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

Abstract

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

CLC Number:

O221

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.

Figures/Tables 5

References 28

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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

A common-weights interval DEA approach for efficiency evaluation and its ranking method

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