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

Abstract

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

CLC Number:

C934

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.

Figures/Tables 13

	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

$\sigma$	$\left(1,2,3\right)$	$\left(1,3,2\right)$	$\left(2,1,3\right)$	$\left(2,3,1\right)$	$\left(3,1,2\right)$	$\left(3,2,1\right)$	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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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

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Efficiency evaluation for the serial system in the absence of a given leader-follower order in the non-cooperative case

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