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

References 30

1	Liang L , Cook W D , Zhu J . DEA models for two-stage processes: Game approach and efficiency decomposition[J]. Naval Research Logistics, 2008, 55 (7): 643- 653. doi: 10.1002/nav.20308
2	Liang L , Yang F , Cook W D , et al. DEA models for supply chain efficiency evaluation[J]. Annals of Operations Research, 2006, 145 (1): 35- 49. doi: 10.1007/s10479-006-0026-7
3	Yang J , Fang L . Average lexicographic efficiency decomposition in two-stage data envelopment analysis: An application to China's regional high-tech innovation systems[J]. Annals of Operations Research, 2022, 312, 1051- 1093. doi: 10.1007/s10479-021-04427-z
4	Li H , Chen C , Cook W D , et al. Two-stage network DEA: Who is the leader?[J]. Omega, 2018, 74, 15- 19. doi: 10.1016/j.omega.2016.12.009
5	Charnes A , Cooper W W , Rhodes E . Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 2 (6): 429- 444. doi: 10.1016/0377-2217(78)90138-8
6	Castelli L , Pesenti R , Ukovich W . DEA-like models for the efficiency evaluation of hierarchically structured units[J]. European Journal of Operational Research, 2004, 154 (2): 465- 476. doi: 10.1016/S0377-2217(03)00182-6
7	Kao C , Hwang S . Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[J]. European Journal of Operational Research, 2008, 185 (1): 418- 429. doi: 10.1016/j.ejor.2006.11.041
8	Kao C , Hwang S . Efficiency measurement for network systems: IT impact on firm performance[J]. Decision Support Systems, 2010, 48 (3): 437- 446. doi: 10.1016/j.dss.2009.06.002
9	Färe R , Grosskopf S . Productivity and intermediate products: A frontier approach[J]. Economics Letters, 1996, 50 (1): 65- 70. doi: 10.1016/0165-1765(95)00729-6
10	Mahmoudabadi M Z , Azar A , Emrouznejad A . A novel multilevel network slacks-based measure with an application in electric utility companies[J]. Energy, 2018, 158, 1120- 1129. doi: 10.1016/j.energy.2018.05.161
11	楚雪芹, 李勇军, 崔峰, 等. 基于两阶段非期望DEA模型的商业银行效率评估[J]. 系统工程理论与实践, 2021, 41 (3): 636- 648.
12	曹莉, 马占新, 马生昀. 复杂多层次指标合成技术及效率分析[J]. 运筹学学报, 2020, 24 (4): 39- 50. doi: 10.15960/j.cnki.issn.1007-6093.2020.04.003
13	杨敏, 费锡玥, 魏字琪, 等. 基于资源共享与子系统交互的两阶段DEA评价方法——兼对我国"一流大学"科研绩效的评价[J].中国管理科学,
14	蓝以信, 温槟楌, 王应明. 基于公共权重的区间DEA效率评价及其排序方法研究[J]. 运筹学学报, 2021, 25 (4): 58- 68. doi: 10.15960/j.cnki.issn.1007-6093.2021.04.005
15	Cook W D , Liang L , Zhu J . Measuring performance of two-stage network structures by DEA: A review and future perspective[J]. Omega, 2010, 38 (6): 423- 430. doi: 10.1016/j.omega.2009.12.001
16	Chen H . Average lexicographic efficiency for data envelopment analysis[J]. Omega, 2018, 74, 82- 91. doi: 10.1016/j.omega.2017.01.008
17	Koronakos G , Sotiros D , Despotis D K . Reformulation of network data envelopment analysis models using a common modelling framework[J]. European Journal of Operational Research, 2019, 278 (2): 472- 480. doi: 10.1016/j.ejor.2018.04.004
18	Despotis D K , Sotiros D , Koronakos G . A network DEA approach for series multi-stage processes[J]. Omega, 2016, 61, 35- 48. doi: 10.1016/j.omega.2015.07.005
19	Liu H , Song Y , Yang G . Cross-efficiency evaluation in data envelopment analysis based on prospect theory[J]. European Journal of Operational Research, 2019, 273 (1): 364- 375. doi: 10.1016/j.ejor.2018.07.046
20	吴辉, 昂胜, 杨锋. 基于前景理论的两阶段DEA交叉效率评价模型[J]. 运筹与管理, 2021, 30 (11): 53- 59.
21	Kahneman D , Tversky A . Prospect theory: An analysis of decisions under risk[J]. Econometrica, 1979, 2 (47): 263- 291.
22	陈磊, 王应明. 基于前景理论的交叉效率集结方法[J]. 系统科学与数学, 2018, 38 (11): 1307- 1316. doi: 10.12341/jssms13490
23	Shao X , Wang M . Two-stage cross-efficiency evaluation based on prospect theory[J]. Journal of the Operational Research Society, 2022, 73 (7): 1620- 1632. doi: 10.1080/01605682.2021.1918587
24	Shi H , Chen S , Chen L , et al. A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior[J]. European Journal of Operational Research, 2021, 290 (3): 1098- 1110. doi: 10.1016/j.ejor.2020.08.055
25	Charnes A , Cooper W W . Programming with linear fractional functionals[J]. Naval Research Logistics Quarterly, 1962, 9 (3): 181- 186.
26	Peng X , Yang Y . Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight[J]. Applied Soft Computing, 2017, 54, 415- 430. doi: 10.1016/j.asoc.2016.06.036
27	Abdellaoui M , Bleichrodt H , Paraschiv C . Loss aversion under prospect theory: A parameterfree measurement[J]. Management Science, 2007, 53 (10): 1659- 1674. doi: 10.1287/mnsc.1070.0711
28	Tversky A , Kahneman D . Advances in prospect theory: Cumulative representation of uncertainty[J]. Journal of Risk and Uncertainty, 1992, 5 (4): 297- 323. doi: 10.1007/BF00122574
29	Li Y , Chen Y , Liang L , et al. DEA models for extended two-stage network structures[J]. Omega, 2012, 40 (5): 611- 618. doi: 10.1016/j.omega.2011.11.007
30	Kao C . Multiplicative aggregation of division efficiencies in network data envelopment analysis[J]. European Journal of Operational Research, 2018, 270 (1): 328- 336. doi: 10.1016/j.ejor.2017.09.047

	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

[1]	CHEN Congli, YANG Hui, YANG Guanghui, WANG Chun. An approximation theorem for n-person non-cooperative games under uncertain parameters [J]. Operations Research Transactions, 2025, 29(1): 105-113.
[2]	YANG Guanghui, YANG Hui, XIANG Shuwen. Stability of solutions to parametric optimization problems under bounded rationality [J]. Operations Research Transactions, 2016, 20(4): 1-10.
[3]	WANG Chun, QIU Xiaoling, WANG Nengfa, CHEN Pinbo. Stability to bounded rationality for nonconvexity [J]. Operations Research Transactions, 2016, 20(3): 107-120.

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

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