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Second order cone programming formulation of the fixed cost allocation in DEA based on Nash bargaining game
1. | Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran |
2. | Department of Applied Mathematics, Faculty of Mathematical Sciences, and Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran |
A vital issue in many organizations is the fair allocation of fixed cost among its subsets. In this paper, using data envelopment analysis, first we study fixed cost allocation based on both additive and multiplicative efficiency decompositions in the cooperative context for a two-stage structure in the presence of exogenous inputs and outputs. A conic relaxation formulation of multiplicative decomposition is given. Then, fixed cost allocation based on the leader-follower paradigm are presented. In the sequel, for allocating a fair fixed cost between the stages, using the results of the leader-follower model, we present the nonlinear Nash bargaining game model that independent of the efficiency score of each unit, allocates fixed cost to the stages. The nonlinear model is reformulated as a second order cone program which is an imporvement over the parametric linear models in the literature. Finally, two examples are used to illustrate the proposed models and compare their results with the existing models.
References:
[1] |
A. Amirteimoori,
A DEA two-stage decision processes with shared resources, Central European Journal of Operations Research, 21 (2013), 141-151.
doi: 10.1007/s10100-011-0218-3. |
[2] |
Q. An, P. Wang, A. Emroznejad and J. Hu,
Fixed cost allocationbased on the principle of efficincy invariance in two-stage systems, European Journal of Operational Research, 283 (2020), 662-675.
doi: 10.1016/j.ejor.2019.11.031. |
[3] |
Q. An, Y. Wen, T. Ding and Y. Li,
Resource sharing and payoff allocation in a three-stage system: integrating network DEA with the Shaplley value method, Omega, 85 (2018), 16-25.
|
[4] |
J. E. Beasley,
Allocating fixed costs and resources via data envelopment analysis, European Journal of Operational Research, 147 (2003), 198-216.
doi: 10.1016/S0377-2217(02)00244-8. |
[5] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge: Cambridge University Press, 2004.
doi: 10.1017/CBO9780511804441.![]() ![]() ![]() |
[6] |
A. Charnes and W. W. Cooper,
Programming with linear fractional functions, Naval Research Logistics Quarterly, 9 (1962), 181-185.
doi: 10.1002/nav.3800090303. |
[7] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
[8] |
C. M. Chen and M. A. Delmas,
Measuring eco-inefficiency: a new frontier approach, Operations Research, 60 (2012), 1064-1079.
doi: 10.1287/opre.1120.1094. |
[9] |
Y. Chen, J. Du, H. D. Sherman and J. Zhu,
DEA model with shared resources and efficiency decomposition, European Journal of Operational Research, 207 (2010), 339-349.
doi: 10.1016/j.ejor.2010.03.031. |
[10] |
L. Chen, F. Lai, Y. M. Wang, Y. Huang and F. M. Wu,
A two-stage network data envelopment analysis approach for measuring and decomposing environmental efficiency, Computers and Industrial Engineering, 119 (2018), 388-403.
doi: 10.1016/j.cie.2018.04.011. |
[11] |
Y. Chen, W. D. Cook, N. Li and J. Zhu,
Additive efficiency decomposition in two-stage DEA, European Journal of Operational Research, 196 (2009), 1170-1176.
doi: 10.1016/j.ejor.2008.05.011. |
[12] |
K. Chen and J. Zhu,
Second order cone programming approach to two-stage network data envelopment analysis, European Journal of Operational Research, 262 (2017), 231-238.
doi: 10.1016/j.ejor.2017.03.074. |
[13] |
K. Chen, W. D. Cook and J. Zhu,
A conic relaxation model for searching for the global optimum of network data envelopment analysis, European Journal of Operational Research, 280 (2020), 242-253.
doi: 10.1016/j.ejor.2019.07.012. |
[14] |
J. Chu, J. Wu, C. Chu and T. Zhang, DEA-based fixed cost allocation in two-stage systems: leader-follower and satisfaction degree bargaining game approaches, Omega, 94 (2020), ID: 102054.
doi: 10.1016/j.omega.2019.03.012. |
[15] |
W. D. Cook and M. Kress,
Characterizing an equitable allocation of shared costs: A DEA approach, European Journal of Operational Research, 119 (1999), 652-661.
doi: 10.1016/S0377-2217(98)00337-3. |
[16] |
D. K. Despotis, G. Koronakos and D. Sotiros,
Composition versus decomposition in two-stage newwork DEA: A reverse approach, Journal of Productivity Analysis, 45 (2014), 71-87.
|
[17] |
T. Ding, Q. Zhu, B. Zhang and L. Liang, Centralized fixed cost allocation for generalized two-stage network DEA, INFOR: Information Systems and Operational Research, 57 (2019), 123-140.
doi: 10.1080/03155986.2017.1397897. |
[18] |
J. Du, W. D. Cook, L. Liang and J. Zhu,
Fixed cost and resource allocation based on DEA cross-efficiency, European Journal of Operational Research, 235 (2014), 206-214.
doi: 10.1016/j.ejor.2013.10.002. |
[19] |
L. Fang,
Centralized resource allocation based on efficiency analysis for step-by step improvement paths, Omega, 51 (2015), 24-28.
doi: 10.1016/j.omega.2014.09.003. |
[20] |
C. Feng, F. Chu, J. Ding, G. Bi and L. Liang,
Carbon emissions abatement (cea) allocation and compensation schemes based on DEA, Omega, 53 (2015), 78-89.
doi: 10.1016/j.omega.2014.12.005. |
[21] |
C. Guo, F. Wei and Y. Chen,
A note on second order cone programming approach to two-stage network data envelopment analysis, European Journal of Operational Research, 263 (2017), 733-735.
doi: 10.1016/j.ejor.2017.06.011. |
[22] |
Z. Y. Hua, Y. Bian and L. Liang,
Eco-efficiency analysis of paper mills along the huai river: an extended DEA approach, Omega, 35 (2007), 578-587.
doi: 10.1016/j.omega.2005.11.001. |
[23] |
C. Kao and S. N. Hwang,
Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan, European Journal of Operational Research, 185 (2008), 418-429.
doi: 10.1016/j.ejor.2006.11.041. |
[24] |
F. Li, Q. Zhu and Z. Chen,
Allocating a fixed cost across the decision making units with two-stage network structures, Omega, 83 (2019), 139-154.
doi: 10.1016/j.omega.2018.02.009. |
[25] |
Y. Li, M. Yang, Y. Chen, Q. Dai and L. Liang,
Allocating a fixed cost based on data envelopment analysis and satisfaction degree, Omega, 41 (2013), 55-60.
doi: 10.1016/j.omega.2011.02.008. |
[26] |
Y. Li, F. Li, A. Emrouznejad, L. Liang and Q. Xie,
Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game, Annals of Operations Reaserch, 274 (2018), 373-394.
doi: 10.1007/s10479-018-2860-9. |
[27] |
R. Lin, Z. Chen and Z. Li,
A new approach for allocating fixed costs among decision making units, Journal of Industrial and Management Optimization, 12 (2016), 211-228.
doi: 10.3934/jimo.2016.12.211. |
[28] |
R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani,
Interdependent demand in the two-period newsvendor problem, Journal of Industrial and Management Optimization, 16 (2018), 117-140.
doi: 10.3934/jimo.2018143. |
[29] |
J. F. Nash,
The bargaining problem, Econometrica; Journal of Econometric Society, 18 (1950), 155-162.
doi: 10.2307/1907266. |
[30] |
J. Nash,
Two-person cooperative games, Econometrica: Journal of Econometric Society, 21 (1953), 128-140.
doi: 10.2307/1906951. |
[31] |
J. Sadeghi, M. Ghiyasi and A. Dehnokhalaji,
Resource allocation and target setting based on virtual profit improvement, Numerical Algebra, Control and Optimization, 10 (2020), 127-142.
doi: 10.3934/naco.2019043. |
[32] |
Y. Sho, G. Bi, F. Yang and Q. Xia,
Resource allocation for branch network system with considering heterogeneity based on DEA method, Central European Journal of Operations Research, 26 (2018), 1005-1025.
doi: 10.1007/s10100-018-0563-6. |
[33] |
J. Sun, J. Wu, L. Liang, R. Y. Zhong and G. Q. Huang,
Allocation of emission permits using DEA: centralised and individual points of view, International Journal of Production Research, 52 (2014), 419-435.
|
[34] |
K. Wang, W. Huang, J. Wu and Y. N. Liu,
Efficiency measures of the Chinese commerical banking system using an additive two-stage DEA, Omega, 44 (2014), 5-20.
doi: 10.1016/j.omega.2013.09.005. |
[35] |
J. Wu, Q. Zhu, X. Ji, J. Chu and L. Liang,
Two-stage network processes with shared resources and resources recovered from undesirable outputs, European Journal of Operational Research, 251 (2016), 182-197.
doi: 10.1016/j.ejor.2015.10.049. |
[36] |
G. L. Yang, Y. Y. Song, D. L. Xu and J. B. Yang,
Overall efficiency and its decomposision in a two-stage network DEA model, Journal of Managment Science and Engineering, 2 (2017), 161-192.
doi: 10.1016/j.ejor.2016.08.002. |
[37] |
M. M. Yu, L. H. Chen and H. Bo,
A fixed cost allocation based on the two-stage network data envelopment approach, Journal of Business Research, 69 (2016), 1817-1822.
|
[38] |
Q. Zhang, D. Koutmos, K. Chen and J. Zhu,
Using operational and stock analytics to measure airline perfoemance: A network DEA approach, Decision Sciences, 52 (2021), 720-748.
doi: 10.1111/deci.12363. |
[39] |
W. Zhu, Q. Zhang and H. Wang,
Fixed costs and shared resources allocation in two-stage network DEA, Annals of Operations Research, 278 (2019), 177-194.
doi: 10.1007/s10479-017-2599-8. |
show all references
References:
[1] |
A. Amirteimoori,
A DEA two-stage decision processes with shared resources, Central European Journal of Operations Research, 21 (2013), 141-151.
doi: 10.1007/s10100-011-0218-3. |
[2] |
Q. An, P. Wang, A. Emroznejad and J. Hu,
Fixed cost allocationbased on the principle of efficincy invariance in two-stage systems, European Journal of Operational Research, 283 (2020), 662-675.
doi: 10.1016/j.ejor.2019.11.031. |
[3] |
Q. An, Y. Wen, T. Ding and Y. Li,
Resource sharing and payoff allocation in a three-stage system: integrating network DEA with the Shaplley value method, Omega, 85 (2018), 16-25.
|
[4] |
J. E. Beasley,
Allocating fixed costs and resources via data envelopment analysis, European Journal of Operational Research, 147 (2003), 198-216.
doi: 10.1016/S0377-2217(02)00244-8. |
[5] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge: Cambridge University Press, 2004.
doi: 10.1017/CBO9780511804441.![]() ![]() ![]() |
[6] |
A. Charnes and W. W. Cooper,
Programming with linear fractional functions, Naval Research Logistics Quarterly, 9 (1962), 181-185.
doi: 10.1002/nav.3800090303. |
[7] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
[8] |
C. M. Chen and M. A. Delmas,
Measuring eco-inefficiency: a new frontier approach, Operations Research, 60 (2012), 1064-1079.
doi: 10.1287/opre.1120.1094. |
[9] |
Y. Chen, J. Du, H. D. Sherman and J. Zhu,
DEA model with shared resources and efficiency decomposition, European Journal of Operational Research, 207 (2010), 339-349.
doi: 10.1016/j.ejor.2010.03.031. |
[10] |
L. Chen, F. Lai, Y. M. Wang, Y. Huang and F. M. Wu,
A two-stage network data envelopment analysis approach for measuring and decomposing environmental efficiency, Computers and Industrial Engineering, 119 (2018), 388-403.
doi: 10.1016/j.cie.2018.04.011. |
[11] |
Y. Chen, W. D. Cook, N. Li and J. Zhu,
Additive efficiency decomposition in two-stage DEA, European Journal of Operational Research, 196 (2009), 1170-1176.
doi: 10.1016/j.ejor.2008.05.011. |
[12] |
K. Chen and J. Zhu,
Second order cone programming approach to two-stage network data envelopment analysis, European Journal of Operational Research, 262 (2017), 231-238.
doi: 10.1016/j.ejor.2017.03.074. |
[13] |
K. Chen, W. D. Cook and J. Zhu,
A conic relaxation model for searching for the global optimum of network data envelopment analysis, European Journal of Operational Research, 280 (2020), 242-253.
doi: 10.1016/j.ejor.2019.07.012. |
[14] |
J. Chu, J. Wu, C. Chu and T. Zhang, DEA-based fixed cost allocation in two-stage systems: leader-follower and satisfaction degree bargaining game approaches, Omega, 94 (2020), ID: 102054.
doi: 10.1016/j.omega.2019.03.012. |
[15] |
W. D. Cook and M. Kress,
Characterizing an equitable allocation of shared costs: A DEA approach, European Journal of Operational Research, 119 (1999), 652-661.
doi: 10.1016/S0377-2217(98)00337-3. |
[16] |
D. K. Despotis, G. Koronakos and D. Sotiros,
Composition versus decomposition in two-stage newwork DEA: A reverse approach, Journal of Productivity Analysis, 45 (2014), 71-87.
|
[17] |
T. Ding, Q. Zhu, B. Zhang and L. Liang, Centralized fixed cost allocation for generalized two-stage network DEA, INFOR: Information Systems and Operational Research, 57 (2019), 123-140.
doi: 10.1080/03155986.2017.1397897. |
[18] |
J. Du, W. D. Cook, L. Liang and J. Zhu,
Fixed cost and resource allocation based on DEA cross-efficiency, European Journal of Operational Research, 235 (2014), 206-214.
doi: 10.1016/j.ejor.2013.10.002. |
[19] |
L. Fang,
Centralized resource allocation based on efficiency analysis for step-by step improvement paths, Omega, 51 (2015), 24-28.
doi: 10.1016/j.omega.2014.09.003. |
[20] |
C. Feng, F. Chu, J. Ding, G. Bi and L. Liang,
Carbon emissions abatement (cea) allocation and compensation schemes based on DEA, Omega, 53 (2015), 78-89.
doi: 10.1016/j.omega.2014.12.005. |
[21] |
C. Guo, F. Wei and Y. Chen,
A note on second order cone programming approach to two-stage network data envelopment analysis, European Journal of Operational Research, 263 (2017), 733-735.
doi: 10.1016/j.ejor.2017.06.011. |
[22] |
Z. Y. Hua, Y. Bian and L. Liang,
Eco-efficiency analysis of paper mills along the huai river: an extended DEA approach, Omega, 35 (2007), 578-587.
doi: 10.1016/j.omega.2005.11.001. |
[23] |
C. Kao and S. N. Hwang,
Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan, European Journal of Operational Research, 185 (2008), 418-429.
doi: 10.1016/j.ejor.2006.11.041. |
[24] |
F. Li, Q. Zhu and Z. Chen,
Allocating a fixed cost across the decision making units with two-stage network structures, Omega, 83 (2019), 139-154.
doi: 10.1016/j.omega.2018.02.009. |
[25] |
Y. Li, M. Yang, Y. Chen, Q. Dai and L. Liang,
Allocating a fixed cost based on data envelopment analysis and satisfaction degree, Omega, 41 (2013), 55-60.
doi: 10.1016/j.omega.2011.02.008. |
[26] |
Y. Li, F. Li, A. Emrouznejad, L. Liang and Q. Xie,
Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game, Annals of Operations Reaserch, 274 (2018), 373-394.
doi: 10.1007/s10479-018-2860-9. |
[27] |
R. Lin, Z. Chen and Z. Li,
A new approach for allocating fixed costs among decision making units, Journal of Industrial and Management Optimization, 12 (2016), 211-228.
doi: 10.3934/jimo.2016.12.211. |
[28] |
R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani,
Interdependent demand in the two-period newsvendor problem, Journal of Industrial and Management Optimization, 16 (2018), 117-140.
doi: 10.3934/jimo.2018143. |
[29] |
J. F. Nash,
The bargaining problem, Econometrica; Journal of Econometric Society, 18 (1950), 155-162.
doi: 10.2307/1907266. |
[30] |
J. Nash,
Two-person cooperative games, Econometrica: Journal of Econometric Society, 21 (1953), 128-140.
doi: 10.2307/1906951. |
[31] |
J. Sadeghi, M. Ghiyasi and A. Dehnokhalaji,
Resource allocation and target setting based on virtual profit improvement, Numerical Algebra, Control and Optimization, 10 (2020), 127-142.
doi: 10.3934/naco.2019043. |
[32] |
Y. Sho, G. Bi, F. Yang and Q. Xia,
Resource allocation for branch network system with considering heterogeneity based on DEA method, Central European Journal of Operations Research, 26 (2018), 1005-1025.
doi: 10.1007/s10100-018-0563-6. |
[33] |
J. Sun, J. Wu, L. Liang, R. Y. Zhong and G. Q. Huang,
Allocation of emission permits using DEA: centralised and individual points of view, International Journal of Production Research, 52 (2014), 419-435.
|
[34] |
K. Wang, W. Huang, J. Wu and Y. N. Liu,
Efficiency measures of the Chinese commerical banking system using an additive two-stage DEA, Omega, 44 (2014), 5-20.
doi: 10.1016/j.omega.2013.09.005. |
[35] |
J. Wu, Q. Zhu, X. Ji, J. Chu and L. Liang,
Two-stage network processes with shared resources and resources recovered from undesirable outputs, European Journal of Operational Research, 251 (2016), 182-197.
doi: 10.1016/j.ejor.2015.10.049. |
[36] |
G. L. Yang, Y. Y. Song, D. L. Xu and J. B. Yang,
Overall efficiency and its decomposision in a two-stage network DEA model, Journal of Managment Science and Engineering, 2 (2017), 161-192.
doi: 10.1016/j.ejor.2016.08.002. |
[37] |
M. M. Yu, L. H. Chen and H. Bo,
A fixed cost allocation based on the two-stage network data envelopment approach, Journal of Business Research, 69 (2016), 1817-1822.
|
[38] |
Q. Zhang, D. Koutmos, K. Chen and J. Zhu,
Using operational and stock analytics to measure airline perfoemance: A network DEA approach, Decision Sciences, 52 (2021), 720-748.
doi: 10.1111/deci.12363. |
[39] |
W. Zhu, Q. Zhang and H. Wang,
Fixed costs and shared resources allocation in two-stage network DEA, Annals of Operations Research, 278 (2019), 177-194.
doi: 10.1007/s10479-017-2599-8. |

Reference | exogenous input or output | efficiency decomposition | system | approach of fair cost allocation | allocation principles |
Li et al. [25] | - | single-stage | Satisfaction degree | Efficiency maximization | |
Du et al. [18] | - | single-stage | Cross efficiency | Efficiency maximization | |
Yu et al. [37] | AED | two-stage | Cross efficiency | Effficiency maximization | |
Zhu et al. [39] | AED | two-stage | Based on different objectives in reality | Effficiency maximization | |
Ding et al. [17] | AED | two-stage | Maximal average satisfaction degree | - | |
An et al. [3] | - | three-stage | The Shapley value | - | |
Li et al. [24] | AED | two-stage | By repeatedly minimizing the maximum deviation between the efficient and size allocation | Efficiency invariance & efficiency maximization | |
Li et al.[26] | - | single-stage | Cooperative game | - | |
Chu et al. [14] | AED | two-stage | Leader-follower & the Nash bargaining | - | |
The present study | AED and MED | two-stage | Cooperative, leader-follower & the Nash bargaining | Independent from efficiency rank and size |
Reference | exogenous input or output | efficiency decomposition | system | approach of fair cost allocation | allocation principles |
Li et al. [25] | - | single-stage | Satisfaction degree | Efficiency maximization | |
Du et al. [18] | - | single-stage | Cross efficiency | Efficiency maximization | |
Yu et al. [37] | AED | two-stage | Cross efficiency | Effficiency maximization | |
Zhu et al. [39] | AED | two-stage | Based on different objectives in reality | Effficiency maximization | |
Ding et al. [17] | AED | two-stage | Maximal average satisfaction degree | - | |
An et al. [3] | - | three-stage | The Shapley value | - | |
Li et al. [24] | AED | two-stage | By repeatedly minimizing the maximum deviation between the efficient and size allocation | Efficiency invariance & efficiency maximization | |
Li et al.[26] | - | single-stage | Cooperative game | - | |
Chu et al. [14] | AED | two-stage | Leader-follower & the Nash bargaining | - | |
The present study | AED and MED | two-stage | Cooperative, leader-follower & the Nash bargaining | Independent from efficiency rank and size |
Notation | Description |
number of DMUs | |
allocated total cost to system | |
number of exogenous inputs of stage 1 | |
number of exogenous inputs of stage 2 | |
number of exogenous outputs of stage 1 | |
number of exogenous outputs of stage 2 | |
number of intermediate products | |
allocated cost to DMU |
|
allocated cost to DMU |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
Notation | Description |
number of DMUs | |
allocated total cost to system | |
number of exogenous inputs of stage 1 | |
number of exogenous inputs of stage 2 | |
number of exogenous outputs of stage 1 | |
number of exogenous outputs of stage 2 | |
number of intermediate products | |
allocated cost to DMU |
|
allocated cost to DMU |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
|
weight assigned to the |
branches | Inputs | Exogenous input | Intermediate products | Exogenous output | Outputs | |||||
1 | 25 | 619 | 538 | 854 | 77237 | 34224 | 2101 | 2947 | 913 | 224 |
2 | 27 | 419 | 489 | 125 | 88031 | 56559 | 1023 | 3138 | 478 | 516 |
3 | 40 | 1670 | 1459 | 120 | 164053 | 62776 | 1440 | 5494 | 1242 | 877 |
4 | 42 | 2931 | 1497 | 86 | 145369 | 65226 | 2458 | 3144 | 870 | 1138 |
5 | 52 | 2587 | 797 | 133 | 166424 | 85886 | 2202 | 6705 | 854 | 618 |
6 | 45 | 2181 | 697 | 149 | 215695 | 30179 | 1653 | 8487 | 1023 | 2096 |
7 | 33 | 989 | 1217 | 144 | 114043 | 43447 | 1919 | 4996 | 767 | 713 |
8 | 107 | 6277 | 2189 | 735 | 727699 | 294126 | 2486 | 21265 | 6282 | 6287 |
9 | 88 | 3197 | 949 | 101 | 186642 | 53223 | 648 | 8574 | 1537 | 1739 |
10 | 146 | 6222 | 1824 | 399 | 614241 | 121784 | 2007 | 21937 | 8008 | 3261 |
11 | 57 | 1532 | 2248 | 83 | 241794 | 83634 | 626 | 8351 | 1530 | 2011 |
12 | 42 | 1194 | 1604 | 447 | 150707 | 57875 | 1538 | 5594 | 858 | 1203 |
13 | 132 | 5608 | 1731 | 141 | 416754 | 168798 | 1263 | 15271 | 4442 | 2743 |
14 | 77 | 2136 | 906 | 145 | 276379 | 38763 | 2686 | 10070 | 2445 | 1487 |
15 | 43 | 1534 | 438 | 750 | 133359 | 48239 | 538 | 4842 | 1172 | 1355 |
16 | 43 | 1711 | 1069 | 106 | 157275 | 27004 | 2419 | 6505 | 1469 | 1217 |
17 | 59 | 3686 | 820 | 119 | 150827 | 60244 | 2927 | 6552 | 1209 | 1082 |
18 | 33 | 1479 | 2347 | 41 | 215012 | 78253 | 2975 | 8624 | 894 | 2228 |
19 | 38 | 1822 | 1577 | 232 | 192746 | 76284 | 2472 | 9422 | 967 | 1367 |
20 | 162 | 5922 | 2330 | 148 | 533273 | 163816 | 1597 | 18700 | 4249 | 6545 |
21 | 60 | 2158 | 1153 | 180 | 252568 | 77887 | 1745 | 10573 | 1611 | 2210 |
22 | 56 | 2666 | 2683 | 469 | 269402 | 158835 | 1035 | 10678 | 1589 | 1834 |
23 | 71 | 2969 | 1521 | 65 | 197684 | 100321 | 2108 | 8563 | 905 | 1316 |
24 | 117 | 5527 | 2369 | 175 | 406475 | 106073 | 1300 | 15545 | 2359 | 2717 |
25 | 78 | 3219 | 2738 | 661 | 371847 | 125323 | 2900 | 14681 | 3477 | 3134 |
26 | 51 | 2431 | 741 | 164 | 190055 | 142422 | 2316 | 7964 | 1318 | 1158 |
27 | 48 | 2924 | 1561 | 183 | 332641 | 94933 | 1529 | 11756 | 2779 | 1398 |
branches | Inputs | Exogenous input | Intermediate products | Exogenous output | Outputs | |||||
1 | 25 | 619 | 538 | 854 | 77237 | 34224 | 2101 | 2947 | 913 | 224 |
2 | 27 | 419 | 489 | 125 | 88031 | 56559 | 1023 | 3138 | 478 | 516 |
3 | 40 | 1670 | 1459 | 120 | 164053 | 62776 | 1440 | 5494 | 1242 | 877 |
4 | 42 | 2931 | 1497 | 86 | 145369 | 65226 | 2458 | 3144 | 870 | 1138 |
5 | 52 | 2587 | 797 | 133 | 166424 | 85886 | 2202 | 6705 | 854 | 618 |
6 | 45 | 2181 | 697 | 149 | 215695 | 30179 | 1653 | 8487 | 1023 | 2096 |
7 | 33 | 989 | 1217 | 144 | 114043 | 43447 | 1919 | 4996 | 767 | 713 |
8 | 107 | 6277 | 2189 | 735 | 727699 | 294126 | 2486 | 21265 | 6282 | 6287 |
9 | 88 | 3197 | 949 | 101 | 186642 | 53223 | 648 | 8574 | 1537 | 1739 |
10 | 146 | 6222 | 1824 | 399 | 614241 | 121784 | 2007 | 21937 | 8008 | 3261 |
11 | 57 | 1532 | 2248 | 83 | 241794 | 83634 | 626 | 8351 | 1530 | 2011 |
12 | 42 | 1194 | 1604 | 447 | 150707 | 57875 | 1538 | 5594 | 858 | 1203 |
13 | 132 | 5608 | 1731 | 141 | 416754 | 168798 | 1263 | 15271 | 4442 | 2743 |
14 | 77 | 2136 | 906 | 145 | 276379 | 38763 | 2686 | 10070 | 2445 | 1487 |
15 | 43 | 1534 | 438 | 750 | 133359 | 48239 | 538 | 4842 | 1172 | 1355 |
16 | 43 | 1711 | 1069 | 106 | 157275 | 27004 | 2419 | 6505 | 1469 | 1217 |
17 | 59 | 3686 | 820 | 119 | 150827 | 60244 | 2927 | 6552 | 1209 | 1082 |
18 | 33 | 1479 | 2347 | 41 | 215012 | 78253 | 2975 | 8624 | 894 | 2228 |
19 | 38 | 1822 | 1577 | 232 | 192746 | 76284 | 2472 | 9422 | 967 | 1367 |
20 | 162 | 5922 | 2330 | 148 | 533273 | 163816 | 1597 | 18700 | 4249 | 6545 |
21 | 60 | 2158 | 1153 | 180 | 252568 | 77887 | 1745 | 10573 | 1611 | 2210 |
22 | 56 | 2666 | 2683 | 469 | 269402 | 158835 | 1035 | 10678 | 1589 | 1834 |
23 | 71 | 2969 | 1521 | 65 | 197684 | 100321 | 2108 | 8563 | 905 | 1316 |
24 | 117 | 5527 | 2369 | 175 | 406475 | 106073 | 1300 | 15545 | 2359 | 2717 |
25 | 78 | 3219 | 2738 | 661 | 371847 | 125323 | 2900 | 14681 | 3477 | 3134 |
26 | 51 | 2431 | 741 | 164 | 190055 | 142422 | 2316 | 7964 | 1318 | 1158 |
27 | 48 | 2924 | 1561 | 183 | 332641 | 94933 | 1529 | 11756 | 2779 | 1398 |
Model (3) | Model (6) | Model (3) | Model (6) | |||||
branches | ||||||||
1 | 1(1) | 1(1) | 246.9783 | 229.0669 | 476.0452(22) | 249.9640 | 241.3908 | 491.3548(26) |
2 | 0.8798(14) | 0.8152(14) | 247.3826 | 256.3008 | 503.6833(12) | 250.6172 | 248.6579 | 499.2751(14) |
3 | 0.7632(23) | 0.5949(22) | 245.3606 | 263.9743 | 509.3349(8) | 249.0929 | 248.1273 | 497.2202(24) |
4 | 0.7382(24) | 0.5849(24) | 244.5442 | 261.6055 | 506.1497(11) | 249.7255 | 248.2464 | 497.97198(20) |
5 | 0.8589(18) | 0.7690(16) | 244.4590 | 256.2162 | 500.6752(16) | 251.6313 | 248.5930 | 500.2244(10) |
6 | 1(1) | 1(1) | 248.9866 | 274.3444 | 523.3309(4) | 250.5248 | 250.8240 | 501.3489(7) |
7 | 0.8644(16) | 0.7747(15) | 245.7330 | 256.5588 | 502.2918(14) | 249.5825 | 248.5230 | 498.1055(19) |
8 | 0.9617(4) | 0.9546(4) | 226.5395 | 244.7763 | 471.3158(25) | 255.3597 | 252.1110 | 507.4707(1) |
9 | 0.7943(21) | 0.5885(23) | 245.7459 | 255.0998 | 500.8457(15) | 250.7254 | 248.7602 | 499.4857(12) |
10 | 0.9336(8) | 0.8670(10) | 235.6404 | 295.7199 | 531.3602(3) | 255.4656 | 249.2222 | 504.6878(4) |
11 | 0.8978(12) | 0.8599(11) | 244.5437 | 232.8622 | 477.4059(20) | 248.6555 | 248.8462 | 497.5017(21) |
12 | 0.8010(20) | 0.69733(19) | 245.1240 | 230.6952 | 475.8192(23) | 249.2772 | 248.0615 | 497.3387(23) |
13 | 0.8624(17) | 0.7247(18) | 237.5553 | 280.0552 | 517.6105(5) | 252.4906 | 248.5284 | 501.0190(8) |
14 | 1(1) | 1(1) | 249.5513 | 265.0496 | 514.6009(6) | 256.0044 | 248.5349 | 504.5393(5) |
15 | 0.9587(5) | 0.9166(7) | 246.8357 | 228.7804 | 475.6061(24) | 248.9389 | 243.5603 | 492.4992(25) |
16 | 0.9172(11) | 0.8314(13) | 249.2900 | 260.6817 | 509.9717(7) | 251.1524 | 248.2845 | 499.4369(13) |
17 | 0.9685(2) | 0.9580(3) | 244.1696 | 264.5992 | 508.7689(9) | 250.3736 | 248.2632 | 498.6368(17) |
18 | 1(1) | 1(1) | 245.3942 | 215.7705 | 461.1648(26) | 249.4011 | 250.3788 | 499.7799(11) |
19 | 0.9638(3) | 0.9277(5) | 244.6776 | 253.1032 | 497.7808(17) | 249.8272 | 248.9734 | 498.8005(16) |
20 | 0.8664(15) | 0.7326(17) | 236.1256 | 304.6363 | 540.7618(2) | 251.2982 | 252.9057 | 504.2039(6) |
21 | 0.8936(13) | 0.8452(12) | 244.6708 | 263.000 | 507.6708(10) | 249.7751 | 248.5778 | 498.3529(18) |
22 | 0.9210(10) | 0.9234(6) | 242.6463 | 245.2438 | 487.8901(18) | 255.0194 | 251.9952 | 507.0145(2) |
23 | 0.8016(19) | 0.6033(21) | 243.8905 | 259.6044 | 503.4949(13) | 252.5173 | 248.3064 | 500.8237(9) |
24 | 0.7912(22) | 0.6329(20) | 240.8019 | 300.7017 | 541.5036(1) | 250.0492 | 248.9657 | 499.0150(15) |
25 | 0.9220(9) | 0.8732(8) | 243.2701 | 232.7953 | 476.0654(21) | 250.1477 | 247.1931 | 497.3408(22) |
26 | 0.9511(6) | 0.9983(2) | 244.5997 | 233.8111 | 478.4109(19) | 256.7994 | 249.7160 | 506.5153(3) |
27 | 0.9353(7) | 0.8705(9) | 0.2413 | 0.2289 | 0.4702(27) | 0.0355 | 0.0015 | 0.0370(27) |
Model (3) | Model (6) | Model (3) | Model (6) | |||||
branches | ||||||||
1 | 1(1) | 1(1) | 246.9783 | 229.0669 | 476.0452(22) | 249.9640 | 241.3908 | 491.3548(26) |
2 | 0.8798(14) | 0.8152(14) | 247.3826 | 256.3008 | 503.6833(12) | 250.6172 | 248.6579 | 499.2751(14) |
3 | 0.7632(23) | 0.5949(22) | 245.3606 | 263.9743 | 509.3349(8) | 249.0929 | 248.1273 | 497.2202(24) |
4 | 0.7382(24) | 0.5849(24) | 244.5442 | 261.6055 | 506.1497(11) | 249.7255 | 248.2464 | 497.97198(20) |
5 | 0.8589(18) | 0.7690(16) | 244.4590 | 256.2162 | 500.6752(16) | 251.6313 | 248.5930 | 500.2244(10) |
6 | 1(1) | 1(1) | 248.9866 | 274.3444 | 523.3309(4) | 250.5248 | 250.8240 | 501.3489(7) |
7 | 0.8644(16) | 0.7747(15) | 245.7330 | 256.5588 | 502.2918(14) | 249.5825 | 248.5230 | 498.1055(19) |
8 | 0.9617(4) | 0.9546(4) | 226.5395 | 244.7763 | 471.3158(25) | 255.3597 | 252.1110 | 507.4707(1) |
9 | 0.7943(21) | 0.5885(23) | 245.7459 | 255.0998 | 500.8457(15) | 250.7254 | 248.7602 | 499.4857(12) |
10 | 0.9336(8) | 0.8670(10) | 235.6404 | 295.7199 | 531.3602(3) | 255.4656 | 249.2222 | 504.6878(4) |
11 | 0.8978(12) | 0.8599(11) | 244.5437 | 232.8622 | 477.4059(20) | 248.6555 | 248.8462 | 497.5017(21) |
12 | 0.8010(20) | 0.69733(19) | 245.1240 | 230.6952 | 475.8192(23) | 249.2772 | 248.0615 | 497.3387(23) |
13 | 0.8624(17) | 0.7247(18) | 237.5553 | 280.0552 | 517.6105(5) | 252.4906 | 248.5284 | 501.0190(8) |
14 | 1(1) | 1(1) | 249.5513 | 265.0496 | 514.6009(6) | 256.0044 | 248.5349 | 504.5393(5) |
15 | 0.9587(5) | 0.9166(7) | 246.8357 | 228.7804 | 475.6061(24) | 248.9389 | 243.5603 | 492.4992(25) |
16 | 0.9172(11) | 0.8314(13) | 249.2900 | 260.6817 | 509.9717(7) | 251.1524 | 248.2845 | 499.4369(13) |
17 | 0.9685(2) | 0.9580(3) | 244.1696 | 264.5992 | 508.7689(9) | 250.3736 | 248.2632 | 498.6368(17) |
18 | 1(1) | 1(1) | 245.3942 | 215.7705 | 461.1648(26) | 249.4011 | 250.3788 | 499.7799(11) |
19 | 0.9638(3) | 0.9277(5) | 244.6776 | 253.1032 | 497.7808(17) | 249.8272 | 248.9734 | 498.8005(16) |
20 | 0.8664(15) | 0.7326(17) | 236.1256 | 304.6363 | 540.7618(2) | 251.2982 | 252.9057 | 504.2039(6) |
21 | 0.8936(13) | 0.8452(12) | 244.6708 | 263.000 | 507.6708(10) | 249.7751 | 248.5778 | 498.3529(18) |
22 | 0.9210(10) | 0.9234(6) | 242.6463 | 245.2438 | 487.8901(18) | 255.0194 | 251.9952 | 507.0145(2) |
23 | 0.8016(19) | 0.6033(21) | 243.8905 | 259.6044 | 503.4949(13) | 252.5173 | 248.3064 | 500.8237(9) |
24 | 0.7912(22) | 0.6329(20) | 240.8019 | 300.7017 | 541.5036(1) | 250.0492 | 248.9657 | 499.0150(15) |
25 | 0.9220(9) | 0.8732(8) | 243.2701 | 232.7953 | 476.0654(21) | 250.1477 | 247.1931 | 497.3408(22) |
26 | 0.9511(6) | 0.9983(2) | 244.5997 | 233.8111 | 478.4109(19) | 256.7994 | 249.7160 | 506.5153(3) |
27 | 0.9353(7) | 0.8705(9) | 0.2413 | 0.2289 | 0.4702(27) | 0.0355 | 0.0015 | 0.0370(27) |
Stage 1 as the leader | Stage 1 as the follower | Model (23) | |||||
branches | |||||||
1 | 0 | 135.7885 | 521.7512 | 0 | 260.8756 | 67.8943 | 328.7698 (21) |
2 | 0 | 140.1356 | 260.8284 | 0 | 130.4142 | 70.0678 | 200.4820 (27) |
3 | 0 | 214.8582 | 357.783 | 0 | 178.8915 | 107.4291 | 286.3206(24) |
4 | 0 | 0.0000 | 602.2915 | 0 | 301.1457 | 0.0000 | 301.1457(23) |
5 | 0 | 341.3245 | 562.1265 | 0 | 281.0632 | 170.6623 | 451.7255(17) |
6 | 0 | 476.9271 | 441.9432 | 0 | 220.9715 | 238.4636 | 459.4352(15) |
7 | 0 | 295.2004 | 469.1469 | 0 | 234.5734 | 147.6002 | 382.1736(19) |
8 | 0 | 687.6763 | 735.7962 | 0 | 367.8980 | 344.8382 | 712.7362(4) |
9 | 0 | 556.8296 | 181.5706 | 0 | 90.7853 | 278.4148 | 369.2001(20) |
10 | 0 | 967.3349 | 599.2162 | 0 | 299.6080 | 483.6675 | 783.2756(1) |
11 | 0 | 379.7576 | 157.2898 | 0 | 78.6449 | 189.8788 | 268.5237(25) |
12 | 0 | 281.0507 | 374.9296 | 0 | 187.4647 | 140.5254 | 327.9901 (22) |
13 | 0 | 726.8723 | 369.9592 | 0 | 184.9796 | 363.4362 | 548.4158(10) |
14 | 0 | 460.0660 | 705.4757 | 0 | 352.7378 | 230.0330 | 582.7708(7) |
15 | 0 | 248.9499 | 154.1661 | 0 | 77.0830 | 124.4750 | 201.5580(26) |
16 | 0 | 371.5729 | 606.3652 | 0 | 303.1825 | 185.7865 | 488.9690(14) |
17 | 0 | 390.0909 | 735.7962 | 0 | 367.8980 | 195.0455 | 562.9435(9) |
18 | 0 | 501.3772 | 725.2381 | 0 | 362.6190 | 250.6887 | 613.3076(6) |
19 | 0 | 623.6072 | 615.4395 | 0 | 307.7197 | 311.8037 | 619.5234(5) |
20 | 0 | 967.3349 | 465.8196 | 0 | 232.9097 | 483.6675 | 716.5773(3) |
21 | 0 | 623.5219 | 462.2460 | 0 | 231.1230 | 311.7610 | 542.8840(11) |
22 | 0 | 569.3522 | 253.7010 | 0 | 126.8505 | 284.6762 | 411.5266(18) |
23 | 0 | 503.6960 | 528.6428 | 0 | 264.3214 | 251.8480 | 516.1694(13) |
24 | 0 | 788.8750 | 360.5408 | 0 | 180.2704 | 394.4376 | 574.7079(8) |
25 | 0 | 806.3711 | 735.7962 | 0 | 367.8980 | 403.1856 | 771.0837 (2) |
26 | 0 | 447.1736 | 597.3741 | 0 | 298.6870 | 223.5869 | 522.2738(12) |
27 | 0 | 492.2555 | 418.7666 | 0 | 209.3832 | 246.1278 | 455.5110(16) |
Stage 1 as the leader | Stage 1 as the follower | Model (23) | |||||
branches | |||||||
1 | 0 | 135.7885 | 521.7512 | 0 | 260.8756 | 67.8943 | 328.7698 (21) |
2 | 0 | 140.1356 | 260.8284 | 0 | 130.4142 | 70.0678 | 200.4820 (27) |
3 | 0 | 214.8582 | 357.783 | 0 | 178.8915 | 107.4291 | 286.3206(24) |
4 | 0 | 0.0000 | 602.2915 | 0 | 301.1457 | 0.0000 | 301.1457(23) |
5 | 0 | 341.3245 | 562.1265 | 0 | 281.0632 | 170.6623 | 451.7255(17) |
6 | 0 | 476.9271 | 441.9432 | 0 | 220.9715 | 238.4636 | 459.4352(15) |
7 | 0 | 295.2004 | 469.1469 | 0 | 234.5734 | 147.6002 | 382.1736(19) |
8 | 0 | 687.6763 | 735.7962 | 0 | 367.8980 | 344.8382 | 712.7362(4) |
9 | 0 | 556.8296 | 181.5706 | 0 | 90.7853 | 278.4148 | 369.2001(20) |
10 | 0 | 967.3349 | 599.2162 | 0 | 299.6080 | 483.6675 | 783.2756(1) |
11 | 0 | 379.7576 | 157.2898 | 0 | 78.6449 | 189.8788 | 268.5237(25) |
12 | 0 | 281.0507 | 374.9296 | 0 | 187.4647 | 140.5254 | 327.9901 (22) |
13 | 0 | 726.8723 | 369.9592 | 0 | 184.9796 | 363.4362 | 548.4158(10) |
14 | 0 | 460.0660 | 705.4757 | 0 | 352.7378 | 230.0330 | 582.7708(7) |
15 | 0 | 248.9499 | 154.1661 | 0 | 77.0830 | 124.4750 | 201.5580(26) |
16 | 0 | 371.5729 | 606.3652 | 0 | 303.1825 | 185.7865 | 488.9690(14) |
17 | 0 | 390.0909 | 735.7962 | 0 | 367.8980 | 195.0455 | 562.9435(9) |
18 | 0 | 501.3772 | 725.2381 | 0 | 362.6190 | 250.6887 | 613.3076(6) |
19 | 0 | 623.6072 | 615.4395 | 0 | 307.7197 | 311.8037 | 619.5234(5) |
20 | 0 | 967.3349 | 465.8196 | 0 | 232.9097 | 483.6675 | 716.5773(3) |
21 | 0 | 623.5219 | 462.2460 | 0 | 231.1230 | 311.7610 | 542.8840(11) |
22 | 0 | 569.3522 | 253.7010 | 0 | 126.8505 | 284.6762 | 411.5266(18) |
23 | 0 | 503.6960 | 528.6428 | 0 | 264.3214 | 251.8480 | 516.1694(13) |
24 | 0 | 788.8750 | 360.5408 | 0 | 180.2704 | 394.4376 | 574.7079(8) |
25 | 0 | 806.3711 | 735.7962 | 0 | 367.8980 | 403.1856 | 771.0837 (2) |
26 | 0 | 447.1736 | 597.3741 | 0 | 298.6870 | 223.5869 | 522.2738(12) |
27 | 0 | 492.2555 | 418.7666 | 0 | 209.3832 | 246.1278 | 455.5110(16) |
Stage 1 of (3) | Stage 2 of (3) | AED of [14] | Model (3) | Model (6) | Model(3) | Model(6) | |
branches | |||||||
1 | 0.7597 | 1 | 0.8634(13) | 0.8799(14) | 0.7884(16) | 306.9362 | 306.6713 |
2 | 1 | 0.7595 | 0.8798(11) | 0.8798(13) | 0.8375(12) | 299.0361 | 307.4420 |
3 | 0.7204 | 0.7839 | 0.7470(21) | 0.7521(24) | 0.5810(23) | 305.4121 | 306.6072 |
4 | 0.5595 | 0.7034 | 0.5726(27) | 0.6314(27) | 0.4292(27) | 300.6593 | 306.9801 |
5 | 0.6884 | 0.8412 | 0.7102(24) | 0.7848(22) | 0.5998(21) | 298.6402 | 307.7304 |
6 | 0.9994 | 0.9996 | 0.9304(5) | 0.9995(2) | 0.9979(4) | 295.3327 | 308.3022 |
7 | 0.7285 | 0.9343 | 0.8152(17) | 0.8314(19) | 0.7136(19) | 308.9644 | 306.5066 |
8 | 0.9983 | 0.9565 | 0.9762(2) | 0.9774(4) | 0.9544(5) | 294.8752 | 310.4954 |
9 | 0.5872 | 1 | 0.7399(22) | 0.7936(21) | 0.5872(22) | 306.4590 | 307.0616 |
10 | 1 | 0.8625 | 0.9225(8) | 0.9313(8) | 0.8624(9) | 453.1254 | 309.8544 |
11 | 0.9380 | 0.8120 | 0.8770(12) | 0.8750(15) | 0.8297(13) | 307.0382 | 306.8330 |
12 | 0.7732 | 0.8288 | 0.7975(19) | 0.8010(20) | 0.6945(20) | 307.1054 | 306.7443 |
13 | 0.7248 | 1 | 0.8402(15) | 0.8624(17) | 0.7247(18) | 299.7402 | 308.6713 |
14 | 1 | 1 | 0.9499(4) | 1(1) | 1(1) | 289.1324 | 308.8396 |
15 | 0.9136 | 0.9942 | 0.9513(3) | 0.9538(5) | 0.9128(7) | 304.4242 | 306.7419 |
16 | 0.6846 | 1 | 0.8023(18) | 0.8423(18) | 0.8124(14) | 311.8755 | 306.8844 |
17 | 0.5531 | 0.9534 | 0.6934(25) | 0.7533(23) | 0.5380(25) | 302.9726 | 306.6634 |
18 | 1 | 0.9752 | 0.9876(1) | 0.9876(3) | 0.9997(2) | 307.5180 | 306.7759 |
19 | 0.8078 | 1 | 0.9036(10) | 0.9039(11) | 0.8090(15) | 308.7589 | 306.9259 |
20 | 0.7328 | 1 | 0.8458(14) | 0.8664(16) | 0.7328(17) | 309.7008 | 307.5808 |
21 | 0.8525 | 0.9232 | 0.8850(10) | 0.8878(12) | 0.8454(11) | 306.4648 | 306.8614 |
22 | 1 | 0.8421 | 0.7935(20) | 0.9210(10) | 0.9253(6) | 286.0109 | 309.9431 |
23 | 0.5549 | 0.8946 | 0.6407(26) | 0.7247(26) | 0.5231(26) | 298.3907 | 308.0263 |
24 | 0.5918 | 0.9036 | 0.7177(23) | 0.7477(25) | 0.5791(24) | 300.7911 | 307.3677 |
25 | 0.8710 | 0.9938 | 0.9239(7) | 0.9324(7) | 0.8731(7) | 308.9031 | 307.0074 |
26 | 1 | 0.9022 | 0.8276(16) | 0.9511(6) | 0.9989(3) | 281.1311 | 310.4377 |
27 | 1 | 0.8505 | 0.9241(6) | 0.9252(9) | 0.8504(10) | 0.6013 | 0.0448 |
Stage 1 of (3) | Stage 2 of (3) | AED of [14] | Model (3) | Model (6) | Model(3) | Model(6) | |
branches | |||||||
1 | 0.7597 | 1 | 0.8634(13) | 0.8799(14) | 0.7884(16) | 306.9362 | 306.6713 |
2 | 1 | 0.7595 | 0.8798(11) | 0.8798(13) | 0.8375(12) | 299.0361 | 307.4420 |
3 | 0.7204 | 0.7839 | 0.7470(21) | 0.7521(24) | 0.5810(23) | 305.4121 | 306.6072 |
4 | 0.5595 | 0.7034 | 0.5726(27) | 0.6314(27) | 0.4292(27) | 300.6593 | 306.9801 |
5 | 0.6884 | 0.8412 | 0.7102(24) | 0.7848(22) | 0.5998(21) | 298.6402 | 307.7304 |
6 | 0.9994 | 0.9996 | 0.9304(5) | 0.9995(2) | 0.9979(4) | 295.3327 | 308.3022 |
7 | 0.7285 | 0.9343 | 0.8152(17) | 0.8314(19) | 0.7136(19) | 308.9644 | 306.5066 |
8 | 0.9983 | 0.9565 | 0.9762(2) | 0.9774(4) | 0.9544(5) | 294.8752 | 310.4954 |
9 | 0.5872 | 1 | 0.7399(22) | 0.7936(21) | 0.5872(22) | 306.4590 | 307.0616 |
10 | 1 | 0.8625 | 0.9225(8) | 0.9313(8) | 0.8624(9) | 453.1254 | 309.8544 |
11 | 0.9380 | 0.8120 | 0.8770(12) | 0.8750(15) | 0.8297(13) | 307.0382 | 306.8330 |
12 | 0.7732 | 0.8288 | 0.7975(19) | 0.8010(20) | 0.6945(20) | 307.1054 | 306.7443 |
13 | 0.7248 | 1 | 0.8402(15) | 0.8624(17) | 0.7247(18) | 299.7402 | 308.6713 |
14 | 1 | 1 | 0.9499(4) | 1(1) | 1(1) | 289.1324 | 308.8396 |
15 | 0.9136 | 0.9942 | 0.9513(3) | 0.9538(5) | 0.9128(7) | 304.4242 | 306.7419 |
16 | 0.6846 | 1 | 0.8023(18) | 0.8423(18) | 0.8124(14) | 311.8755 | 306.8844 |
17 | 0.5531 | 0.9534 | 0.6934(25) | 0.7533(23) | 0.5380(25) | 302.9726 | 306.6634 |
18 | 1 | 0.9752 | 0.9876(1) | 0.9876(3) | 0.9997(2) | 307.5180 | 306.7759 |
19 | 0.8078 | 1 | 0.9036(10) | 0.9039(11) | 0.8090(15) | 308.7589 | 306.9259 |
20 | 0.7328 | 1 | 0.8458(14) | 0.8664(16) | 0.7328(17) | 309.7008 | 307.5808 |
21 | 0.8525 | 0.9232 | 0.8850(10) | 0.8878(12) | 0.8454(11) | 306.4648 | 306.8614 |
22 | 1 | 0.8421 | 0.7935(20) | 0.9210(10) | 0.9253(6) | 286.0109 | 309.9431 |
23 | 0.5549 | 0.8946 | 0.6407(26) | 0.7247(26) | 0.5231(26) | 298.3907 | 308.0263 |
24 | 0.5918 | 0.9036 | 0.7177(23) | 0.7477(25) | 0.5791(24) | 300.7911 | 307.3677 |
25 | 0.8710 | 0.9938 | 0.9239(7) | 0.9324(7) | 0.8731(7) | 308.9031 | 307.0074 |
26 | 1 | 0.9022 | 0.8276(16) | 0.9511(6) | 0.9989(3) | 281.1311 | 310.4377 |
27 | 1 | 0.8505 | 0.9241(6) | 0.9252(9) | 0.8504(10) | 0.6013 | 0.0448 |
Model (23) | Chu et al. [14] | Li et al. [24] | |||||||
branches | |||||||||
1 | 44.2099 | 41.7809 | 86.2678 | 29.2523 | 54.8286 | 84.0809 | 34.8394 | 99.5911 | 134.4306 |
2 | 50.3884 | 43.1185 | 93.5068 | 33.3404 | 61.0391 | 94.3795 | 57.6112 | 4.1483 | 61.7595 |
3 | 93.9028 | 56.1099 | 160.0128 | 62.1326 | 102.6452 | 164.7778 | 66.9629 | 83.9139 | 150.8768 |
4 | 83.2082 | 0.0000 | 83.2082 | 55.0563 | 50.3562 | 105.4125 | 42.5563 | 5.3306 | 47.8869 |
5 | 95.2600 | 105.0225 | 200.2825 | 63.0305 | 130.1635 | 193.1941 | 105.6896 | 19.9776 | 125.6671 |
6 | 123.4624 | 146.7462 | 270.2086 | 81.6912 | 185.8070 | 267.4982 | 149.2000 | 46.4915 | 195.6915 |
7 | 65.2774 | 90.8305 | 156.1080 | 43.1920 | 105.1728 | 148.3648 | 27.0534 | 58.2580 | 85.3113 |
8 | 416.5300 | 212.2072 | 628.7372 | 275.6048 | 412.7297 | 688.3345 | 662.6315 | 455.6247 | 1118.2562 |
9 | 106.8326 | 171.3315 | 278.1641 | 70.6878 | 192.9383 | 263.626 | 55.8416 | 158.4308 | 214.2724 |
10 | 351.5874 | 297.6403 | 649.2277 | 232.6343 | 421.0993 | 653.7337 | 428.1954 | 448.9607 | 877.1561 |
11 | 138.4013 | 116.8480 | 255.2492 | 91.5758 | 170.7374 | 262.3132 | 91.0412 | 79.0747 | 170.1160 |
12 | 86.2637 | 86.4768 | 172.7404 | 57.0780 | 116.1171 | 173.1951 | 38.3474 | 35.4254 | 73.7728 |
13 | 238.5472 | 223.6521 | 462.1993 | 157.8392 | 305.5089 | 463.3481 | 257.0286 | 451.538 | 708.5666 |
14 | 158.1975 | 141.5582 | 299.7556 | 104.6743 | 195.2432 | 299.9174 | 164.9817 | 245.7357 | 410.7174 |
15 | 76.3338 | 76.5996 | 152.9334 | 50.5077 | 104.8872 | 155.3949 | 85.7256 | 103.1206 | 188.8462 |
16 | 90.0231 | 114.3296 | 204.3528 | 59.5655 | 138.6559 | 198.2214 | 62.9564 | 161.9881 | 224.9445 |
17 | 86.3324 | 120.0275 | 206.3598 | 57.1234 | 140.0173 | 197.1407 | 65.8529 | 108.8606 | 174.7134 |
18 | 123.0714 | 154.2693 | 277.3407 | 81.4325 | 192.0992 | 273.5317 | 84.4604 | 4.1483 | 88.6087 |
19 | 110.3265 | 191.8783 | 302.2048 | 72.9996 | 207.1934 | 280.193 | 100.2016 | 53.5750 | 153.7766 |
20 | 305.2419 | 297.6403 | 602.8821 | 201.9689 | 421.0993 | 623.0683 | 306.3559 | 340.4241 | 646.7800 |
21 | 144.5682 | 191.8521 | 336.4203 | 95.6562 | 230.5790 | 326.2353 | 164.1695 | 115.4121 | 279.5816 |
22 | 154.2039 | 175.1846 | 329.3884 | 102.0319 | 220.4889 | 322.5207 | 131.0596 | 56.5463 | 187.6059 |
23 | 113.1530 | 154.9827 | 268.1357 | 74.8698 | 181.0649 | 255.9346 | 76.9843 | 13.9235 | 90.9078 |
24 | 232.6635 | 242.7298 | 475.3933 | 153.9462 | 316.4011 | 470.3472 | 196.4414 | 133.2967 | 329.7382 |
25 | 212.8427 | 248.1131 | 460.9559 | 140.8313 | 313.3001 | 454.1314 | 195.7660 | 344.9362 | 540.7023 |
26 | 108.7862 | 137.5913 | 246.3775 | 71.9804 | 164.8987 | 236.8791 | 163.0222 | 66.0493 | 229.0715 |
27 | 190.4015 | 151.4626 | 341.8641 | 125.9827 | 218.2432 | 344.2259 | 250.7998 | 239.4424 | 490.2422 |
Model (23) | Chu et al. [14] | Li et al. [24] | |||||||
branches | |||||||||
1 | 44.2099 | 41.7809 | 86.2678 | 29.2523 | 54.8286 | 84.0809 | 34.8394 | 99.5911 | 134.4306 |
2 | 50.3884 | 43.1185 | 93.5068 | 33.3404 | 61.0391 | 94.3795 | 57.6112 | 4.1483 | 61.7595 |
3 | 93.9028 | 56.1099 | 160.0128 | 62.1326 | 102.6452 | 164.7778 | 66.9629 | 83.9139 | 150.8768 |
4 | 83.2082 | 0.0000 | 83.2082 | 55.0563 | 50.3562 | 105.4125 | 42.5563 | 5.3306 | 47.8869 |
5 | 95.2600 | 105.0225 | 200.2825 | 63.0305 | 130.1635 | 193.1941 | 105.6896 | 19.9776 | 125.6671 |
6 | 123.4624 | 146.7462 | 270.2086 | 81.6912 | 185.8070 | 267.4982 | 149.2000 | 46.4915 | 195.6915 |
7 | 65.2774 | 90.8305 | 156.1080 | 43.1920 | 105.1728 | 148.3648 | 27.0534 | 58.2580 | 85.3113 |
8 | 416.5300 | 212.2072 | 628.7372 | 275.6048 | 412.7297 | 688.3345 | 662.6315 | 455.6247 | 1118.2562 |
9 | 106.8326 | 171.3315 | 278.1641 | 70.6878 | 192.9383 | 263.626 | 55.8416 | 158.4308 | 214.2724 |
10 | 351.5874 | 297.6403 | 649.2277 | 232.6343 | 421.0993 | 653.7337 | 428.1954 | 448.9607 | 877.1561 |
11 | 138.4013 | 116.8480 | 255.2492 | 91.5758 | 170.7374 | 262.3132 | 91.0412 | 79.0747 | 170.1160 |
12 | 86.2637 | 86.4768 | 172.7404 | 57.0780 | 116.1171 | 173.1951 | 38.3474 | 35.4254 | 73.7728 |
13 | 238.5472 | 223.6521 | 462.1993 | 157.8392 | 305.5089 | 463.3481 | 257.0286 | 451.538 | 708.5666 |
14 | 158.1975 | 141.5582 | 299.7556 | 104.6743 | 195.2432 | 299.9174 | 164.9817 | 245.7357 | 410.7174 |
15 | 76.3338 | 76.5996 | 152.9334 | 50.5077 | 104.8872 | 155.3949 | 85.7256 | 103.1206 | 188.8462 |
16 | 90.0231 | 114.3296 | 204.3528 | 59.5655 | 138.6559 | 198.2214 | 62.9564 | 161.9881 | 224.9445 |
17 | 86.3324 | 120.0275 | 206.3598 | 57.1234 | 140.0173 | 197.1407 | 65.8529 | 108.8606 | 174.7134 |
18 | 123.0714 | 154.2693 | 277.3407 | 81.4325 | 192.0992 | 273.5317 | 84.4604 | 4.1483 | 88.6087 |
19 | 110.3265 | 191.8783 | 302.2048 | 72.9996 | 207.1934 | 280.193 | 100.2016 | 53.5750 | 153.7766 |
20 | 305.2419 | 297.6403 | 602.8821 | 201.9689 | 421.0993 | 623.0683 | 306.3559 | 340.4241 | 646.7800 |
21 | 144.5682 | 191.8521 | 336.4203 | 95.6562 | 230.5790 | 326.2353 | 164.1695 | 115.4121 | 279.5816 |
22 | 154.2039 | 175.1846 | 329.3884 | 102.0319 | 220.4889 | 322.5207 | 131.0596 | 56.5463 | 187.6059 |
23 | 113.1530 | 154.9827 | 268.1357 | 74.8698 | 181.0649 | 255.9346 | 76.9843 | 13.9235 | 90.9078 |
24 | 232.6635 | 242.7298 | 475.3933 | 153.9462 | 316.4011 | 470.3472 | 196.4414 | 133.2967 | 329.7382 |
25 | 212.8427 | 248.1131 | 460.9559 | 140.8313 | 313.3001 | 454.1314 | 195.7660 | 344.9362 | 540.7023 |
26 | 108.7862 | 137.5913 | 246.3775 | 71.9804 | 164.8987 | 236.8791 | 163.0222 | 66.0493 | 229.0715 |
27 | 190.4015 | 151.4626 | 341.8641 | 125.9827 | 218.2432 | 344.2259 | 250.7998 | 239.4424 | 490.2422 |
Model | Model(23) | Li et al. [24] |
Technique | Bargaining game | Goal programming |
Max-Cost(Efficiency rank) | DMU 10 (7) | DMU 8 (4) |
Min-Cost(Efficiency rank) | DMU 4 (27) | DMU 4 (27) |
Mean cost (stage1, stage2) | (148.1488,148.1475) | (150.5813,145.712) |
Model | Model(23) | Li et al. [24] |
Technique | Bargaining game | Goal programming |
Max-Cost(Efficiency rank) | DMU 10 (7) | DMU 8 (4) |
Min-Cost(Efficiency rank) | DMU 4 (27) | DMU 4 (27) |
Mean cost (stage1, stage2) | (148.1488,148.1475) | (150.5813,145.712) |
Model(23) | Chu et al. [14] | Chu et al. [14] | Chu et al. [14] | |
Model | (100 iterations) | (500 iterations) | (1000 iterations) | |
Time (s) | 1.7 | 109.7 | 515.7 | 1000 |
0.52 | 0.52 | 0.52 | 0.52 | |
0.51 | 0.54 | 0.53 | 0.53 | |
Mean cost | ||||
(stage1, stage2) | (97.9866,198.3097) | (98.6419,197.6544) | (97.8199,198.4764) | (98.0254,198.2709) |
Model(23) | Chu et al. [14] | Chu et al. [14] | Chu et al. [14] | |
Model | (100 iterations) | (500 iterations) | (1000 iterations) | |
Time (s) | 1.7 | 109.7 | 515.7 | 1000 |
0.52 | 0.52 | 0.52 | 0.52 | |
0.51 | 0.54 | 0.53 | 0.53 | |
Mean cost | ||||
(stage1, stage2) | (97.9866,198.3097) | (98.6419,197.6544) | (97.8199,198.4764) | (98.0254,198.2709) |
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