American Institute of Mathematical Sciences

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doi: 10.3934/jimo.2021061
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Decision framework for location and selection of container multimodal hubs: A case in china under the belt and road initiative

Xinfang Zhang , Jing Lu , and  Yan Peng

College of Transportation Engineering, Dalian Maritime University, Dalian 116026, China

* Corresponding author: Jing Lu

Received  October 2020 Revised  January 2021 Early access March 2021

Fund Project: The first author is supported by National Natural Science Foundation grant No.71473023, National Social Science Fund of China grant No.19VHQ012 and No.18VHQ005, Fundamental Research Funds for the Central Universities grant No.3132019159, Ministry of Education Foundation of Humanities and Social Science grant No.16YJAZH030

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 & Management Optimization, doi: 10.3934/jimo.2021061
References:
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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.  Google Scholar

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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.  Google Scholar

[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.  Google Scholar

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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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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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.  Google Scholar

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M. E. O'Kelly, The location of interacting hub facilities, Transportation Science, 20 (1986), 92-106.   Google Scholar

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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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[40]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

J. Deng, Control problems of grey systems, Systems and Control Letters, 1 (1982), 288-294.  doi: 10.1016/S0167-6911(82)80025-X.  Google Scholar

[10]

J. Deng, Introduction to grey theory system, J. Grey System, 1 (1989), 1-24.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[31]

M. E. O'Kelly, The location of interacting hub facilities, Transportation Science, 20 (1986), 92-106.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[40]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

Figure 1.  Value function
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Figure 2.  Location decision framework for CICMHs
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Figure 3.  Transport networks in China
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Figure 4.  Preliminary evaluation index system
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Figure 5.  Final evaluation index system
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Figure 6.  Results of the location evaluation of CICMHs
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Figure 7.  Sensitivity analysis of the sub-criteria in logistics trade scale and service quality of hub stations
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Figure 8.  Sensitivity analysis of the sub-criteria in transport location advantages
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Figure 9.  Sensitivity analysis of the sub-criteria in socio-economic support
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Figure 10.  Sensitivity analysis of the sub-criteria in urban infrastructure
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Figure 11.  Sensitivity analysis of different $ \theta $
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Figure 12.  Sensitivity analysis of the preference coefficient
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Figure 13.  Scatter diagrams of evaluation values and serial numbers
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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
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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
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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 $ D_i^+ $ $ D_i^- $ $ Q_i^+ $ $ Q_i^- $ $ C_i $ 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
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Node $ D_i^+ $ $ D_i^- $ $ Q_i^+ $ $ Q_i^- $ $ C_i $ 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 $
$ \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
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$ \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
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
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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
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Method TOPSIS TODIM GRA-TOPSIS eGRA-TOPSIS
Discrimination 1.0422 1.0775 1.0922 1.0817
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