非合作情形下无领导者-跟随者顺序时的串联系统效率评价

doi:10.15960/j.cnki.issn.1007-6093.2025.01.007

摘要/Abstract

摘要：

非合作情形下, 用数据包络分析(data envelopment analysis, DEA)方法对串联系统进行效率评价的研究中, 经典的领导者-追随者网络DEA模型(或非合作网络DEA模型)可为系统及其子系统提供唯一的评价结果。但其前提是预先给定系统内部的领导者-追随者顺序。不同的顺序产生不同的评价结果, 且并非所有系统均在同一顺序中获得最佳效率。另外, 现有网络DEA研究多认为决策者是完全理性的, 与现实中决策者有限理性的表现不符。本文针对“非合作情形下无领导者-跟随者顺序时如何评价串联系统及其子系统效率”的问题, 基于字典式优化算法和前景理论, 提出新的串联系统效率评价方法。该方法可提供唯一的、全面的、可比较的效率评价结果。最后, 用14家电力公司数据验证该方法。

关键词: 网络DEA, 串联系统, 领导者-跟随者顺序, 有限理性, 字典式优化

Abstract:

In the non-cooperative case, among the studies of efficiency evaluation of serial systems using data envelopment analysis (DEA) method, the excellent leader-follower or non-cooperative network DEA model can provide a unique evaluation result for the serial system and their internal sub-systems. However, the premise is a given leader-follower order that reveals which stage is more important for improving system's efficiency. Different leader-follower orders yield various evaluation results and not necessarily all systems obtain their best efficiency in the same order. Furthermore, existing studies on network DEA mostly look decision makers completely rational, which is not in line with the bounded rational behavior in practice. This study focuses on the question of "In the non-cooperative case without a given leader-follower order, how to evaluate efficiencies of the serial system and its internal sub-systems". To answer this question, we propose a novel approach for measuring efficiencies of the serial system and its sub-systems based on a lexicographical optimization approach and the prospect theory, considering the bounded rationality of decision makers and all leader-follower orders. This method can provide a unique, comprehensive, and comparable efficiency composition result. The experiment with the data of 14 electric power companies is used to validate this method.

Key words: network data envelopment analysis, serial system, leader-follower order, bounded rationality, lexicographic optimization

中图分类号:

C934

文瑶, 胡军华. 非合作情形下无领导者-跟随者顺序时的串联系统效率评价[J]. 运筹学学报（中英文）, 2025, 29(1): 77-97.

Yao WEN, Junhua HU. Efficiency evaluation for the serial system in the absence of a given leader-follower order in the non-cooperative case[J]. Operations Research Transactions, 2025, 29(1): 77-97.

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	子系统1		子系统2
	损失	获益	损失	获益
$\sigma=(1,2)$	0	$ \Delta \phi_{10}^{\text {gain }}=e_0^{\sigma_{12}^{(1)}}-e_0^{1 A L} $	$\Delta \phi_{20}^{\text {loss }}=e_0^{2 A L}-e_0^{\sigma_{12}^{(2)}}$	0
$\sigma=(2,1)$	$\Delta \phi_{10}^{\mathrm{loss}}=e_0^{1 A L}-e_0^{\sigma_{21}^{(1)}}$	0	0	$\Delta \phi_{20}^{\text {gain }}=e_0^{\sigma_{21}^{(2)}}-e_0^{2 A L}$

DMU	$ x_{1j}^1 $	$ x_{2j}^1 $	$ g_{1j}^1 $	$ x_{1j}^2 $	$ y_{1j}^2 $	$ g_{1j}^2 $	$ x_{1j}^3 $	$ y_{1j}^3 $
1	0.092 2	0.052 7	0.090 4	0.062 1	0.064 3	0.068 2	0.095 0	0.093 8
2	0.066 4	0.110 3	0.063 4	0.065 8	0.111 7	0.072 2	0.070 9	0.056 2
3	0.160 1	0.186 4	0.157 8	0.106 8	0.197 1	0.086 9	0.143 6	0.098 9
4	0.059 0	0.080 6	0.056 1	0.047 2	0.077 3	0.051 8	0.046 8	0.059 1
5	0.148 8	0.093 3	0.155 6	0.188 8	0.144 5	0.131 4	0.158 0	0.155 3
6	0.049 0	0.033 1	0.046 3	0.049 7	0.037 6	0.057 6	0.051 5	0.051 7
7	0.021 9	0.014 7	0.022 3	0.012 4	0.019 3	0.044 0	0.022 0	0.022 1
8	0.060 3	0.035 7	0.057 6	0.154 0	0.019 5	0.138 7	0.069 2	0.069 4
9	0.053 2	0.057 4	0.050 8	0.068 3	0.048 4	0.075 0	0.050 9	0.081 1
10	0.103 3	0.097 5	0.098 7	0.088 2	0.093 3	0.096 8	0.102 1	0.102 4
11	0.042 5	0.033 4	0.040 6	0.036 0	0.039 1	0.045 3	0.044 9	0.045 0
12	0.059 5	0.078 3	0.056 8	0.053 4	0.065 3	0.058 6	0.061 1	0.061 5
13	0.052 8	0.081 9	0.074 1	0.036 0	0.055 6	0.039 5	0.052 4	0.052 6
14	0.030 9	0.044 7	0.029 5	0.031 1	0.026 9	0.034 1	0.031 5	0.051 1

DMU	子系统1效率		子系统2效率		子系统3效率		系统总效率
DMU	BR	CR	BR	CR	BR	CR	BR	CR
1	1.00	1.00	0.57	0.56	0.99	0.92	0.56	0.52
2	0.68	0.68	1.00	1.00	0.52	0.52	0.36	0.35
3	0.79	0.77	1.00	1.00	0.78	0.76	0.62	0.58
4	0.71	0.71	0.94	0.94	0.77	0.71	0.52	0.48
5	1.00	1.00	0.54	0.54	0.84	0.79	0.45	0.43
6	0.89	0.89	0.72	0.72	0.62	0.62	0.39	0.39
7	0.96	0.96	1.00	0.91	0.62	0.62	0.59	0.54
8	0.95	0.95	0.99	0.28	0.62	0.62	0.58	0.16
9	0.75	0.78	0.85	0.55	0.98	0.98	0.62	0.42
10	0.73	0.28	0.62	0.65	0.78	0.71	0.35	0.13
11	0.86	0.86	0.62	0.72	0.86	0.65	0.46	0.40
12	0.73	0.70	0.75	0.76	0.70	0.69	0.38	0.37
13	0.95	0.05	0.86	0.86	0.76	0.26	0.62	0.01
14	0.70	0.70	0.71	0.72	1.00	0.70	0.49	0.35

$ \sigma $	$ \left(1,2,3\right) $	$ \left(1,3,2\right) $	$ \left(2,1,3\right) $	$ \left(2,3,1\right) $	$ \left(3,1,2\right) $	$ \left(3,2,1\right) $	本文方法
最好	DMU13	DMU13	DMU13	DMU9	DMU7	DMU7	DMU9
最差	DMU10	DMU10	DMU2	DMU13	DMU8	DMU13	DMU10

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