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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

 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.

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 and Management Optimization, doi: 10.3934/jimo.2021179
##### References:

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##### References:
Overview of the 3EM-ULSND problem
Overview of the 3EM-ULSND problem
Illustration of Pareto front in tri-objective optimization problem
Model decomposition and algorithmic flowchart
Pareto-optimal front obtained with MOPSO
Pareto-optimal front obtained with MOPSO
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 $$10^6 parcel per-day Eu Euclidean distance of arc k , arc r and arc h , respectively – \theta depreciation coefficient of M-ULS network facilities 1/25550 Binary variables {X_i} 1, if metro station i is selected as NFS {\delta _{smj}} 1, if d_m^s is transferred at IFS j {Y_m} 1, if SC m is selected as UD {W_h} 1, if arc h is selected as CP {U_{smi}} 1, if the trip of d_m^s on the second-tier M-ULS network is assigned by NFS i 0-1 variable {V_{smm'}} 1, if the trip of d_m^s on the third-tier M-ULS network is assigned by UD {m'} {\xi _{smr}} 1, if d_m^s traverses on arc r via road segment {{\bf{O}}_{smk}} 1, if d_m^s traverses on arc k via metro segment {{\bf{T}}_{smh}} 1, if d_m^s traverses on arc h via CP segment  Note Definition Attribute Notation of indices S set of LPWs, i.e., set of metro lines indexed by s M set of SCs, i.e., set of candidate location of UDs indexed by m N set of metro stations, i.e., set of candidate location of NFSs indexed by i L set of metro interchanges, i.e., set of activated IFSs indexed by j K set of metro line arcs between two adjacent metro stations indexed by k H set of arcs between metro stations and SCs indexed by h R set of arcs between two SCs indexed by r Exogenous parameters g_m^s size of delivery orders from LPW s to SC m (original value) [0, 15] parcel per-day d_m^s size of delivery orders from LPW s to SC m (after evaluated) – c freight travel cost by LGV \yen 0.2 per-parcel per-km \alpha ratio of the freight travel cost by metro to the freight travel cost by LGV 10% \beta ratio of the freight travel cost by CPs to the freight travel cost by LGV 25% w underground transfer cost at IFS \yen 0.1 per-parcel {\lambda _1} fixed cost for CP construction \yen 4 \times$$ 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
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
 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
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%
 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%
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 1 NFS-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 12.5 1.89 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).
 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 1 NFS-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 12.5 1.89 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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