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Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand
May
2022, 18(3): 2163-2190.
doi: 10.3934/jimo.2021061
Decision framework for location and selection of container multimodal hubs: A case in china under the belt and road initiative
College of Transportation Engineering, Dalian Maritime University, Dalian 116026, China |
The location and selection of logistics nodes that facilitate the China Railway Express and rail-sea intermodal transportation has received increasing attention in China under the Belt and Road Initiative. The objective is to solve problems caused by the increasing number of origin cities opening international trains, such as disorderly competition, insufficient cargoes and low overall coordination. This study screens 22 cities as candidate Chinese international container multimodal hubs (CICMHs) in consideration of the actual situation of China's trade transportation. Thirteen indicators are screened using the information contribution rate-information substitutability method. Then, a comprehensive evaluation model is proposed to evaluate the candidate CICMHs and rank them. The model is based on the extended grey relational analysis-technique for order preference similar to ideal solution in combination with prospect theory. Chongqing, Guangzhou, Shanghai, Wuhan, Chengdu, Xi'an, Nanjing, Tianjin, Zhengzhou and Dalian are selected as the CICMHs. Moreover, a sensitivity analysis of the index weight fluctuations and decision-makers' preference and a comparative analysis of different decision-making methods are performed. The robustness and stability of the proposed model are demonstrated. This study can support the location and selection of CICMHs and expand the methods and applications in the decision-making field.
Keywords:
Belt and road initiative,
logistics hub,
location selection,
GRA-TOPSIS method,
prospect theory.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
Xinfang Zhang, Jing Lu, Yan Peng. Decision framework for location and selection of container multimodal hubs: A case in china under the belt and road initiative. Journal of Industrial and Management Optimization,
2022, 18
(3)
: 2163-2190.
doi: 10.3934/jimo.2021061
![]()
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X. Li, X. Li, X. Li and H. Qiu,
Multi-agent fare optimization model of two modes problem and its analysis based on edge of chaos, Phys. A, 469 (2017), 405-419.
doi: 10.1016/j.physa.2016.11.022. |
| [20] |
D. Li, L. Zhao, C. Wang, W. Sun and J. Xue,
Selection of China's imported grain distribution centers in the context of the belt and road initiative, Transportation Research Part E: Logistics and Transportation Review, 120 (2018), 16-34.
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Y.-H. Lin, P.-C. Lee and T.-P. Chang,
Practical expert diagnosis model based on the grey relational analysis technique, Expert Systems with Applications, 36 (2009), 1523-1528.
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C.-C. Lin and S.-W. Lin,
Two-stage approach to the intermodal terminal location problem, Comput. Oper. Res., 67 (2016), 113-119.
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| [23] |
D. Liu, C. Liu, Q. Fu, T. Li, K. M. Imran, S. Cui and F. M. Abrar,
ELM evaluation model of regional groundwater quality based on the crow search algorithm, Ecological Indicators, 81 (2017), 302-314.
doi: 10.1016/j.ecolind.2017.06.009. |
| [24] |
D. Liu, X. Qi and Q. Fu,
A resilience evaluation method for a combined regional agricultural water and soil resource system based on Weighted Mahalanobis distance and a Gray-TOPSIS model, Journal of Cleaner Production, 229 (2019), 667-679.
doi: 10.1016/j.jclepro.2019.04.406. |
| [25] |
S. Liu, N. Xie and J. Forrest,
Novel models of grey relational analysis based on visual angle of similarity and nearness, Grey Systems: Theory and Application, 1 (2011), 8-18.
doi: 10.1108/20439371111106696. |
| [26] |
S. Long and S. E. Grasman,
A strategic decision model for evaluating inland freight hub locations, Research in Transportation Business & Management, 5 (2012), 92-98.
doi: 10.1016/j.rtbm.2012.11.004. |
| [27] |
M. Lu, Node importance evaluation based on neighborhood structure hole and improved TOPSIS, Computer Networks, 178 (2020), 107336.
doi: 10.1016/j.comnet.2020.107336. |
| [28] |
C. Ma, Y. Yang, J. Wang, Y. Chen and D. Yang,
Determining the location of a Swine farming facility based on grey correlation and the TOPSIS method, Transactions of the ASABE, 60 (2017), 1281-1289.
doi: 10.13031/trans.11968. |
| [29] |
H. Mokhtar, A. A. N. P. Redi, M. Krishnamoorthy and A. T. Ernst,
An intermodal hub location problem for container distribution in indonesia, Comput. Oper. Res., 104 (2019), 415-432.
doi: 10.1016/j.cor.2018.08.012. |
| [30] |
D. Muravev, H. Hu, H. Zhou and D. Pamucar, Location optimization of CR express international logistics centers, Symmetry, 12 (2020), 143.
doi: 10.3390/sym12010143. |
| [31] |
M. E. O'Kelly,
The location of interacting hub facilities, Transportation Science, 20 (1986), 92-106.
|
| [32] |
X. Pan, L. Ning and L. Shi,
Visualisation and determinations of hub locations: Evidence from China's interregional trade network, Research in Transportation Economics, 75 (2019), 36-44.
|
| [33] |
P. Peng, Y. Yang, F. Lu, S. Cheng, N. Mou and R. Yang,
Modelling the competitiveness of the ports along the Maritime Silk Road with big data, Transportation Research Part A: Policy and Practice, 118 (2018), 852-867.
doi: 10.1016/j.tra.2018.10.041. |
| [34] |
H. Quan, S. Li, H. Wei and J. Hu, Personalized product evaluation based on GRA-TOPSIS and Kansei engineering, Symmetry, 11 (2019), 867.
doi: 10.3390/sym11070867. |
| [35] |
C. Rao, M. Goh, Y. Zhao and J. Zheng,
Location selection of city logistics centers under sustainability, Transportation Research Part D: Transport and Environment, 36 (2015), 29-44.
doi: 10.1016/j.trd.2015.02.008. |
| [36] |
C. Salavati, A. Abdollahpouri and Z. Manbari,
Ranking nodes in complex networks based on local structure and improving closeness centrality, Neurocomputing, 336 (2019), 36-45.
doi: 10.1016/j.neucom.2018.04.086. |
| [37] |
B. Sennaroglu and G. V. Celebi,
A military airport location selection by AHP integrated PROMETHEE and VIKOR methods, Transportation Research Part D: Transport and Environment, 59 (2018), 160-173.
doi: 10.1016/j.trd.2017.12.022. |
| [38] |
J. B. Sheu and T. Kundu,
Forecasting time-varying logistics distribution flows in the One Belt-One Road strategic context, Transportation Research Part E: Logistics and Transportation Review, 117 (2018), 5-22.
doi: 10.1016/j.tre.2017.03.003. |
| [39] |
W. Sun, L. Zhao, C. Wang, D. Li and J. Xue,
Selection of consolidation centres for China railway express, International Journal of Logistics Research and Applications, 23 (2020), 417-442.
doi: 10.1080/13675567.2019.1703917. |
| [40] |
A. Tversky and D. Kahneman,
Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.
|
| [41] |
Z. Y. Wang,
A method of multi-object decision-making based on maximum deviations and entropy, Journal of PLA University of Science and Technology, 3 (2002), 93-95.
|
| [42] |
W. Wu and Y. Peng,
Extension of grey relational analysis for facilitating group consensus to oil spill emergency management, Ann. Oper. Res., 238 (2016), 615-635.
doi: 10.1007/s10479-015-2067-2. |
| [43] |
X. Zhang, W. Zhang and P. T.-W. Lee,
Importance rankings of nodes in the China railway express network under the belt and road initiative, Transportation Research Part A: Policy and Practice, 139 (2020), 134-147.
|
| [44] |
L. Zhao, H. Li, M. Li, Y. Sun, Q. Hu, S. Mao, J. Li and J. Xue,
Location selection of intra-city distribution hubs in the metro-integrated logistics system, Tunnelling and Underground Space Technology, 80 (2018), 246-256.
doi: 10.1016/j.tust.2018.06.024. |
| [45] |
J. Zhou, Y. Wu, C. Wu, F. He, B. Zhang and F. Liu, A geographical information system based multi-criteria decision-making approach for location analysis and evaluation of urban photovoltaic charging station: A case study in Beijing, Energy Conversion and Management, 205 (2020), 112340.
doi: 10.1016/j.enconman.2019.112340. |
show all references
References:
| [1] |
R. P. Brooker and N. Qin,
Identification of potential locations of electric vehicle supply equipment, Journal of Power Sources, 299 (2015), 76-84.
doi: 10.1016/j.jpowsour.2015.08.097. |
| [2] |
J. W. K. Chan and T. K. L. Tong,
Multi-criteria material selections and end-of-life product strategy: Grey relational analysis approach, Materials & Design, 28 (2007), 1539-1546.
doi: 10.1016/j.matdes.2006.02.016. |
| [3] |
G. Chen, W. Cheung, S.-C. Chu and L. Xu,
Transshipment hub selection from a shipper's and freight forwarder's perspective, Expert Systems with Applications, 83 (2017), 396-404.
doi: 10.1016/j.eswa.2017.04.044. |
| [4] |
M.-F. Chen and G.-H. Tzeng,
Combining grey relation and TOPSIS concepts for selecting an expatriate host country, Mathematical and Computer Modelling, 40 (2004), 1473-1490.
doi: 10.1016/j.mcm.2005.01.006. |
| [5] |
S. K. Das, M. Pervin, S. K. Roy and G.-W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Annals of Operations Research, (2021).
doi: 10.1007/s10479-020-03809-z. |
| [6] |
S. K. Das and S. K. Roy,
Effect of variable carbon emission in a multiobjective transportation-p-facility location problem under neutrosophic environment, Computers & Industrial Engineering, 132 (2019), 311-324.
|
| [7] |
S. K. Das, S. K. Roy and G.-W. Weber,
Application of type-2 fuzzy logic to a multi-objective green solid transportation-location problem with dwell time under carbon tax, cap and offset policy: Fuzzy vs. non-fuzzy techniques, IEEE Transactions on Fuzzy Systems, 28 (2020), 2711-2725.
doi: 10.1109/TFUZZ.2020.3011745. |
| [8] |
S. K. Das, S. K. Roy and G.-W. Weber,
Heuristic approaches for solid transportation-$p$-facility location problem, CEJOR Cent. Eur. J. Oper. Res., 28 (2020), 939-961.
doi: 10.1007/s10100-019-00610-7. |
| [9] |
J. Deng,
Control problems of grey systems, Systems and Control Letters, 1 (1982), 288-294.
doi: 10.1016/S0167-6911(82)80025-X. |
| [10] |
J. Deng,
Introduction to grey theory system, J. Grey System, 1 (1989), 1-24.
|
| [11] |
B. Dey, B. Bairagi, B. Sarkar and S. K. Sanyal,
Group heterogeneity in multi member decision making model with an application to warehouse location selection in a supply chain, Computers & Industrial Engineering, 105 (2017), 101-122.
doi: 10.1016/j.cie.2016.12.025. |
| [12] |
I. Essaadi, B. Grabot and P. Féniès,
Location of global logistic hubs within Africa based on a fuzzy multi-criteria approach, Computers & Industrial Engineering, 132 (2019), 1-22.
doi: 10.1016/j.cie.2019.03.046. |
| [13] |
Y.-P. Hu, X.-Y. You, L. Wang and H.-C. Liu,
An integrated approach for failure mode and effect analysis based on uncertain linguistic GRA-TOPSIS method, Soft Computing, 23 (2019), 8801-8814.
doi: 10.1007/s00500-018-3480-7. |
| [14] |
Y. Jiang, J.-B. Sheu, Z. Peng and B. Yu,
Hinterland patterns of China Railway (CR) express in China under the Belt and road initiative: A preliminary analysis, Transportation Research Part E: Logistics and Transportation Review, 119 (2018), 189-201.
doi: 10.1016/j.tre.2018.10.002. |
| [15] |
S. Khalilpourazari and A. Arshadi Khamseh,
Bi-objective emergency blood supply chain network design in earthquake considering earthquake magnitude: A comprehensive study with real world application, Ann. Oper. Res., 283 (2019), 355-393.
doi: 10.1007/s10479-017-2588-y. |
| [16] |
S. Khalilpourazari, B. Naderi and S. Khalilpourazary,
Multi-objective stochastic fractal search: A powerful algorithm for solving complex multi-objective optimization problems, Soft Computing, 24 (2020), 3037-3066.
doi: 10.1007/s00500-019-04080-6. |
| [17] |
S. Khalilpourazari, S. Soltanzadeh, G.-W. Weber and S. K. Roy,
Designing an efficient blood supply chain network in crisis: Neural learning, optimization and case study, Ann. Oper. Res., 289 (2020), 123-152.
doi: 10.1007/s10479-019-03437-2. |
| [18] |
B. Kirubakaran and M. Ilangkumaran,
Selection of optimum maintenance strategy based on FAHP integrated with GRA-TOPSIS, Ann. Oper. Res., 245 (2016), 285-313.
doi: 10.1007/s10479-014-1775-3. |
| [19] |
X. Li, X. Li, X. Li and H. Qiu,
Multi-agent fare optimization model of two modes problem and its analysis based on edge of chaos, Phys. A, 469 (2017), 405-419.
doi: 10.1016/j.physa.2016.11.022. |
| [20] |
D. Li, L. Zhao, C. Wang, W. Sun and J. Xue,
Selection of China's imported grain distribution centers in the context of the belt and road initiative, Transportation Research Part E: Logistics and Transportation Review, 120 (2018), 16-34.
doi: 10.1016/j.tre.2018.10.007. |
| [21] |
Y.-H. Lin, P.-C. Lee and T.-P. Chang,
Practical expert diagnosis model based on the grey relational analysis technique, Expert Systems with Applications, 36 (2009), 1523-1528.
doi: 10.1016/j.eswa.2007.11.046. |
| [22] |
C.-C. Lin and S.-W. Lin,
Two-stage approach to the intermodal terminal location problem, Comput. Oper. Res., 67 (2016), 113-119.
doi: 10.1016/j.cor.2015.09.009. |
| [23] |
D. Liu, C. Liu, Q. Fu, T. Li, K. M. Imran, S. Cui and F. M. Abrar,
ELM evaluation model of regional groundwater quality based on the crow search algorithm, Ecological Indicators, 81 (2017), 302-314.
doi: 10.1016/j.ecolind.2017.06.009. |
| [24] |
D. Liu, X. Qi and Q. Fu,
A resilience evaluation method for a combined regional agricultural water and soil resource system based on Weighted Mahalanobis distance and a Gray-TOPSIS model, Journal of Cleaner Production, 229 (2019), 667-679.
doi: 10.1016/j.jclepro.2019.04.406. |
| [25] |
S. Liu, N. Xie and J. Forrest,
Novel models of grey relational analysis based on visual angle of similarity and nearness, Grey Systems: Theory and Application, 1 (2011), 8-18.
doi: 10.1108/20439371111106696. |
| [26] |
S. Long and S. E. Grasman,
A strategic decision model for evaluating inland freight hub locations, Research in Transportation Business & Management, 5 (2012), 92-98.
doi: 10.1016/j.rtbm.2012.11.004. |
| [27] |
M. Lu, Node importance evaluation based on neighborhood structure hole and improved TOPSIS, Computer Networks, 178 (2020), 107336.
doi: 10.1016/j.comnet.2020.107336. |
| [28] |
C. Ma, Y. Yang, J. Wang, Y. Chen and D. Yang,
Determining the location of a Swine farming facility based on grey correlation and the TOPSIS method, Transactions of the ASABE, 60 (2017), 1281-1289.
doi: 10.13031/trans.11968. |
| [29] |
H. Mokhtar, A. A. N. P. Redi, M. Krishnamoorthy and A. T. Ernst,
An intermodal hub location problem for container distribution in indonesia, Comput. Oper. Res., 104 (2019), 415-432.
doi: 10.1016/j.cor.2018.08.012. |
| [30] |
D. Muravev, H. Hu, H. Zhou and D. Pamucar, Location optimization of CR express international logistics centers, Symmetry, 12 (2020), 143.
doi: 10.3390/sym12010143. |
| [31] |
M. E. O'Kelly,
The location of interacting hub facilities, Transportation Science, 20 (1986), 92-106.
|
| [32] |
X. Pan, L. Ning and L. Shi,
Visualisation and determinations of hub locations: Evidence from China's interregional trade network, Research in Transportation Economics, 75 (2019), 36-44.
|
| [33] |
P. Peng, Y. Yang, F. Lu, S. Cheng, N. Mou and R. Yang,
Modelling the competitiveness of the ports along the Maritime Silk Road with big data, Transportation Research Part A: Policy and Practice, 118 (2018), 852-867.
doi: 10.1016/j.tra.2018.10.041. |
| [34] |
H. Quan, S. Li, H. Wei and J. Hu, Personalized product evaluation based on GRA-TOPSIS and Kansei engineering, Symmetry, 11 (2019), 867.
doi: 10.3390/sym11070867. |
| [35] |
C. Rao, M. Goh, Y. Zhao and J. Zheng,
Location selection of city logistics centers under sustainability, Transportation Research Part D: Transport and Environment, 36 (2015), 29-44.
doi: 10.1016/j.trd.2015.02.008. |
| [36] |
C. Salavati, A. Abdollahpouri and Z. Manbari,
Ranking nodes in complex networks based on local structure and improving closeness centrality, Neurocomputing, 336 (2019), 36-45.
doi: 10.1016/j.neucom.2018.04.086. |
| [37] |
B. Sennaroglu and G. V. Celebi,
A military airport location selection by AHP integrated PROMETHEE and VIKOR methods, Transportation Research Part D: Transport and Environment, 59 (2018), 160-173.
doi: 10.1016/j.trd.2017.12.022. |
| [38] |
J. B. Sheu and T. Kundu,
Forecasting time-varying logistics distribution flows in the One Belt-One Road strategic context, Transportation Research Part E: Logistics and Transportation Review, 117 (2018), 5-22.
doi: 10.1016/j.tre.2017.03.003. |
| [39] |
W. Sun, L. Zhao, C. Wang, D. Li and J. Xue,
Selection of consolidation centres for China railway express, International Journal of Logistics Research and Applications, 23 (2020), 417-442.
doi: 10.1080/13675567.2019.1703917. |
| [40] |
A. Tversky and D. Kahneman,
Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.
|
| [41] |
Z. Y. Wang,
A method of multi-object decision-making based on maximum deviations and entropy, Journal of PLA University of Science and Technology, 3 (2002), 93-95.
|
| [42] |
W. Wu and Y. Peng,
Extension of grey relational analysis for facilitating group consensus to oil spill emergency management, Ann. Oper. Res., 238 (2016), 615-635.
doi: 10.1007/s10479-015-2067-2. |
| [43] |
X. Zhang, W. Zhang and P. T.-W. Lee,
Importance rankings of nodes in the China railway express network under the belt and road initiative, Transportation Research Part A: Policy and Practice, 139 (2020), 134-147.
|
| [44] |
L. Zhao, H. Li, M. Li, Y. Sun, Q. Hu, S. Mao, J. Li and J. Xue,
Location selection of intra-city distribution hubs in the metro-integrated logistics system, Tunnelling and Underground Space Technology, 80 (2018), 246-256.
doi: 10.1016/j.tust.2018.06.024. |
| [45] |
J. Zhou, Y. Wu, C. Wu, F. He, B. Zhang and F. Liu, A geographical information system based multi-criteria decision-making approach for location analysis and evaluation of urban photovoltaic charging station: A case study in Beijing, Energy Conversion and Management, 205 (2020), 112340.
doi: 10.1016/j.enconman.2019.112340. |
Figure 2.
Location decision framework for CICMHs
Figure 3.
Transport networks in China
Figure 4.
Preliminary evaluation index system
Figure 5.
Final evaluation index system
Figure 6.
Results of the location evaluation of CICMHs
Figure 7.
Sensitivity analysis of the sub-criteria in logistics trade scale and service quality of hub stations
Figure 8.
Sensitivity analysis of the sub-criteria in transport location advantages
Figure 9.
Sensitivity analysis of the sub-criteria in socio-economic support
Figure 10.
Sensitivity analysis of the sub-criteria in urban infrastructure
Figure 11.
Sensitivity analysis of different $ \theta $
Figure 12.
Sensitivity analysis of the preference coefficient
Figure 13.
Scatter diagrams of evaluation values and serial numbers
Table 1.
Advantages and limitations of MCDM methods
| Methods | Advantages | Limitations |
| AHP | Flexible, concise, easy to calculate | Does not consider the interaction between indicators |
| TOPSIS | Can measure the proximity between alternative and ideal solutions | Cannot distinguish vertical line nodes in positive and negative ideal solutions |
| GRA | Can measure the similarity degree of curve shapes between sequences | Does not consider the closeness of the sequence and the directionality of the numerical value |
| ELECTRE | Applicable when incomparable substitutes exist | Needs many parameters defined by decision-makers, and the calculation process is cumbersome |
| PROMETHEE | Can avoid information loss by focusing on various properties of attributes | Fails to consider DMí »s risk aversion psychology |
| VIKOR | Considers the maximum benefit of the group and minimum regret of the individual | The evaluation of uncertainty factors is unsatisfactory |
| TODIM | Can reflect DMí»s evasion of losses and risk psychology | Regression coefficient is not clearly defined, and evaluation results vary with the DMs |
| DEMATEL | Can avoid consistency errors due to too many comparison times | Cannot reflect the fuzziness of decision information and the subjectivity of DMs |
| BWM | Can reduce the number of comparisons and provide comparisons with consistency, leading to reliable results | Needs to be scored by experts with certain subjectivity; DMsí» confidence in their comparisons is not considered |
| Methods | Advantages | Limitations |
| AHP | Flexible, concise, easy to calculate | Does not consider the interaction between indicators |
| TOPSIS | Can measure the proximity between alternative and ideal solutions | Cannot distinguish vertical line nodes in positive and negative ideal solutions |
| GRA | Can measure the similarity degree of curve shapes between sequences | Does not consider the closeness of the sequence and the directionality of the numerical value |
| ELECTRE | Applicable when incomparable substitutes exist | Needs many parameters defined by decision-makers, and the calculation process is cumbersome |
| PROMETHEE | Can avoid information loss by focusing on various properties of attributes | Fails to consider DMí »s risk aversion psychology |
| VIKOR | Considers the maximum benefit of the group and minimum regret of the individual | The evaluation of uncertainty factors is unsatisfactory |
| TODIM | Can reflect DMí»s evasion of losses and risk psychology | Regression coefficient is not clearly defined, and evaluation results vary with the DMs |
| DEMATEL | Can avoid consistency errors due to too many comparison times | Cannot reflect the fuzziness of decision information and the subjectivity of DMs |
| BWM | Can reduce the number of comparisons and provide comparisons with consistency, leading to reliable results | Needs to be scored by experts with certain subjectivity; DMsí» confidence in their comparisons is not considered |
Table 2.
Weight of the evaluation index
| Index | A1 | A2 | A3 | A4 | A5 | B1 | B2 | B3 | C1 | C2 | C3 | D1 | D2 |
| Weight | 0.0888 | 0.1615 | 0.1163 | 0.0998 | 0.0554 | 0.03 | 0.1037 | 0.0237 | 0.1163 | 0.0349 | 0.0348 | 0.0701 | 0.0647 |
| Index | A1 | A2 | A3 | A4 | A5 | B1 | B2 | B3 | C1 | C2 | C3 | D1 | D2 |
| Weight | 0.0888 | 0.1615 | 0.1163 | 0.0998 | 0.0554 | 0.03 | 0.1037 | 0.0237 | 0.1163 | 0.0349 | 0.0348 | 0.0701 | 0.0647 |
Table 3.
Weight of the evaluation index
| Node | Ranking | |||||
| Chongqing | 0.0681 | 1.0000 | 1.0000 | 0.8495 | 0.6855 | 1 |
| Chengdu | 0.3259 | 0.7244 | 0.9498 | 0.8952 | 0.5783 | 5 |
| Zhengzhou | 0.3362 | 0.5597 | 0.9166 | 0.9241 | 0.5395 | 9 |
| Xi'an | 0.3269 | 0.6633 | 0.9347 | 0.9069 | 0.5643 | 6 |
| Suzhou | 0.55 | 0.6076 | 0.9219 | 0.9297 | 0.5083 | 13 |
| Wuhan | 0.1838 | 0.6908 | 0.9257 | 0.9024 | 0.5981 | 4 |
| Changsha | 0.3888 | 0.4129 | 0.888 | 0.9572 | 0.4915 | 14 |
| Hefei | 0.5098 | 0.4152 | 0.8817 | 0.9553 | 0.4696 | 18 |
| Lanzhou | 0.3519 | 0.3349 | 0.8713 | 0.9851 | 0.4743 | 17 |
| Shenyang | 1.0000 | 0.2845 | 0.858 | 1.0000 | 0.3636 | 22 |
| Harbin | 0.6944 | 0.3196 | 0.8673 | 0.9899 | 0.4134 | 21 |
| Nanjing | 0.2759 | 0.5634 | 0.9055 | 0.9244 | 0.5503 | 7 |
| Hangzhou | 0.43 | 0.5315 | 0.9036 | 0.9367 | 0.5122 | 11 |
| Nanning | 0.6054 | 0.3407 | 0.8685 | 0.9785 | 0.4329 | 20 |
| Urumqi | 0.5853 | 0.3767 | 0.8791 | 0.993 | 0.4431 | 19 |
| Shanghai | 0.2839 | 0.8857 | 0.9707 | 0.8955 | 0.6115 | 3 |
| Ningbo | 0.3697 | 0.4831 | 0.8877 | 0.9444 | 0.5106 | 12 |
| Guangzhou | 0.2633 | 0.883 | 0.9686 | 0.8883 | 0.6166 | 2 |
| Tianjin | 0.3155 | 0.5932 | 0.9154 | 0.9222 | 0.5493 | 8 |
| Qingdao | 0.4115 | 0.4219 | 0.8826 | 0.9526 | 0.4888 | 15 |
| Dalian | 0.4104 | 0.545 | 0.896 | 0.9515 | 0.5141 | 10 |
| Xiamen | 0.4029 | 0.3858 | 0.8699 | 0.9767 | 0.4765 | 16 |
| Node | Ranking | |||||
| Chongqing | 0.0681 | 1.0000 | 1.0000 | 0.8495 | 0.6855 | 1 |
| Chengdu | 0.3259 | 0.7244 | 0.9498 | 0.8952 | 0.5783 | 5 |
| Zhengzhou | 0.3362 | 0.5597 | 0.9166 | 0.9241 | 0.5395 | 9 |
| Xi'an | 0.3269 | 0.6633 | 0.9347 | 0.9069 | 0.5643 | 6 |
| Suzhou | 0.55 | 0.6076 | 0.9219 | 0.9297 | 0.5083 | 13 |
| Wuhan | 0.1838 | 0.6908 | 0.9257 | 0.9024 | 0.5981 | 4 |
| Changsha | 0.3888 | 0.4129 | 0.888 | 0.9572 | 0.4915 | 14 |
| Hefei | 0.5098 | 0.4152 | 0.8817 | 0.9553 | 0.4696 | 18 |
| Lanzhou | 0.3519 | 0.3349 | 0.8713 | 0.9851 | 0.4743 | 17 |
| Shenyang | 1.0000 | 0.2845 | 0.858 | 1.0000 | 0.3636 | 22 |
| Harbin | 0.6944 | 0.3196 | 0.8673 | 0.9899 | 0.4134 | 21 |
| Nanjing | 0.2759 | 0.5634 | 0.9055 | 0.9244 | 0.5503 | 7 |
| Hangzhou | 0.43 | 0.5315 | 0.9036 | 0.9367 | 0.5122 | 11 |
| Nanning | 0.6054 | 0.3407 | 0.8685 | 0.9785 | 0.4329 | 20 |
| Urumqi | 0.5853 | 0.3767 | 0.8791 | 0.993 | 0.4431 | 19 |
| Shanghai | 0.2839 | 0.8857 | 0.9707 | 0.8955 | 0.6115 | 3 |
| Ningbo | 0.3697 | 0.4831 | 0.8877 | 0.9444 | 0.5106 | 12 |
| Guangzhou | 0.2633 | 0.883 | 0.9686 | 0.8883 | 0.6166 | 2 |
| Tianjin | 0.3155 | 0.5932 | 0.9154 | 0.9222 | 0.5493 | 8 |
| Qingdao | 0.4115 | 0.4219 | 0.8826 | 0.9526 | 0.4888 | 15 |
| Dalian | 0.4104 | 0.545 | 0.896 | 0.9515 | 0.5141 | 10 |
| Xiamen | 0.4029 | 0.3858 | 0.8699 | 0.9767 | 0.4765 | 16 |
Table 4.
Ranking orders with different $ \theta $
| L0 | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | Ranking | |
| 1 | 0.6865 | 0.5813 | 0.5441 | 0.5677 | 0.6011 | 0.5544 | 0.6096 | 0.6152 | 0.5529 | 0.5143 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 1.5 | 0.6861 | 0.5801 | 0.5423 | 0.5664 | 0.5999 | 0.5529 | 0.6103 | 0.6157 | 0.5515 | 0.5141 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2 | 0.6857 | 0.5789 | 0.5405 | 0.565 | 0.5987 | 0.5512 | 0.6111 | 0.6162 | 0.5501 | 0.514 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2.25 | 0.6855 | 0.5783 | 0.5395 | 0.5643 | 0.5981 | 0.5503 | 0.6115 | 0.6166 | 0.5493 | 0.5141 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2.5 | 0.6853 | 0.5776 | 0.5384 | 0.5636 | 0.5975 | 0.5494 | 0.612 | 0.6169 | 0.5485 | 0.5142 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 3 | 0.6847 | 0.5761 | 0.5363 | 0.562 | 0.5961 | 0.5475 | 0.6132 | 0.6178 | 0.5469 | 0.5146 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 3.5 | 0.6842 | 0.5746 | 0.534 | 0.5603 | 0.5946 | 0.5455 | 0.6146 | 0.6189 | 0.5451 | 0.5154 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 4 | 0.6835 | 0.5729 | 0.5316 | 0.5584 | 0.593 | 0.5432 | 0.6163 | 0.6204 | 0.5432 | 0.5168 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| L0 | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | Ranking | |
| 1 | 0.6865 | 0.5813 | 0.5441 | 0.5677 | 0.6011 | 0.5544 | 0.6096 | 0.6152 | 0.5529 | 0.5143 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 1.5 | 0.6861 | 0.5801 | 0.5423 | 0.5664 | 0.5999 | 0.5529 | 0.6103 | 0.6157 | 0.5515 | 0.5141 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2 | 0.6857 | 0.5789 | 0.5405 | 0.565 | 0.5987 | 0.5512 | 0.6111 | 0.6162 | 0.5501 | 0.514 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2.25 | 0.6855 | 0.5783 | 0.5395 | 0.5643 | 0.5981 | 0.5503 | 0.6115 | 0.6166 | 0.5493 | 0.5141 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 2.5 | 0.6853 | 0.5776 | 0.5384 | 0.5636 | 0.5975 | 0.5494 | 0.612 | 0.6169 | 0.5485 | 0.5142 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 3 | 0.6847 | 0.5761 | 0.5363 | 0.562 | 0.5961 | 0.5475 | 0.6132 | 0.6178 | 0.5469 | 0.5146 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 3.5 | 0.6842 | 0.5746 | 0.534 | 0.5603 | 0.5946 | 0.5455 | 0.6146 | 0.6189 | 0.5451 | 0.5154 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
| 4 | 0.6835 | 0.5729 | 0.5316 | 0.5584 | 0.593 | 0.5432 | 0.6163 | 0.6204 | 0.5432 | 0.5168 | L0>L7>L6>L4>L1>L3>L5>L8>L2>L9 |
Table 5.
Ranking results for different methods
| Cities | TOPSIS | TODIM | GRA-TOPSIS | eGRA-TOPSIS | ||||
| Value | Ranking | Value | Ranking | Value | Ranking | Value | Ranking | |
| Chongqing | 0.6877 | 1 | 0.5801 | 1 | 0.6278 | 1 | 0.6855 | 1 |
| Chengdu | 0.5324 | 4 | 0.5102 | 6 | 0.5111 | 5 | 0.5783 | 5 |
| Zhengzhou | 0.3927 | 10 | 0.4978 | 7 | 0.4512 | 10 | 0.5395 | 9 |
| Xi'an | 0.4621 | 6 | 0.5154 | 5 | 0.4913 | 6 | 0.5643 | 6 |
| Wuhan | 0.4906 | 5 | 0.5195 | 4 | 0.5147 | 4 | 0.5981 | 4 |
| Nanjing | 0.415 | 8 | 0.4858 | 9 | 0.457 | 9 | 0.5503 | 7 |
| Shanghai | 0.6169 | 3 | 0.5382 | 3 | 0.5875 | 3 | 0.6115 | 3 |
| Guangzhou | 0.6415 | 2 | 0.5411 | 2 | 0.5967 | 2 | 0.6166 | 2 |
| Tianjin | 0.4366 | 7 | 0.4959 | 8 | 0.4696 | 7 | 0.5493 | 8 |
| Dalian | 0.4058 | 9 | 0.4676 | 10 | 0.466 | 8 | 0.5141 | 10 |
| Cities | TOPSIS | TODIM | GRA-TOPSIS | eGRA-TOPSIS | ||||
| Value | Ranking | Value | Ranking | Value | Ranking | Value | Ranking | |
| Chongqing | 0.6877 | 1 | 0.5801 | 1 | 0.6278 | 1 | 0.6855 | 1 |
| Chengdu | 0.5324 | 4 | 0.5102 | 6 | 0.5111 | 5 | 0.5783 | 5 |
| Zhengzhou | 0.3927 | 10 | 0.4978 | 7 | 0.4512 | 10 | 0.5395 | 9 |
| Xi'an | 0.4621 | 6 | 0.5154 | 5 | 0.4913 | 6 | 0.5643 | 6 |
| Wuhan | 0.4906 | 5 | 0.5195 | 4 | 0.5147 | 4 | 0.5981 | 4 |
| Nanjing | 0.415 | 8 | 0.4858 | 9 | 0.457 | 9 | 0.5503 | 7 |
| Shanghai | 0.6169 | 3 | 0.5382 | 3 | 0.5875 | 3 | 0.6115 | 3 |
| Guangzhou | 0.6415 | 2 | 0.5411 | 2 | 0.5967 | 2 | 0.6166 | 2 |
| Tianjin | 0.4366 | 7 | 0.4959 | 8 | 0.4696 | 7 | 0.5493 | 8 |
| Dalian | 0.4058 | 9 | 0.4676 | 10 | 0.466 | 8 | 0.5141 | 10 |
Table 6.
Weight of the evaluation index
| Method | TOPSIS | TODIM | GRA-TOPSIS | eGRA-TOPSIS |
| Discrimination | 1.0422 | 1.0775 | 1.0922 | 1.0817 |
| Method | TOPSIS | TODIM | GRA-TOPSIS | eGRA-TOPSIS |
| Discrimination | 1.0422 | 1.0775 | 1.0922 | 1.0817 |
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