考虑后悔规避的基于数据包络分析的资源配置方法

doi:10.15960/j.cnki.issn.1007-6093.2024.04.007

摘要/Abstract

摘要：

针对决策单元在资源配置中存在倾向选择避免让自己感到后悔的方案的后悔规避心理, 提出一种考虑后悔规避的资源配置方法。基于数据包络分析方法对决策单元的配置效率进行测量, 区分效益型和成本型资源的效用函数, 建立决策单元对资源配置方案的欣喜-后悔函数。通过Max-min欣喜值和Min-max后悔绝对值来确定相应的资源配置方案。研究结果表明, 考虑后悔规避的资源配置方法能为决策单元确定一组有效的资源配置方案, 并且有助于资源在决策单元间的公平分配。

关键词: 数据包络分析, 资源配置, 后悔规避, 后悔值, 欣喜值

Abstract:

Considering a resources allocation scenario, in which the decision makers always tend to choose an allocation plan that does not render them regret. To this end, this paper proposes to employ regret aversion to help to allocate resources. Firstly, the data envelopment analysis approach is applied to measure the allocation performance. Then, the utility functions of beneficial resources and cost resources are distinguished. Thereafter, the regret value and rejoice value functions for resources allocation are built. With the help of Max-min rejoice value and Min-max regret value, the optimal resources allocation plan is determined. A numerical example is employed to show the applicability of the proposed approach. It shows that the method based on the regret aversion can help the decision maker to find an efficient resources allocation scheme and fairly distribute resources among decision making units.

Key words: data envelopment analysis, resources allocation, regret aversion, regret value, rejoice value

中图分类号:

王旭, 王应明, 蓝以信. 考虑后悔规避的基于数据包络分析的资源配置方法[J]. 运筹学学报（中英文）, 2024, 28(4): 75-90.

Xu WANG, Yingming WANG, Yixin LAN. Study on DEA-based resources allocation with regret aversion[J]. Operations Research Transactions, 2024, 28(4): 75-90.

图/表 4

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超市	工作时间/kh	规模/km$ ^2 $	营业额/百万马克	利润/百万马克
1	79.1	4.99	115.3	1.71
2	60.1	3.30	75.2	1.81
3	126.7	8.12	225.5	10.39
4	153.9	6.70	185.6	10.42
5	65.7	4.74	84.5	2.36
6	76.8	4.08	103.3	4.35
7	50.2	2.53	78.8	0.16
8	44.8	2.47	59.3	1.30
9	48.1	2.32	65.7	1.49
10	89.7	4.91	163.2	6.26
11	56.9	2.24	70.7	2.80
12	112.6	5.42	142.6	2.75
13	106.9	6.28	127.8	2.70
14	54.9	3.14	62.4	1.42
15	48.8	4.43	55.2	1.38
16	59.2	3.98	95.9	0.74
17	74.5	5.32	121.6	3.06
18	94.6	3.69	107.0	2.98
19	47.0	3.00	65.4	0.62
20	54.6	3.87	71.0	0.01
21	90.1	3.31	81.2	5.12
22	95.2	4.25	128.3	3.89
23	80.1	3.79	135.0	4.73
24	68.7	2.99	98.9	1.86
25	62.3	3.10	66.7	7.41

超市	$ R_{j}^{L} $	$ R_{j}^{U} $	${{R}_{j}}$ (文献[25])	满意度	${{R}_{j}}$(Max-min欣喜值)	欣喜值	${{R}_{j}}$(Min-max绝对后悔值)	绝对后悔值
1	0.833 4	2.018 0	1.428 9	0.502 7	1.407 4	0.155 0	1.122 9	0.297 2
2	0.566 3	1.163 1	0.897 3	0.554 5	1.027 5	0.127 3	0.728 0	0.136 6
3	3.487 9	7.791 7	5.159 6	0.388 4	4.147 6	0.167 5	6.419 0	0.429 4
4	2.150 4	5.108 5	3.588 6	0.486 2	3.722 6	0.359 0	4.274 9	0.255 7
5	0.751 8	1.307 0	0.998 4	0.444 1	1.069 4	0.089 3	1.031 0	0.084 2
6	1.562 8	2.131 4	1.824 8	0.460 8	1.783 1	0.061 9	2.055 6	0.022 0
7	0.074 1	1.675 4	0.939 7	0.540 5	0.912 9	0.220 6	0.458 8	0.429 4
8	0.590 9	0.917 2	0.750 9	0.490 3	0.806 9	0.061 9	0.613 7	0.093 8
9	0.728 1	1.129 4	0.925 3	0.491 5	0.958 6	0.065 7	0.760 5	0.114 7
10	2.524 3	5.273 5	3.611 5	0.395 5	2.922 6	0.107 0	4.154 6	0.357 3
11	0.890 4	1.473 5	1.181 2	0.498 7	1.265 5	0.104 3	1.166 5	0.093 8
12	0.897 5	2.304 3	1.678 3	0.555 0	1.948 0	0.263 8	1.125 9	0.407 2
13	0.441 4	1.976 7	1.259 1	0.532 6	1.592 8	0.287 1	0.888 7	0.373 3
14	0.051 6	0.965 2	0.570 2	0.567 7	0.784 7	0.195 9	0.378 7	0.189 6
15	0	0.853 8	0.331 6	0.388 4	0.491 4	0.136 4	0.378 4	0.151 3
16	0.358 3	1.950 8	1.199 3	0.528 1	1.080 0	0.192 2	0.872 7	0.369 5
17	1.459 2	2.689 9	1.972 3	0.416 9	1.685 8	0.063 8	2.083 1	0.189 5
18	0.283 2	1.873 2	1.289 3	0.632 8	1.665 3	0.334 1	0.881 7	0.335 6
19	0.300 5	1.056 5	0.666 6	0.484 2	0.717 1	0.116 4	0.399 3	0.214 5
20	0	1.098 2	0.426 6	0.388 4	0.585 2	0.160 1	0	0.385 2
21	0	2.510 1	1.158 3	0.461 5	1.670 9	0.389 2	1.273 3	0.429 4
22	1.851 6	2.312 8	2.030 7	0.388 4	2.073 1	0.061 9	1.880 2	0.132 5
23	2.088 1	3.761 4	2.792 4	0.420 9	2.379 7	0.080 2	3.015 3	0.232 6
24	0.908 1	1.913 9	1.447 2	0.536 0	1.447 1	0.146 1	1.111 6	0.263 1
25	0.388 3	3.636 9	1.871 8	0.456 6	1.854 7	0.349 6	2.925 7	0.221 2

超市	$ F_{j}^{L} $	$ F_{j}^{U} $	${{R}_{j}}$ (文献[25])	满意度	${{R}_{j}}$(Max-min欣喜值)	欣喜值	${{R}_{j}}$(Min-max绝对后悔值)	绝对后悔值
1	0.833 4	2.018 0	1.414 3	0.509 6	1.478 9	0.003 3	1.673 0	0.005 2
2	0.566 3	1.163 1	0.857 0	0.512 9	0.688 2	0.002 9	1.005 5	0.002 7
3	3.487 9	7.791 7	5.531 4	0.525 2	6.789 1	0.006 9	4.524 2	0.006 8
4	2.150 4	5.108 5	3.608 7	0.507 0	3.333 7	0.011 5	3.042 3	0.005 7
5	0.751 8	1.307 0	1.044 0	0.473 7	0.880 0	0.002 6	1.114 0	0.002 2
6	1.562 8	2.131 4	1.862 1	0.473 7	1.884 0	0.001 5	1.685 7	0.000 8
7	0.074 1	1.675 4	0.861 5	0.508 3	1.005 3	0.004 1	1.182 9	0.006 8
8	0.590 9	0.917 2	0.724 7	0.589 9	0.663 7	0.001 5	0.835 7	0.001 5
9	0.728 1	1.129 4	0.884 0	0.611 5	0.877 0	0.001 5	0.988 0	0.001 6
10	2.524 3	5.273 5	3.782 7	0.542 3	4.733 6	0.003 6	3.265 1	0.004 7
11	0.890 4	1.473 5	1.133 2	0.583 6	1.040 6	0.002 7	1.104 3	0.001 3
12	0.897 5	2.304 3	1.531 7	0.549 2	1.253 2	0.006 5	1.930 3	0.006 4
13	0.441 4	1.976 7	1.181 3	0.518 1	0.720 7	0.007 7	1.542 1	0.006 8
14	0.051 6	0.965 2	0.521 2	0.486 0	0.222 1	0.004 5	0.710 3	0.004 0
15	0	0.853 8	0.393 7	0.538 9	0.065 7	0.004 8	0.511 8	0.003 1
16	0.358 3	1.950 8	1.196 5	0.473 7	1.412 9	0.003 3	1.454 7	0.006 7
17	1.459 2	2.689 9	2.078 8	0.496 6	2.445 3	0.001 5	2.029 0	0.003 5
18	0.283 2	1.873 2	1.120 0	0.473 7	0.680 3	0.007 3	1.387 4	0.006 8
19	0.300 5	1.056 5	0.638 4	0.553 1	0.594 8	0.002 8	0.867 4	0.003 4
20	0	1.098 2	0.379 6	0.654 3	0.182 4	0.005 6	0.773 3	0.004 7
21	0	2.510 1	1.046 4	0.583 1	0.298 9	0.013 6	0.963 3	0.005 9
22	1.851 6	2.312 8	1.964 5	0.755 2	1.965 9	0.002 2	2.018 9	0.001 0
23	2.088 1	3.761 4	2.855 1	0.541 6	3.468 8	0.001 9	2.578 7	0.003 1
24	0.908 1	1.913 9	1.365 2	0.545 5	1.461 4	0.002 8	1.553 4	0.004 0
25	0.388 3	3.636 9	2.024 0	0.496 5	1.853 5	0.011 2	1.258 7	0.005 3

超市	效益型资源配置			成本型资源配置
	Max-Min	Max-Min	Min-Max	Max-Min	Max-Min	Min-Max
	满意度	欣喜值	绝对后悔值	满意度	欣喜值	绝对后悔值
变异系数	0.692 9	0.560 1	0.925 1	0.743 2	0.955 5	0.567 4
泰尔指数	0.088 6	0.061 0	0.155 2	0.099 1	0.162 3	0.060 3
基尼系数	0.120 7	0.089 1	0.160 5	0.128 8	0.168 1	0.100 3

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