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

Abstract

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

CLC Number:

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

Figures/Tables 4

References 47

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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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Study on DEA-based resources allocation with regret aversion

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