American Institute of Mathematical Sciences

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doi: 10.3934/jimo.2021179
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Multi-objective optimization model for planning metro-based underground logistics system network: Nanjing case study

Xiliang Sun 1,, , Wanjie Hu 2,, , Xiaolong Xue 3, and  Jianjun Dong 4,

1. 

School of Management, Harbin Institute of Technology, Harbin 150001, China
2. 

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
3. 

School of Management, Harbin Institute of Technology, Harbin 150001, China
4. 

College of Civil Engineering, Nanjing Tech University, Nanjing 211800, China

* Corresponding authors: Xiliang Sun and Wanjie Hu

Received  April 2021 Revised  August 2021 Early access October 2021

Utilizing rail transit system for collaborative passenger-and-freight transport is a sustainable option to conquer urban congestion. This study proposes effective modeling and optimization techniques for planning a city-wide metro-based underground logistics system (M-ULS) network. Firstly, a novel metro prototype integrating retrofitted underground stations and newly-built capsule pipelines is designed to support automated inbound delivery from urban logistics gateways to in-city destinations. Based on four indicators (i.e. unity of freight flows, regional accessibility, environmental cost-saving, and order priority), an entropy-based fuzzy TOPSIS evaluation model is proposed to select appropriate origin-destination flows for underground freight transport. Then, a mixed integer programming model, with a well-matched solution framework combining multi-objective PSO algorithm and A* algorithm, are developed to optimize the location-allocation-routing (LAR) decisions of M-ULS network. Finally, real-world simulation based on Nanjing metro case is conducted for validation. The best facility configurations and flow assignments of the three-tier M-ULS network are reported in details. Results confirm that the proposed algorithm has good ability in providing high-quality Pareto-optimal LAR decisions. Moreover, the Nanjing M-ULS project shows strong economic feasibility while bringing millions of Yuan of annual external benefit to the society and environment.

Keywords: Urban freight transport, underground logistics system (ULS), rail transit, network design, location-routing problem, multi-objective optimization, case study.
Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 90C27.
Citation: Xiliang Sun, Wanjie Hu, Xiaolong Xue, Jianjun Dong. Multi-objective optimization model for planning metro-based underground logistics system network: Nanjing case study. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021179
References:
[1]

A. B. Arabani, M. Zandieh and S. M. T. F. Ghomi, Multi-objective genetic-based algorithms for a cross-docking scheduling problem, Applied Soft Computing, 11 (2011), 4954-4970.  doi: 10.1016/j.asoc.2011.06.004.  Google Scholar

[2]

W. Behiri, S. Belmokhtar-Berraf and C. Chu, Urban freight transport using passenger rail network: Scientific issues and quantitative analysis, Transportation Research Part E: Logistics and Transportation Review, 115 (2018), 227-245.  doi: 10.1016/j.tre.2018.05.002.  Google Scholar

[3]

C. Cleophas, C. Cottrill, J. F. Ehmke and K. Tierney, Collaborative urban transportation: Recent advances in theory and practice, European J. Oper. Res., 273 (2019), 801-816.  doi: 10.1016/j.ejor.2018.04.037.  Google Scholar

[4]

P. Chen, Effects of normalization on the entropy-based TOPSIS method, Expert Systems with Applications, 136 (2019), 33-41.  doi: 10.1016/j.eswa.2019.06.035.  Google Scholar

[5]

J. Cui, J. Dodson and P. V. Hall, Planning for urban freight transport: An overview, Transport Reviews, 35, (2015), 583–598. doi: 10.1080/01441647.2015.1038666.  Google Scholar

[6]

N. Coulombel, L. Dablanc, M. Gardrat and M. Koning, The environmental social cost of urban road freight: Evidence from the Paris region, Transportation Research Part D: Transport and Environment, 63, (2018), 514–532. doi: 10.1016/j.trd.2018.06.002.  Google Scholar

[7]

Z. Chen, J. Dong and R. Ren, Urban underground logistics system in China: Opportunities or challenges?, Underground Space, 2 (2017), 195-208.  doi: 10.1016/j.undsp.2017.08.002.  Google Scholar

[8]

J. Dong, Y. Xu, B. Hwang, R. Ren and Z. Chen, The impact of underground logistics system on urban sustainable development: A system dynamics approach, Sustainability, 11 (2019), 1223.  doi: 10.3390/su11051223.  Google Scholar

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J. Dong, W. Hu, S. Yan, R. Ren and X. Zhao, Network planning method for capacitated metro-based underground logistics system, Advances in Civil Engineering, 2018 (2018), Article ID 6958086. doi: 10.1155/2018/6958086.  Google Scholar

[10]

A. Dampier and M. Marinov, A study of the feasibility and potential implementation of metro-based freight transportation in newcastle upon tyne, Urban Rail Transit, 1 (2015), 164-182.  doi: 10.1007/s40864-015-0024-7.  Google Scholar

[11]

L, Dablanc, Freight Transport for Development Toolkit: Urban Freight, The World Bank, Washington, DC. 2009 Google Scholar

[12]

A. Devari, A. G. Nikolaev and Q, He, Crowdsourcing the last mile delivery of online orders by exploiting the social networks of retail store customers, Transportation Research. Part E, Logistics and Transportation Review, 105, (2017), 105–122. doi: 10.1016/j.tre.2017.06.011.  Google Scholar

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O. N. Egbunike and A. T. Potter, Are freight pipelines a pipe dream? A critical review of the UK and European perspective, J. Transport Geography, 19 (2021), 499-508.  doi: 10.1016/j.jtrangeo.2010.05.004.  Google Scholar

[14]

K. Govindan, M. Fattahi and E. Keyvanshokooh, Supply chain network design under uncertainty: A comprehensive review and future research directions, European J. Oper. Res., 263 (2017), 108-141.  doi: 10.1016/j.ejor.2017.04.009.  Google Scholar

[15]

W. Hu, J. Dong, B. Hwang, R. Ren and Z. Chen, A preliminary prototyping approach for emerging metro-based underground logistics systems: Operation mechanism and facility layout, International J. Production Research, 19 (2020), 1-21.  doi: 10.1080/00207543.2020.1844333.  Google Scholar

[16]

C. L. Hwang and K. Yoon, Methods for multiple attribute decision making, In Multiple Attribute Decision Making, Springer, Berlin, Heidelberg, (1981), 58–191. Google Scholar

[17]

W. Hu, J. Dong, B. Hwang, R. Ren, Y. Chen and Z. Chen, Using system dynamics to analyze the development of urban freight transportation system based on rail transit: A case study of Beijing, Sustainable Cities and Society, 53 (2020), 101923.  doi: 10.1016/j.scs.2019.101923.  Google Scholar

[18]

P. E. Hart, N. J. Nilsson and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Transactions on Systems Science and Cybernetics, 4 (1968), 100-107.  doi: 10.1109/TSSC.1968.300136.  Google Scholar

[19]

T. Howgego and M. Roe, The use of pipelines for the urban distribution of goods, Transport Policy, 5 (1998), 61-72.  doi: 10.1016/S0967-070X(98)00012-2.  Google Scholar

[20]

J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95-International Conference on Neural Networks, 4 (1995), 1942-1948.  doi: 10.1109/ICNN.1995.488968.  Google Scholar

[21]

M. Mokhtarzadeh, R. Tavakkoli-Moghaddam, C. Triki and Y. Rahimi, A hybrid of clustering and meta-heuristic algorithms to solve a p-mobile hub location-allocation problem with the depreciation cost of hub facilities, Engineering Applications of Artificial Intelligence, 98 (2021), 104121.  doi: 10.1016/j.engappai.2020.104121.  Google Scholar

[22]

A. Memari, A. R. A. Rahim, N. Absi, R. Ahmad and A. Hassan, Carbon-capped distribution planning: A JIT perspective, Computers & Industrial Engineering, 97 (2016), 111-127.  doi: 10.1016/j.cie.2016.04.015.  Google Scholar

[23]

M. Najafi, S. Ardekani and S. M. Shahandashti, Integrating Underground Freight Transportation into Existing Intermodal Systems, 2016. Available from: https://library.ctr.utexas.edu/hostedpdfs/uta/0-6870-1.pdf. Google Scholar

[24]

G. Nagy and S. Salhi, Location-routing: Issues, models and methods, European J. Oper. Res., 177 (2007), 649-672.  doi: 10.1016/j.ejor.2006.04.004.  Google Scholar

[25]

D. Paddeu and G. Parkhurst, The potential for automation to transform urban deliveries: Drivers, barriers and policy priorities, Advances in Transport Policy and Planning, 5, (2020), 291–314. doi: 10.1016/bs.atpp.2020.01.003.  Google Scholar

[26]

P. Potti and M. Marinov, Evaluation of actual timetables and utilization levels of west midlands metro using event-based simulations, Urban Rail Transit, 6 (2020), 28-41.  doi: 10.1007/s40864-019-00120-4.  Google Scholar

[27]

H. Quak, N. Nesterova and T. van Rooijen, Possibilities and barriers for using electric-powered vehicles in city logistics practice, Transportation Research Procedia, 12, (2016), 157–169. doi: 10.1016/j.trpro.2016.02.055.  Google Scholar

[28]

M. Strale, The Cargo Tram: Current Status and Perspectives, the Example of Brussels, Sustainable Logistics, Emerald Group Publishing Limited, 2014. doi: 10.1108/S2044-994120140000006010.  Google Scholar

[29]

E. Taniguchi and R. G. Thompson, City logistics 3: Towards Sustainable and Liveable Cities, John Wiley & Sons, 2018. doi: 10.1002/9781119425472.  Google Scholar

[30]

J. G. S. N. Visser, The development of underground freight transport: An overview, Tunnelling and Underground Space Technology, 80 (2018), 123-127.  doi: 10.1016/j.tust.2018.06.006.  Google Scholar

[31]

Y. Wang, S. Zhang, X. Guan, S. Peng, H. Wang, Y. Liu and M. Xu, Collaborative multi-depot logistics network design with time window assignment, Expert Systems with Applications, 140 (2020), 112910.  doi: 10.1016/j.eswa.2019.112910.  Google Scholar

[32]

C. Zheng, X. Zhao and J. Shen, Research on Location Optimization of Metro-Based Underground Logistics System With Voronoi Diagram, IEEE Access, 8 (2020), 34407-34417.  doi: 10.1109/ACCESS.2020.2974497.  Google Scholar

[33]

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

[34]

China Federation of Logistics and Purchasing, National Logistics Operation Status Report, 2019. Available from: http://www.chinawuliu.com.cn/lhhzq/202004/20/499790.shtml. Google Scholar

[35]

European Commission, EU transport in figures. Statistical pocketbook, 2015. Available from: https://ec.europa.eu/transport/sites/transport/files/pocketbook2015.pdf. Google Scholar

[36]

Cargo Sous Terrain, 2021. Available from: https://www.cst.ch. Google Scholar

[37]

DP World CargoSpeed with Virgin Hyperloop One, 2021. Available from: https://www.dpworld.com/smart-trade/cargospeed. Google Scholar

[38]

Nanjing Municipal Postal Administration, Annual Report of Nanjing Urban Traffic, 2019. Available from: http://jsnj.spb.gov.cn/xytj_3323/tjxx/202005/t20200527_2248042.html. Google Scholar

show all references

References:
[1]

A. B. Arabani, M. Zandieh and S. M. T. F. Ghomi, Multi-objective genetic-based algorithms for a cross-docking scheduling problem, Applied Soft Computing, 11 (2011), 4954-4970.  doi: 10.1016/j.asoc.2011.06.004.  Google Scholar

[2]

W. Behiri, S. Belmokhtar-Berraf and C. Chu, Urban freight transport using passenger rail network: Scientific issues and quantitative analysis, Transportation Research Part E: Logistics and Transportation Review, 115 (2018), 227-245.  doi: 10.1016/j.tre.2018.05.002.  Google Scholar

[3]

C. Cleophas, C. Cottrill, J. F. Ehmke and K. Tierney, Collaborative urban transportation: Recent advances in theory and practice, European J. Oper. Res., 273 (2019), 801-816.  doi: 10.1016/j.ejor.2018.04.037.  Google Scholar

[4]

P. Chen, Effects of normalization on the entropy-based TOPSIS method, Expert Systems with Applications, 136 (2019), 33-41.  doi: 10.1016/j.eswa.2019.06.035.  Google Scholar

[5]

J. Cui, J. Dodson and P. V. Hall, Planning for urban freight transport: An overview, Transport Reviews, 35, (2015), 583–598. doi: 10.1080/01441647.2015.1038666.  Google Scholar

[6]

N. Coulombel, L. Dablanc, M. Gardrat and M. Koning, The environmental social cost of urban road freight: Evidence from the Paris region, Transportation Research Part D: Transport and Environment, 63, (2018), 514–532. doi: 10.1016/j.trd.2018.06.002.  Google Scholar

[7]

Z. Chen, J. Dong and R. Ren, Urban underground logistics system in China: Opportunities or challenges?, Underground Space, 2 (2017), 195-208.  doi: 10.1016/j.undsp.2017.08.002.  Google Scholar

[8]

J. Dong, Y. Xu, B. Hwang, R. Ren and Z. Chen, The impact of underground logistics system on urban sustainable development: A system dynamics approach, Sustainability, 11 (2019), 1223.  doi: 10.3390/su11051223.  Google Scholar

[9]

J. Dong, W. Hu, S. Yan, R. Ren and X. Zhao, Network planning method for capacitated metro-based underground logistics system, Advances in Civil Engineering, 2018 (2018), Article ID 6958086. doi: 10.1155/2018/6958086.  Google Scholar

[10]

A. Dampier and M. Marinov, A study of the feasibility and potential implementation of metro-based freight transportation in newcastle upon tyne, Urban Rail Transit, 1 (2015), 164-182.  doi: 10.1007/s40864-015-0024-7.  Google Scholar

[11]

L, Dablanc, Freight Transport for Development Toolkit: Urban Freight, The World Bank, Washington, DC. 2009 Google Scholar

[12]

A. Devari, A. G. Nikolaev and Q, He, Crowdsourcing the last mile delivery of online orders by exploiting the social networks of retail store customers, Transportation Research. Part E, Logistics and Transportation Review, 105, (2017), 105–122. doi: 10.1016/j.tre.2017.06.011.  Google Scholar

[13]

O. N. Egbunike and A. T. Potter, Are freight pipelines a pipe dream? A critical review of the UK and European perspective, J. Transport Geography, 19 (2021), 499-508.  doi: 10.1016/j.jtrangeo.2010.05.004.  Google Scholar

[14]

K. Govindan, M. Fattahi and E. Keyvanshokooh, Supply chain network design under uncertainty: A comprehensive review and future research directions, European J. Oper. Res., 263 (2017), 108-141.  doi: 10.1016/j.ejor.2017.04.009.  Google Scholar

[15]

W. Hu, J. Dong, B. Hwang, R. Ren and Z. Chen, A preliminary prototyping approach for emerging metro-based underground logistics systems: Operation mechanism and facility layout, International J. Production Research, 19 (2020), 1-21.  doi: 10.1080/00207543.2020.1844333.  Google Scholar

[16]

C. L. Hwang and K. Yoon, Methods for multiple attribute decision making, In Multiple Attribute Decision Making, Springer, Berlin, Heidelberg, (1981), 58–191. Google Scholar

[17]

W. Hu, J. Dong, B. Hwang, R. Ren, Y. Chen and Z. Chen, Using system dynamics to analyze the development of urban freight transportation system based on rail transit: A case study of Beijing, Sustainable Cities and Society, 53 (2020), 101923.  doi: 10.1016/j.scs.2019.101923.  Google Scholar

[18]

P. E. Hart, N. J. Nilsson and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Transactions on Systems Science and Cybernetics, 4 (1968), 100-107.  doi: 10.1109/TSSC.1968.300136.  Google Scholar

[19]

T. Howgego and M. Roe, The use of pipelines for the urban distribution of goods, Transport Policy, 5 (1998), 61-72.  doi: 10.1016/S0967-070X(98)00012-2.  Google Scholar

[20]

J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95-International Conference on Neural Networks, 4 (1995), 1942-1948.  doi: 10.1109/ICNN.1995.488968.  Google Scholar

[21]

M. Mokhtarzadeh, R. Tavakkoli-Moghaddam, C. Triki and Y. Rahimi, A hybrid of clustering and meta-heuristic algorithms to solve a p-mobile hub location-allocation problem with the depreciation cost of hub facilities, Engineering Applications of Artificial Intelligence, 98 (2021), 104121.  doi: 10.1016/j.engappai.2020.104121.  Google Scholar

[22]

A. Memari, A. R. A. Rahim, N. Absi, R. Ahmad and A. Hassan, Carbon-capped distribution planning: A JIT perspective, Computers & Industrial Engineering, 97 (2016), 111-127.  doi: 10.1016/j.cie.2016.04.015.  Google Scholar

[23]

M. Najafi, S. Ardekani and S. M. Shahandashti, Integrating Underground Freight Transportation into Existing Intermodal Systems, 2016. Available from: https://library.ctr.utexas.edu/hostedpdfs/uta/0-6870-1.pdf. Google Scholar

[24]

G. Nagy and S. Salhi, Location-routing: Issues, models and methods, European J. Oper. Res., 177 (2007), 649-672.  doi: 10.1016/j.ejor.2006.04.004.  Google Scholar

[25]

D. Paddeu and G. Parkhurst, The potential for automation to transform urban deliveries: Drivers, barriers and policy priorities, Advances in Transport Policy and Planning, 5, (2020), 291–314. doi: 10.1016/bs.atpp.2020.01.003.  Google Scholar

[26]

P. Potti and M. Marinov, Evaluation of actual timetables and utilization levels of west midlands metro using event-based simulations, Urban Rail Transit, 6 (2020), 28-41.  doi: 10.1007/s40864-019-00120-4.  Google Scholar

[27]

H. Quak, N. Nesterova and T. van Rooijen, Possibilities and barriers for using electric-powered vehicles in city logistics practice, Transportation Research Procedia, 12, (2016), 157–169. doi: 10.1016/j.trpro.2016.02.055.  Google Scholar

[28]

M. Strale, The Cargo Tram: Current Status and Perspectives, the Example of Brussels, Sustainable Logistics, Emerald Group Publishing Limited, 2014. doi: 10.1108/S2044-994120140000006010.  Google Scholar

[29]

E. Taniguchi and R. G. Thompson, City logistics 3: Towards Sustainable and Liveable Cities, John Wiley & Sons, 2018. doi: 10.1002/9781119425472.  Google Scholar

[30]

J. G. S. N. Visser, The development of underground freight transport: An overview, Tunnelling and Underground Space Technology, 80 (2018), 123-127.  doi: 10.1016/j.tust.2018.06.006.  Google Scholar

[31]

Y. Wang, S. Zhang, X. Guan, S. Peng, H. Wang, Y. Liu and M. Xu, Collaborative multi-depot logistics network design with time window assignment, Expert Systems with Applications, 140 (2020), 112910.  doi: 10.1016/j.eswa.2019.112910.  Google Scholar

[32]

C. Zheng, X. Zhao and J. Shen, Research on Location Optimization of Metro-Based Underground Logistics System With Voronoi Diagram, IEEE Access, 8 (2020), 34407-34417.  doi: 10.1109/ACCESS.2020.2974497.  Google Scholar

[33]

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

[34]

China Federation of Logistics and Purchasing, National Logistics Operation Status Report, 2019. Available from: http://www.chinawuliu.com.cn/lhhzq/202004/20/499790.shtml. Google Scholar

[35]

European Commission, EU transport in figures. Statistical pocketbook, 2015. Available from: https://ec.europa.eu/transport/sites/transport/files/pocketbook2015.pdf. Google Scholar

[36]

Cargo Sous Terrain, 2021. Available from: https://www.cst.ch. Google Scholar

[37]

DP World CargoSpeed with Virgin Hyperloop One, 2021. Available from: https://www.dpworld.com/smart-trade/cargospeed. Google Scholar

[38]

Nanjing Municipal Postal Administration, Annual Report of Nanjing Urban Traffic, 2019. Available from: http://jsnj.spb.gov.cn/xytj_3323/tjxx/202005/t20200527_2248042.html. Google Scholar

Figure 1.  Overview of the 3EM-ULSND problem
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Figure 2.  Overview of the 3EM-ULSND problem
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Figure 3.  Illustration of Pareto front in tri-objective optimization problem
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Figure 4.  Model decomposition and algorithmic flowchart
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Figure 5.  Pareto-optimal front obtained with MOPSO
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Figure 6.  Pareto-optimal front obtained with MOPSO
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Table 1.  Model parameters and values
Note Definition Attribute
Notation of indices
$ S $ set of LPWs, i.e., set of metro lines indexed by $ s $
$ M $ set of SCs, i.e., set of candidate location of UDs indexed by $ m $
$ N $ set of metro stations, i.e., set of candidate location of NFSs indexed by $ i $
$ L $ set of metro interchanges, i.e., set of activated IFSs indexed by $ j $
$ K $ set of metro line arcs between two adjacent metro stations indexed by $ k $
$ H $ set of arcs between metro stations and SCs indexed by $ h $
$ R $ set of arcs between two SCs indexed by $ r $
Exogenous parameters
$ g_m^s $ size of delivery orders from LPW $ s $ to SC $ m $ (original value) [0, 15] parcel per-day
$ d_m^s $ size of delivery orders from LPW $ s $ to SC $ m $ (after evaluated) –
$ c $ freight travel cost by LGV $ \yen $ 0.2 per-parcel per-km
$ \alpha $ ratio of the freight travel cost by metro to the freight travel cost by LGV 10%
$ \beta $ ratio of the freight travel cost by CPs to the freight travel cost by LGV 25%
$ w $ underground transfer cost at IFS $ \yen $0.1 per-parcel
$ {\lambda _1} $ fixed cost for CP construction $ \yen $4$ \times $$ 10^7 $ per-km
$ {\lambda _2} $ fixed cost for NFS retrofit $ \yen $1$ \times $$ 10^8 $
$ {\lambda _3} $ fixed cost for UD construction $ \yen $2$ \times $$ 10^7 $
$ {\eta _{NFS}} $ allowable level for low load operations at UD 60%
$ {\eta _{CP}} $ allowable level for low load operations at CP 50%
$ {\sigma _{NFS}} $ penalty cost due to low load operations of UD $ \yen $2 per-parcel
$ {\sigma _{CP}} $ penalty cost due to low load operations of CP $ \yen $1.5 per-parcel
$ [{R_{max}}] $ maximal road travel distance from UD to SC 2km
$ \left[ {{Q_{max}}} \right] $ order handling capacity of NFS 1$ \times $$ 10^5 $ parcel per-day
$ [{Z_{max}}] $ transport capacity of CP 4$ \times $$ 10^4 $ parcel per-day
$ [{G_{max}}] $ order handling capacity of UD 3.5$ \times $$ 10^4 $ parcel per-day
$ \left[ {{T_{max}}} \right] $ order transfer capacity of IFS 1.5$ \times $$ 10^6 $ parcel per-day
$ Eu $ Euclidean distance of arc $ k $, arc $ r $ and arc $ h $, respectively –
$ \theta $ depreciation coefficient of M-ULS network facilities 1/25550
Binary variables
$ {X_i} $ 1, if metro station $ i $ is selected as NFS
$ {\delta _{smj}} $ 1, if $ d_m^s $ is transferred at IFS $ j $
$ {Y_m} $ 1, if SC $ m $ is selected as UD
$ {W_h} $ 1, if arc $ h $ is selected as CP
$ {U_{smi}} $ 1, if the trip of $ d_m^s $ on the second-tier M-ULS network is assigned by NFS $ i $ 0-1 variable
$ {V_{smm'}} $ 1, if the trip of $ d_m^s $ on the third-tier M-ULS network is assigned by UD $ {m'} $
$ {\xi _{smr}} $ 1, if $ d_m^s $ traverses on arc $ r $ via road segment
$ {{\bf{O}}_{smk}} $ 1, if $ d_m^s $ traverses on arc $ k $ via metro segment
$ {{\bf{T}}_{smh}} $ 1, if $ d_m^s $ traverses on arc $ h $ via CP segment
Table Options

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Note Definition Attribute
Notation of indices
$ S $ set of LPWs, i.e., set of metro lines indexed by $ s $
$ M $ set of SCs, i.e., set of candidate location of UDs indexed by $ m $
$ N $ set of metro stations, i.e., set of candidate location of NFSs indexed by $ i $
$ L $ set of metro interchanges, i.e., set of activated IFSs indexed by $ j $
$ K $ set of metro line arcs between two adjacent metro stations indexed by $ k $
$ H $ set of arcs between metro stations and SCs indexed by $ h $
$ R $ set of arcs between two SCs indexed by $ r $
Exogenous parameters
$ g_m^s $ size of delivery orders from LPW $ s $ to SC $ m $ (original value) [0, 15] parcel per-day
$ d_m^s $ size of delivery orders from LPW $ s $ to SC $ m $ (after evaluated) –
$ c $ freight travel cost by LGV $ \yen $ 0.2 per-parcel per-km
$ \alpha $ ratio of the freight travel cost by metro to the freight travel cost by LGV 10%
$ \beta $ ratio of the freight travel cost by CPs to the freight travel cost by LGV 25%
$ w $ underground transfer cost at IFS $ \yen $0.1 per-parcel
$ {\lambda _1} $ fixed cost for CP construction $ \yen $4$ \times $$ 10^7 $ per-km
$ {\lambda _2} $ fixed cost for NFS retrofit $ \yen $1$ \times $$ 10^8 $
$ {\lambda _3} $ fixed cost for UD construction $ \yen $2$ \times $$ 10^7 $
$ {\eta _{NFS}} $ allowable level for low load operations at UD 60%
$ {\eta _{CP}} $ allowable level for low load operations at CP 50%
$ {\sigma _{NFS}} $ penalty cost due to low load operations of UD $ \yen $2 per-parcel
$ {\sigma _{CP}} $ penalty cost due to low load operations of CP $ \yen $1.5 per-parcel
$ [{R_{max}}] $ maximal road travel distance from UD to SC 2km
$ \left[ {{Q_{max}}} \right] $ order handling capacity of NFS 1$ \times $$ 10^5 $ parcel per-day
$ [{Z_{max}}] $ transport capacity of CP 4$ \times $$ 10^4 $ parcel per-day
$ [{G_{max}}] $ order handling capacity of UD 3.5$ \times $$ 10^4 $ parcel per-day
$ \left[ {{T_{max}}} \right] $ order transfer capacity of IFS 1.5$ \times $$ 10^6 $ parcel per-day
$ Eu $ Euclidean distance of arc $ k $, arc $ r $ and arc $ h $, respectively –
$ \theta $ depreciation coefficient of M-ULS network facilities 1/25550
Binary variables
$ {X_i} $ 1, if metro station $ i $ is selected as NFS
$ {\delta _{smj}} $ 1, if $ d_m^s $ is transferred at IFS $ j $
$ {Y_m} $ 1, if SC $ m $ is selected as UD
$ {W_h} $ 1, if arc $ h $ is selected as CP
$ {U_{smi}} $ 1, if the trip of $ d_m^s $ on the second-tier M-ULS network is assigned by NFS $ i $ 0-1 variable
$ {V_{smm'}} $ 1, if the trip of $ d_m^s $ on the third-tier M-ULS network is assigned by UD $ {m'} $
$ {\xi _{smr}} $ 1, if $ d_m^s $ traverses on arc $ r $ via road segment
$ {{\bf{O}}_{smk}} $ 1, if $ d_m^s $ traverses on arc $ k $ via metro segment
$ {{\bf{T}}_{smh}} $ 1, if $ d_m^s $ traverses on arc $ h $ via CP segment
Table 2.  Number of model variables and constraints
Number at most Nanjing metro case
Variables $ {X_i} $, $ {Y_m} $, Constraint 22 $ \left\| N \right\| + {\rm{3}} \times \left\| M \right\| $ 1,402
Variable $ {\delta _{smj}} $, Constraints 18, 23 $ \left\| S \right\| \times \left\| M \right\| \times \left( {{\rm{6}} + \left\| L \right\|} \right) $ 35,200
Variables $ {W_h} $, $ {W_r} $ $ \left\| M \right\| \times \left\| N \right\| + C_{\left\| M \right\|}^{\rm{2}} $ 132,660
Variables $ {U_{smi}} $, $ {V_{smm'}} $, Constraint 19 $ \left\| S \right\| \times \left\| M \right\| \times \left( {{\rm{2}}\left\| N \right\| + {\rm{2}}\left\| M \right\| - {\rm{2}}} \right) $ 1,833,920
Variables $ {\xi _{smr}} $, Constraints 16, 21 $ \left\| M \right\| + C_{\left\| M \right\|}^{\rm{2}} + \left\| S \right\| \times \left\| M \right\| \times C_{\left\| M \right\|}^{\rm{2}} + \left\| S \right\| \times P_{\left\| M \right\|}^{\rm{2}} $ 170,850,460
Variable $ {{\bf{O}}_{smk}} $, Constraint 15 $ \left\| S \right\| \times \left\| M \right\| \times \left( {\left\| N \right\| - {\rm{1}}} \right) + \left\| L \right\| + \left\| N \right\| $ 142,649
Variable $ {{\bf{T}}_{smh}} $, Constraints 17, 20 $ {\rm{2}} \times \left\| S \right\| \times {\left\| M \right\|^{\rm{2}}} \times \left\| N \right\| + \left\| M \right\| \times \left\| N \right\| $ 127,037,680
Sum of constraints and variables 300,033,971
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Number at most Nanjing metro case
Variables $ {X_i} $, $ {Y_m} $, Constraint 22 $ \left\| N \right\| + {\rm{3}} \times \left\| M \right\| $ 1,402
Variable $ {\delta _{smj}} $, Constraints 18, 23 $ \left\| S \right\| \times \left\| M \right\| \times \left( {{\rm{6}} + \left\| L \right\|} \right) $ 35,200
Variables $ {W_h} $, $ {W_r} $ $ \left\| M \right\| \times \left\| N \right\| + C_{\left\| M \right\|}^{\rm{2}} $ 132,660
Variables $ {U_{smi}} $, $ {V_{smm'}} $, Constraint 19 $ \left\| S \right\| \times \left\| M \right\| \times \left( {{\rm{2}}\left\| N \right\| + {\rm{2}}\left\| M \right\| - {\rm{2}}} \right) $ 1,833,920
Variables $ {\xi _{smr}} $, Constraints 16, 21 $ \left\| M \right\| + C_{\left\| M \right\|}^{\rm{2}} + \left\| S \right\| \times \left\| M \right\| \times C_{\left\| M \right\|}^{\rm{2}} + \left\| S \right\| \times P_{\left\| M \right\|}^{\rm{2}} $ 170,850,460
Variable $ {{\bf{O}}_{smk}} $, Constraint 15 $ \left\| S \right\| \times \left\| M \right\| \times \left( {\left\| N \right\| - {\rm{1}}} \right) + \left\| L \right\| + \left\| N \right\| $ 142,649
Variable $ {{\bf{T}}_{smh}} $, Constraints 17, 20 $ {\rm{2}} \times \left\| S \right\| \times {\left\| M \right\|^{\rm{2}}} \times \left\| N \right\| + \left\| M \right\| \times \left\| N \right\| $ 127,037,680
Sum of constraints and variables 300,033,971
Table 3.  Evaluation outputs of Nanjing M-ULS network flows
LPW 1 LPW 2 LPW 3 LPW 4
Accessed metro line Line 1 Line 2 Line 3 Line 4
Total demand orders ($ \times $10$ ^3 $ parcel per-day) 1,237 1,028 1,141 654
Average value of $ R{C_{sm}} $ 0.3025 0.269 0.3207 0.3436
Average value of $ R{C_{sm}} $ 0.3025 0.269 0.3207 0.3436
Maximum value of $ R{C_{sm}} $ 0.9471 0.9226 0.8901 0.9284
Average value of $ a_{m1}^s $ ($ \times $10$ ^3 $ parcel·km) 58.47 60.2 58.01 21.83
Average value of $ a_{m2}^s $ (kmh) 36.59 37.98 41.31 22.84
Average value of $ a_{m3}^s $ ($ \yen $ per-day) 1,332 1,997 2,189 462
Average value of $ a_{m4}^s $ ($ \yen $ per-day) 13,921 10,380 8,990 3,897
Size of orders inputted into metro 704 647 621 446
Served SC number 255 265 264 271
Utilization rate of metro line 93.9% 86.3% 82.8% 59.5%
Fulfillment rate of underground logistics 57.9% 60.2% 60% 61.6%
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LPW 1 LPW 2 LPW 3 LPW 4
Accessed metro line Line 1 Line 2 Line 3 Line 4
Total demand orders ($ \times $10$ ^3 $ parcel per-day) 1,237 1,028 1,141 654
Average value of $ R{C_{sm}} $ 0.3025 0.269 0.3207 0.3436
Average value of $ R{C_{sm}} $ 0.3025 0.269 0.3207 0.3436
Maximum value of $ R{C_{sm}} $ 0.9471 0.9226 0.8901 0.9284
Average value of $ a_{m1}^s $ ($ \times $10$ ^3 $ parcel·km) 58.47 60.2 58.01 21.83
Average value of $ a_{m2}^s $ (kmh) 36.59 37.98 41.31 22.84
Average value of $ a_{m3}^s $ ($ \yen $ per-day) 1,332 1,997 2,189 462
Average value of $ a_{m4}^s $ ($ \yen $ per-day) 13,921 10,380 8,990 3,897
Size of orders inputted into metro 704 647 621 446
Served SC number 255 265 264 271
Utilization rate of metro line 93.9% 86.3% 82.8% 59.5%
Fulfillment rate of underground logistics 57.9% 60.2% 60% 61.6%
Table 4.  Best configurations of Nanjing M-ULS network
ID Station full name $ {N_{SC}} $1 $ {N_{UD}} $2 $ \sum {d_m^s} $3 $ \overline {d_m^s} $4 $ {L_{CP}} $5 $ {R_{UD}} $6
Line 1 NFS-1 Er-Qiao-Gong-Yuan 11 6 40.5 6.8 5.5 4.63
NFS-2 Ba-Dou-Shan 17 5 44.9 9 8.87 11.23
NFS-3 Yan-Zi-Ji 17 9 80.5 8.9 13.14 6.6
NFS-4 Xin-Mo-Fan-Ma-Lu 11 4 98.5 24.6 7.44 8.18
NFS-5 Xuan-Wu-Men 9 3 77.8 25.9 3.36 3.87
NFS-6 Zhang-Fu-Yuan 8 6 67.6 11.3 4.29 1.68
NFS-7 San-Shan-Jie 4 3 37 12.3 3.66 0.84
NFS-8 Zhong-Hua-Men 6 2 35 17.5 3.95 4.87
NFS-9 Ruan-Jian-Da-Dao 9 4 44.9 11.2 6.01 4.51
NFS-10 Hua-Shen-Miao 8 5 39.4 7.9 4.66 2.26
NFS-11 Sheng-Tai-Lu 18 4 93.1 23.3 9.58 12.85
NFS-12 Zhu-Shan-Lu 32 12 95.4 8 20.2 17.29
NFS-13 Nan-Jing-Jiao-Yuan 9 4 35.1 8.8 4.34 5.23
Line 2 NFS-14 Qing-Lian-Jie 8 1 32.1 32.1 0.29 10.04
NFS-15 You-Fang-Qiao 15 4 71.8 18 3.09 11.65
NFS-16 Yuan-Tong 6 3 44.8 14.9 3.39 2.07
NFS-17 Xiong-Long-Da-Jie 13 7 84.6 12.1 8.6 6.29
NFS-18 Yun-Jing-Lu 14 7 90.5 12.9 10.99 6.45
NFS-19 Virtual station 8 4 49.6 12.4 3.48 3.19
NFS-20 Ming-Gu-Gong 19 9 79.3 8.8 13.83 9.47
NFS-21 Xia-Ma-Fang 5 1 34 34 2.17 3.27
NFS-22 Ma-Qun 13 3 55.6 18.5 2.45 10.65
NFS-23 Xian-Lin-Zhong-Xin 14 8 44.8 5.6 12.54 4.49
Line 3 NFS-24 Virtual station 7 2 38.4 19.2 2.53 5.55
NFS-25 Fu-Qiao 9 6 59.4 9.9 5.65 2.46
NFS-26 Virtual station 2 1 34.8 34.8 0.29 0.36
NFS-27 Ka-Zi-Men 11 7 74.1 10.6 9.41 2.82
NFS-28 Hong-Yun-Da-Dao 5 2 41.6 20.8 1.65 1.72
NFS-29 Tian-Yuan-Xi-Lu 26 9 98.4 10.9 13.02 12.26
NFS-30 Cheng-Xin-Da-Dao 24 9 97.8 10.9 11.06 16.12
Line 4 NFS-31 Hui-Tong-Lu 16 6 85.1 14.2 11.63 9.38
NFS-32 Wang-Jia-Wan 4 1 33.4 33.4 1.48 2.7
NFS-33 Gang-Zi-Cun 7 3 31.5 10.5 3.23 3.9
NFS-34 Yun-Nan-Lu 11 6 96 16 9.76 2.61
IFS-1 & NFS-35 Nan-Jing-Zhan 13 9 83.8 9.3 11 3.09
IFS-2 & NFS-36 Gu-Lou 7 5 91 18.2 6.93 0.99
IFS-3 & NFS-37 Xin-Jie-Kou 8 4 89.3 22.3 4.91 2.55
IFS-4 & NFS-38 Nan-Jing-Nan-Zhan 8 3 67.4 22.5 3.01 4.54
IFS-5 & NFS-39 Da-Xing-Gong 8 4 46 11.5 2.38 1.92
IFS-6 Jin-Ma-Lu – – – – – –
IFS-7 Ji-Ming-Si – – – – – –
ID Station full name $ {T_{1{\rm{st}}}} $ $ {T_{2{\rm{nd}}}} $ $ {T_{3{\rm{rd}}}} $ $ {P_{NFS}} $ $ {P_{CP}} $ $ {V_{IFS}} $
Line 1NFS-1 Er-Qiao-Gong-Yuan 21.6 1.39 2.08 39 13.2 –
NFS-2 Ba-Dou-Shan 20 3.78 7.64 30.2 11 –
NFS-3 Yan-Zi-Ji 37.8 4.41 6.28 0 11.1 –
NFS-4 Xin-Mo-Fan-Ma-Lu 56.3 6.49 19.69 0 0 –
NFS-5 Xuan-Wu-Men 27.7 3.4 7.1 0 0 –
NFS-6 Zhang-Fu-Yuan8 42.9 2.29 1.57 0 8.7 –
NFS-7 San-Shan-Jie 13.2 2.33 0.64 46 7.7 –
NFS-8 Zhong-Hua-Men 16.4 3.8 9.11 50 2.5 –
NFS-9 Ruan-Jian-Da-Dao 19.4 4.44 2.09 30.2 8.8 –
NFS-10 Hua-Shen-Miao 22.5 2.48 1.1 41.2 12.1 –
NFS-11 Sheng-Tai-Lu 53.2 12.18 27.86 0 0 –
NFS-12 Zhu-Shan-Lu 59.4 9.99 14.86 0 12 –
NFS-13 Nan-Jing-Jiao-Yuan 12.51.89 3.04 49.8 11.2 –
Line 2 NFS-14 Qing-Lian-Jie 17.9 0.52 13.54 55.8 0 –
NFS-15 You-Fang-Qiao 40.1 3.29 5.16 0 2 –
NFS-16 Yuan-Tong 17.1 2.34 1.30 30.4 5.1 –
NFS-17 Xiong-Long-Da-Jie 33.3 4.87 5.53 0 7.9 –
NFS-18 Yun-Jing-Lu 56.3 6.45 8.99 0 7.1 –
NFS-19 Virtual station 20.2 2.92 2.97 20.8 7.6 –
NFS-20 Ming-Gu-Gong 38.3 7.19 8.4 0 11.2 –
NFS-21 Xia-Ma-Fang 3.69 5.67 52 0 –
NFS-22 Ma-Qun 35.3 2.68 8.16 8.8 1.5 –
NFS-23 Xian-Lin-Zhong-Xin 27.9 4.41 2.41 30.4 14.4 –
Line 3 NFS-24 Virtual station 13.7 2.41 5.69 43.2 0.8 –
NFS-25 Fu-Qiao 25.6 3.48 2.24 1.2 10.1 –
NFS-26 Virtual station 11 0.61 0.86 50.4 0 –
NFS-27 Ka-Zi-Men 40.5 3.67 1.15 0 9.4 –
NFS-28 Hong-Yun-Da-Dao 18 2.06 2.71 36.8 0 –
NFS-29 Tian-Yuan-Xi-Lu 51.2 6 4.89 0 9.1 –
NFS-30 Cheng-Xin-Da-Dao 53.4 6.58 7.59 0 9.1 –
Line 4 NFS-31 Hui-Tong-Lu 33.5 11.11 5.42 0 5.8 –
NFS-32 Wang-Jia-Wan 15.3 2.65 4.76 53.2 0 –
NFS-33 Gang-Zi-Cun 15.2 1.17 4.33 57 9.5 –
NFS-34 Yun-Nan-Lu 53.6 9.16 4.06 0 4 –
IFS-1 & NFS-35 Nan-Jing-Zhan 36.2 5.02 1.13 0 10.7 871
IFS-2 & NFS-36 Gu-Lou 40.4 7.34 1.58 0 1.8 759
IFS-3 & NFS-37 Xin-Jie-Kou 47.6 4.93 4.01 0 0 1,259
IFS-4 & NFS-38 Nan-Jing-Nan-Zhan 24 2.96 9.24 0 0 804
IFS-5 & NFS-39 Da-Xing-Gong 16.4 1.87 1.95 28 8.5 1,090
IFS-6 Jin-Ma-Lu – – – – – 565
IFS-7 Ji-Ming-Si – – – – – 622
1 number of SCs allocated to NFS;
2 number of UDs covered by NFS;
3 total size of orders handled by NFS ($\times$10$^3$ parcel per-day);
4 average size of orders handled by UD ($\times$10$^3$ parcel per-day);
5 length of CP segments connected to NFS (km);
6 average service radius of UD (km).
7 transport cost of NFS orders on first-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
8 transport cost of NFS orders on second-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
9 transport cost of NFS orders on third-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
10 penalty cost of NFS ($\times$10$^3$ $\yen$ per-day);
11 penalty cost of CP segments connected to NFS ($\times$10$^3$ $\yen$ per-day);
12 size of orders transferred at IFS ($\times$10$^3$ parcel per-day).
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ID Station full name $ {N_{SC}} $1 $ {N_{UD}} $2 $ \sum {d_m^s} $3 $ \overline {d_m^s} $4 $ {L_{CP}} $5 $ {R_{UD}} $6
Line 1 NFS-1 Er-Qiao-Gong-Yuan 11 6 40.5 6.8 5.5 4.63
NFS-2 Ba-Dou-Shan 17 5 44.9 9 8.87 11.23
NFS-3 Yan-Zi-Ji 17 9 80.5 8.9 13.14 6.6
NFS-4 Xin-Mo-Fan-Ma-Lu 11 4 98.5 24.6 7.44 8.18
NFS-5 Xuan-Wu-Men 9 3 77.8 25.9 3.36 3.87
NFS-6 Zhang-Fu-Yuan 8 6 67.6 11.3 4.29 1.68
NFS-7 San-Shan-Jie 4 3 37 12.3 3.66 0.84
NFS-8 Zhong-Hua-Men 6 2 35 17.5 3.95 4.87
NFS-9 Ruan-Jian-Da-Dao 9 4 44.9 11.2 6.01 4.51
NFS-10 Hua-Shen-Miao 8 5 39.4 7.9 4.66 2.26
NFS-11 Sheng-Tai-Lu 18 4 93.1 23.3 9.58 12.85
NFS-12 Zhu-Shan-Lu 32 12 95.4 8 20.2 17.29
NFS-13 Nan-Jing-Jiao-Yuan 9 4 35.1 8.8 4.34 5.23
Line 2 NFS-14 Qing-Lian-Jie 8 1 32.1 32.1 0.29 10.04
NFS-15 You-Fang-Qiao 15 4 71.8 18 3.09 11.65
NFS-16 Yuan-Tong 6 3 44.8 14.9 3.39 2.07
NFS-17 Xiong-Long-Da-Jie 13 7 84.6 12.1 8.6 6.29
NFS-18 Yun-Jing-Lu 14 7 90.5 12.9 10.99 6.45
NFS-19 Virtual station 8 4 49.6 12.4 3.48 3.19
NFS-20 Ming-Gu-Gong 19 9 79.3 8.8 13.83 9.47
NFS-21 Xia-Ma-Fang 5 1 34 34 2.17 3.27
NFS-22 Ma-Qun 13 3 55.6 18.5 2.45 10.65
NFS-23 Xian-Lin-Zhong-Xin 14 8 44.8 5.6 12.54 4.49
Line 3 NFS-24 Virtual station 7 2 38.4 19.2 2.53 5.55
NFS-25 Fu-Qiao 9 6 59.4 9.9 5.65 2.46
NFS-26 Virtual station 2 1 34.8 34.8 0.29 0.36
NFS-27 Ka-Zi-Men 11 7 74.1 10.6 9.41 2.82
NFS-28 Hong-Yun-Da-Dao 5 2 41.6 20.8 1.65 1.72
NFS-29 Tian-Yuan-Xi-Lu 26 9 98.4 10.9 13.02 12.26
NFS-30 Cheng-Xin-Da-Dao 24 9 97.8 10.9 11.06 16.12
Line 4 NFS-31 Hui-Tong-Lu 16 6 85.1 14.2 11.63 9.38
NFS-32 Wang-Jia-Wan 4 1 33.4 33.4 1.48 2.7
NFS-33 Gang-Zi-Cun 7 3 31.5 10.5 3.23 3.9
NFS-34 Yun-Nan-Lu 11 6 96 16 9.76 2.61
IFS-1 & NFS-35 Nan-Jing-Zhan 13 9 83.8 9.3 11 3.09
IFS-2 & NFS-36 Gu-Lou 7 5 91 18.2 6.93 0.99
IFS-3 & NFS-37 Xin-Jie-Kou 8 4 89.3 22.3 4.91 2.55
IFS-4 & NFS-38 Nan-Jing-Nan-Zhan 8 3 67.4 22.5 3.01 4.54
IFS-5 & NFS-39 Da-Xing-Gong 8 4 46 11.5 2.38 1.92
IFS-6 Jin-Ma-Lu – – – – – –
IFS-7 Ji-Ming-Si – – – – – –
ID Station full name $ {T_{1{\rm{st}}}} $ $ {T_{2{\rm{nd}}}} $ $ {T_{3{\rm{rd}}}} $ $ {P_{NFS}} $ $ {P_{CP}} $ $ {V_{IFS}} $
Line 1NFS-1 Er-Qiao-Gong-Yuan 21.6 1.39 2.08 39 13.2 –
NFS-2 Ba-Dou-Shan 20 3.78 7.64 30.2 11 –
NFS-3 Yan-Zi-Ji 37.8 4.41 6.28 0 11.1 –
NFS-4 Xin-Mo-Fan-Ma-Lu 56.3 6.49 19.69 0 0 –
NFS-5 Xuan-Wu-Men 27.7 3.4 7.1 0 0 –
NFS-6 Zhang-Fu-Yuan8 42.9 2.29 1.57 0 8.7 –
NFS-7 San-Shan-Jie 13.2 2.33 0.64 46 7.7 –
NFS-8 Zhong-Hua-Men 16.4 3.8 9.11 50 2.5 –
NFS-9 Ruan-Jian-Da-Dao 19.4 4.44 2.09 30.2 8.8 –
NFS-10 Hua-Shen-Miao 22.5 2.48 1.1 41.2 12.1 –
NFS-11 Sheng-Tai-Lu 53.2 12.18 27.86 0 0 –
NFS-12 Zhu-Shan-Lu 59.4 9.99 14.86 0 12 –
NFS-13 Nan-Jing-Jiao-Yuan 12.51.89 3.04 49.8 11.2 –
Line 2 NFS-14 Qing-Lian-Jie 17.9 0.52 13.54 55.8 0 –
NFS-15 You-Fang-Qiao 40.1 3.29 5.16 0 2 –
NFS-16 Yuan-Tong 17.1 2.34 1.30 30.4 5.1 –
NFS-17 Xiong-Long-Da-Jie 33.3 4.87 5.53 0 7.9 –
NFS-18 Yun-Jing-Lu 56.3 6.45 8.99 0 7.1 –
NFS-19 Virtual station 20.2 2.92 2.97 20.8 7.6 –
NFS-20 Ming-Gu-Gong 38.3 7.19 8.4 0 11.2 –
NFS-21 Xia-Ma-Fang 3.69 5.67 52 0 –
NFS-22 Ma-Qun 35.3 2.68 8.16 8.8 1.5 –
NFS-23 Xian-Lin-Zhong-Xin 27.9 4.41 2.41 30.4 14.4 –
Line 3 NFS-24 Virtual station 13.7 2.41 5.69 43.2 0.8 –
NFS-25 Fu-Qiao 25.6 3.48 2.24 1.2 10.1 –
NFS-26 Virtual station 11 0.61 0.86 50.4 0 –
NFS-27 Ka-Zi-Men 40.5 3.67 1.15 0 9.4 –
NFS-28 Hong-Yun-Da-Dao 18 2.06 2.71 36.8 0 –
NFS-29 Tian-Yuan-Xi-Lu 51.2 6 4.89 0 9.1 –
NFS-30 Cheng-Xin-Da-Dao 53.4 6.58 7.59 0 9.1 –
Line 4 NFS-31 Hui-Tong-Lu 33.5 11.11 5.42 0 5.8 –
NFS-32 Wang-Jia-Wan 15.3 2.65 4.76 53.2 0 –
NFS-33 Gang-Zi-Cun 15.2 1.17 4.33 57 9.5 –
NFS-34 Yun-Nan-Lu 53.6 9.16 4.06 0 4 –
IFS-1 & NFS-35 Nan-Jing-Zhan 36.2 5.02 1.13 0 10.7 871
IFS-2 & NFS-36 Gu-Lou 40.4 7.34 1.58 0 1.8 759
IFS-3 & NFS-37 Xin-Jie-Kou 47.6 4.93 4.01 0 0 1,259
IFS-4 & NFS-38 Nan-Jing-Nan-Zhan 24 2.96 9.24 0 0 804
IFS-5 & NFS-39 Da-Xing-Gong 16.4 1.87 1.95 28 8.5 1,090
IFS-6 Jin-Ma-Lu – – – – – 565
IFS-7 Ji-Ming-Si – – – – – 622
1 number of SCs allocated to NFS;
2 number of UDs covered by NFS;
3 total size of orders handled by NFS ($\times$10$^3$ parcel per-day);
4 average size of orders handled by UD ($\times$10$^3$ parcel per-day);
5 length of CP segments connected to NFS (km);
6 average service radius of UD (km).
7 transport cost of NFS orders on first-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
8 transport cost of NFS orders on second-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
9 transport cost of NFS orders on third-tier M-ULS network ($\times$10$^3$ $\yen$ per-day);
10 penalty cost of NFS ($\times$10$^3$ $\yen$ per-day);
11 penalty cost of CP segments connected to NFS ($\times$10$^3$ $\yen$ per-day);
12 size of orders transferred at IFS ($\times$10$^3$ parcel per-day).
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