 5	0.949 0	1.000 0	1.000 0	1.000 0
浙江/福建	0.896 3	0.854 0	0.811 7	0.769 4	0.727 1	0.684 9	0.642 6	0.600 3	0.558 0	0.515 8	0.473 5
上海/浙江	0.819 2	0.844 1	0.869 1	0.894 1	0.919 1	0.944 1	0.969 1	0.994 1	1.000 0	1.000 0	1.000 0
山东/广东	0.240 6	0.291 0	0.341 4	0.391 7	0.442 1	0.492 5	0.542 8	0.593 2	0.643 6	0.693 9	0.744 3
海南/辽宁	1.000 0	1.000 0	0.994 8	0.931 4	0.867 9	0.804 5	0.741 1	0.677 6	0.614 2	0.550 8	0.487 3

	天津	河北	辽宁	上海	江苏	浙江	福建	山东	广东	广西	海南
天津	0.500 0	1.000 0	1.000 0	0.481 3	0.102 6	0.890 5	0.884 2	0.209 1	0.181 1	1.000 0	1.000 0
河北	0.000 0	0.500 0	0.206 0	0.000 0	0.000 0	0.005 7	0.000 0	0.000 0	0.000 0	1.000 0	0.026 0
辽宁	0.000 0	0.794 0	0.500 0	0.005 4	0.000 0	0.021 6	0.006 7	0.000 0	0.004 4	1.000 0	0.258 9
上海	0.518 7	1.000 0	0.994 6	0.500 0	0.040 5	0.969 1	0.944 1	0.167 5	0.119 9	1.000 0	1.000 0
江苏	0.897 4	1.000 0	1.000 0	0.959 5	0.500 0	1.000 0	1.000 0	0.633 5	0.738 1	1.000 0	1.000 0
浙江	0.109 5	0.994 3	0.978 4	0.030 9	0.000 0	0.500 0	0.642 6	0.000 0	0.000 0	1.000 0	1.000 0
福建	0.115 8	1.000 0	0.993 3	0.055 9	0.000 0	0.357 4	0.500 0	0.000 0	0.000 0	1.000 0	1.000 0
山东	0.790 9	1.000 0	1.000 0	0.832 5	0.366 5	1.000 0	1.000 0	0.500 0	0.542 8	1.000 0	1.000 0
广东	0.818 9	1.000 0	1.000 0	0.880 1	0.261 9	1.000 0	1.000 0	0.457 2	0.500 0	1.000 0	1.000 0
广西	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.500 0	0.000 0
海南	0.000 0	0.974 0	0.741 1	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	1.000 0	0.500 0