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April  2018, 14(2): 447-472. doi: 10.3934/jimo.2017055

The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty

1. 

Av. Pedro de Alba, San Nicolás de los Garza, NL 66450, México, PhD Student in Program for Economy and Enterprise at the University of Málaga

2. 

Universidad Autónoma de Nuevo León, Av. Pedro de Alba, San Nicolás de los Garza, NL 66450, México

3. 

Universidad de Málaga, Campus El Ejido S/N, Málaga, 29071, España

* Corresponding author: Paulina Avila-Torres

Received  January 2016 Revised  November 2016 Published  June 2017

Fund Project: CONACyT, AUIP, DoA, Spanish MINECO and Andalucia Goverment.

The urban transport planning process has four main activities: Network design, Timetable construction, Vehicle scheduling and Crew scheduling; each activity has subactivities. In this paper the authors work with the subactivities of timetable construction: minimal frequency calculation and departure time scheduling. The authors propose to solve both subactivities in an integrated way. The developed mathematical model allows multi-period planning and it can also be used for multimodal urban transportation systems. The authors consider demand uncertainty and the authors employ fuzzy programming to solve the problem. The authors formulate the urban transportation timetabling construction problem as a bi-objective problem: to minimize the total operational cost and to maximize the number of multi-period synchronizations. Finally, the authors implemented the SAUGMECON method to solve the problem.

Citation: Paulina Ávila-Torres, Fernando López-Irarragorri, Rafael Caballero, Yasmín Ríos-Solís. The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty. Journal of Industrial & Management Optimization, 2018, 14 (2) : 447-472. doi: 10.3934/jimo.2017055
References:
[1]

P. Avila and F. López, Two multiobjective metaheuristics for solving the integrated problem of frequencies calculation and departures planning in an urban transport system, Annals of Management Science, 3 (2014), 29-42.   Google Scholar

[2]

R. Baskaran and K. Krishnaiah, Simulation model to determine frequency of a single bus route with single and multiple headways, Int. J. Business Performance and Supply Chain Modelling, 4 (2012), 40-59.   Google Scholar

[3]

L. Cadarso and A. Marín, Integration of timetable planning and rolling stock in rapid transit networks, Annals of Operations Research, 199 (2012), 113-135.  doi: 10.1007/s10479-011-0978-0.  Google Scholar

[4]

L. Campos and J. L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32 (1989), 1-11.  doi: 10.1016/0165-0114(89)90084-5.  Google Scholar

[5] A. Ceder, Public Transit Planning and Operation: Theory, Modeling and Practice, 1 edition, Elsevier, USA, 2007.   Google Scholar
[6]

P. Chakroborty, Genetic algorithms for optimal urban transit network design, Computer-Aided Civil and Infrastructure Engineering, 18 (2003), 184-200.  doi: 10.1111/1467-8667.00309.  Google Scholar

[7]

H. Chen, Stochastic optimization in computing multiple headways for a single bus line, Proceedings of the 35th Annual Simulation Symposium, (2002), 316-323.   Google Scholar

[8]

C. DaraioD. MarcoF. Di CostaC. LeporelliG. Matteucci and A. Nastasi, Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research, European Journal of Operational Research, 248 (2016), 1-20.   Google Scholar

[9]

G. Desaulniers and M. D. Hickman, Public transit, in Handbook in OR & MS (eds C. Barnhart and G. Laporte), Elsevier, (2007), 69-127. Google Scholar

[10]

A. Eranki, A model to create bus timetables to attain maximum synchronization considering waiting times at transfer stops, Thesis University of South Florida, 2004. Google Scholar

[11]

H. Fazlollahtabar and M. Saidi-Mehrabad, Optimizing multi-objective decision making having qualitative evaluation, Journal of Industrial and Management Optimization, 11 (2016), 747-762.  doi: 10.3934/jimo.2015.11.747.  Google Scholar

[12]

Y. Hadas and M. Shnaiderman, Public-transit frequency setting using minimum-cost approach with stochastic demand and travel time, Transportation Research Part B: Methodological, 46 (2012), 1068-1084.  doi: 10.1016/j.trb.2012.02.010.  Google Scholar

[13]

O. J. Ibarra-Rojas and Y. A. Rios-Solis, Synchronization of bus timetabling, Transportation Research Part B: Methodological, 46 (2012), 599-614.  doi: 10.1016/j.trb.2012.01.006.  Google Scholar

[14]

J. Jensen, O. Nielsen and C. Prato, Public transport optimisation emphasising passengers' travel behaviour, Thesis Technical University of DenmarkDanmarks Tekniske Universitet, 2015. Google Scholar

[15]

L. LinzhongY. JuhuaM. HaiboL. Xiaojing and W. Fang, Exact algorithms for multi-criteria multi-modal shortest path with transfer delaying and arriving time-window in urban transit network, Applied Mathematical Modeling, 38 (2014), 2613-2629.  doi: 10.1016/j.apm.2013.10.059.  Google Scholar

[16]

S. H. Nasseri and E. Behmanesh, Linear programming with triangular fuzzy numbers--A case study in a finance and credit institute, Fuzzy Information and Engineering, 5 (2013), 295-315.  doi: 10.1007/s12543-013-0151-3.  Google Scholar

[17]

F. PerezT. Gomez and R. Caballero, Un modelo difuso para la selección de carteras de proyectos con incertidumbre en los costes, Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 13 (2012), 129-143.   Google Scholar

[18]

F. Perez and T. Gomez, Multiobjective project portfolio selection with fuzzy constraints, Annals of Operation Research, 245 (2016), 7-29.  doi: 10.1007/s10479-014-1556-z.  Google Scholar

[19]

T. RasmussenM. AndersonO. Nielsen and C. Prato, Timetable-based simulation method for choice set generation in large-scale public transport networks, EJTIR, 16 (2016), 467-489.   Google Scholar

[20]

V. Sahinidis Nikolaos, Optimization under uncertainty: State-of-the-art and opportunities, Computers and Chemical Engineering, 28 (2004), 971-983.   Google Scholar

[21]

Y. ShangyaoC. Chin-Jen and T. Ching-Hui, Inter-city bus routing and timetable setting under stochastic demands, Transportation research part A, 40 (2006), 572-586.   Google Scholar

[22]

L. SunZ. Gao and Y. Wang, A Stackelberg game management model of the urban public transport, Journal of Industrial and Management Optimization, 8 (2012), 507-520.  doi: 10.3934/jimo.2012.8.507.  Google Scholar

[23]

W. Y. Szeto and W. Yongzhong, A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong, European Journal of Operational Research, 209 (2011), 141-155.  doi: 10.1016/j.ejor.2010.08.020.  Google Scholar

[24]

S. L. Tilahun and H. C. Ong, Bus timetabling as a fuzzy multiobjective optimization problem using preference based genetic algorithm, Promet -Traffic & Transportation, 24 (2012), 183-191.  doi: 10.7307/ptt.v24i3.311.  Google Scholar

[25]

I. VerbasC. FreiH. Mahmassani and R. Chan, Stretching resources: Sensitivity of optimal bus frequency allocation to stop-level demand elasticities, Public Transport, 7 (2015), 1-20.   Google Scholar

[26]

I. Verbas and H. Mahmassani, Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems, Transportation Research Part B: Methodological, 81 (2015), 577-595.   Google Scholar

[27]

Y. WangX. Zhu and L. B. Wu, Integrated multimodal metropolitan transportation model, Procedia Social and Behavioral Sciences, 96 (2013), 2138-2146.  doi: 10.1016/j.sbspro.2013.08.241.  Google Scholar

[28]

J. ZhangT. Arentze and H. Timmermans, A multimodal transport network model for advanced traveler information system, Journal of Ubiquitous System and Pervasive Networks, 4 (2012), 21-27.   Google Scholar

[29]

W. Zhang and M. Reimann, A simple augmented e-constraint method for multi-objective mathematical integer programming problems, European Journal of Operations Research, 234 (2014), 15-24.  doi: 10.1016/j.ejor.2013.09.001.  Google Scholar

[30]

F. Zhao and Z. Xiaogang, Optimization of transit route network, vehicle headways and timetables for large-scale transit networks, European Journal of Operational Research, 186 (2008), 841-855.  doi: 10.1016/j.ejor.2007.02.005.  Google Scholar

[31]

Y. Zhu, B. Mao, L. Liu and M. Li, Timetable design for urban rail line with capacity constraints Discrete Dynamics in Nature and Society 2015 (2015), Art. ID 429219, 11 pp. doi: 10.1155/2015/429219.  Google Scholar

show all references

References:
[1]

P. Avila and F. López, Two multiobjective metaheuristics for solving the integrated problem of frequencies calculation and departures planning in an urban transport system, Annals of Management Science, 3 (2014), 29-42.   Google Scholar

[2]

R. Baskaran and K. Krishnaiah, Simulation model to determine frequency of a single bus route with single and multiple headways, Int. J. Business Performance and Supply Chain Modelling, 4 (2012), 40-59.   Google Scholar

[3]

L. Cadarso and A. Marín, Integration of timetable planning and rolling stock in rapid transit networks, Annals of Operations Research, 199 (2012), 113-135.  doi: 10.1007/s10479-011-0978-0.  Google Scholar

[4]

L. Campos and J. L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32 (1989), 1-11.  doi: 10.1016/0165-0114(89)90084-5.  Google Scholar

[5] A. Ceder, Public Transit Planning and Operation: Theory, Modeling and Practice, 1 edition, Elsevier, USA, 2007.   Google Scholar
[6]

P. Chakroborty, Genetic algorithms for optimal urban transit network design, Computer-Aided Civil and Infrastructure Engineering, 18 (2003), 184-200.  doi: 10.1111/1467-8667.00309.  Google Scholar

[7]

H. Chen, Stochastic optimization in computing multiple headways for a single bus line, Proceedings of the 35th Annual Simulation Symposium, (2002), 316-323.   Google Scholar

[8]

C. DaraioD. MarcoF. Di CostaC. LeporelliG. Matteucci and A. Nastasi, Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research, European Journal of Operational Research, 248 (2016), 1-20.   Google Scholar

[9]

G. Desaulniers and M. D. Hickman, Public transit, in Handbook in OR & MS (eds C. Barnhart and G. Laporte), Elsevier, (2007), 69-127. Google Scholar

[10]

A. Eranki, A model to create bus timetables to attain maximum synchronization considering waiting times at transfer stops, Thesis University of South Florida, 2004. Google Scholar

[11]

H. Fazlollahtabar and M. Saidi-Mehrabad, Optimizing multi-objective decision making having qualitative evaluation, Journal of Industrial and Management Optimization, 11 (2016), 747-762.  doi: 10.3934/jimo.2015.11.747.  Google Scholar

[12]

Y. Hadas and M. Shnaiderman, Public-transit frequency setting using minimum-cost approach with stochastic demand and travel time, Transportation Research Part B: Methodological, 46 (2012), 1068-1084.  doi: 10.1016/j.trb.2012.02.010.  Google Scholar

[13]

O. J. Ibarra-Rojas and Y. A. Rios-Solis, Synchronization of bus timetabling, Transportation Research Part B: Methodological, 46 (2012), 599-614.  doi: 10.1016/j.trb.2012.01.006.  Google Scholar

[14]

J. Jensen, O. Nielsen and C. Prato, Public transport optimisation emphasising passengers' travel behaviour, Thesis Technical University of DenmarkDanmarks Tekniske Universitet, 2015. Google Scholar

[15]

L. LinzhongY. JuhuaM. HaiboL. Xiaojing and W. Fang, Exact algorithms for multi-criteria multi-modal shortest path with transfer delaying and arriving time-window in urban transit network, Applied Mathematical Modeling, 38 (2014), 2613-2629.  doi: 10.1016/j.apm.2013.10.059.  Google Scholar

[16]

S. H. Nasseri and E. Behmanesh, Linear programming with triangular fuzzy numbers--A case study in a finance and credit institute, Fuzzy Information and Engineering, 5 (2013), 295-315.  doi: 10.1007/s12543-013-0151-3.  Google Scholar

[17]

F. PerezT. Gomez and R. Caballero, Un modelo difuso para la selección de carteras de proyectos con incertidumbre en los costes, Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 13 (2012), 129-143.   Google Scholar

[18]

F. Perez and T. Gomez, Multiobjective project portfolio selection with fuzzy constraints, Annals of Operation Research, 245 (2016), 7-29.  doi: 10.1007/s10479-014-1556-z.  Google Scholar

[19]

T. RasmussenM. AndersonO. Nielsen and C. Prato, Timetable-based simulation method for choice set generation in large-scale public transport networks, EJTIR, 16 (2016), 467-489.   Google Scholar

[20]

V. Sahinidis Nikolaos, Optimization under uncertainty: State-of-the-art and opportunities, Computers and Chemical Engineering, 28 (2004), 971-983.   Google Scholar

[21]

Y. ShangyaoC. Chin-Jen and T. Ching-Hui, Inter-city bus routing and timetable setting under stochastic demands, Transportation research part A, 40 (2006), 572-586.   Google Scholar

[22]

L. SunZ. Gao and Y. Wang, A Stackelberg game management model of the urban public transport, Journal of Industrial and Management Optimization, 8 (2012), 507-520.  doi: 10.3934/jimo.2012.8.507.  Google Scholar

[23]

W. Y. Szeto and W. Yongzhong, A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong, European Journal of Operational Research, 209 (2011), 141-155.  doi: 10.1016/j.ejor.2010.08.020.  Google Scholar

[24]

S. L. Tilahun and H. C. Ong, Bus timetabling as a fuzzy multiobjective optimization problem using preference based genetic algorithm, Promet -Traffic & Transportation, 24 (2012), 183-191.  doi: 10.7307/ptt.v24i3.311.  Google Scholar

[25]

I. VerbasC. FreiH. Mahmassani and R. Chan, Stretching resources: Sensitivity of optimal bus frequency allocation to stop-level demand elasticities, Public Transport, 7 (2015), 1-20.   Google Scholar

[26]

I. Verbas and H. Mahmassani, Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems, Transportation Research Part B: Methodological, 81 (2015), 577-595.   Google Scholar

[27]

Y. WangX. Zhu and L. B. Wu, Integrated multimodal metropolitan transportation model, Procedia Social and Behavioral Sciences, 96 (2013), 2138-2146.  doi: 10.1016/j.sbspro.2013.08.241.  Google Scholar

[28]

J. ZhangT. Arentze and H. Timmermans, A multimodal transport network model for advanced traveler information system, Journal of Ubiquitous System and Pervasive Networks, 4 (2012), 21-27.   Google Scholar

[29]

W. Zhang and M. Reimann, A simple augmented e-constraint method for multi-objective mathematical integer programming problems, European Journal of Operations Research, 234 (2014), 15-24.  doi: 10.1016/j.ejor.2013.09.001.  Google Scholar

[30]

F. Zhao and Z. Xiaogang, Optimization of transit route network, vehicle headways and timetables for large-scale transit networks, European Journal of Operational Research, 186 (2008), 841-855.  doi: 10.1016/j.ejor.2007.02.005.  Google Scholar

[31]

Y. Zhu, B. Mao, L. Liu and M. Li, Timetable design for urban rail line with capacity constraints Discrete Dynamics in Nature and Society 2015 (2015), Art. ID 429219, 11 pp. doi: 10.1155/2015/429219.  Google Scholar

5]">Figure 1.  Transport planning process [5]
5]">Figure 2.  Departure times[5]
13]">Figure 3.  Types of synchronization nodes [13]
Figure 4.  Multiperiod Scheduling Urban Transportation Problem. $S_{h}$ is the scheduling horizon, $T^v$ are the time periods. In each $T^v$ demand is considered almost constant
Figure 5.  Differences of how to represent departures
Figure 6.  Policies headways for departures
Figure 7.  First departure
Figure 8.  Consecutive departure
Figure 9.  Last departure
5]">Figure 10.  Flowchart to determine the frequency [5]
Figure 11.  Window time for synchronization
Figure 12.  Correlation
Figure 13.  Execution time effect
Figure 14.  Cost vs. Synchronization (Instance 20)
Figure 15.  Cost vs. Synchronization (Instance 24)
Figure 16.  Cost behaviour in relation to instance parameters
Figure 17.  Synchronizations behaviour in relation to instance parameters
Table 1.  Literature review
AuthorsFrequencyTransfer nodesBunching nodesCostMultimodalUncertain DemandMultiperiodIntegration
Chen et al.xxx
Chakrobortyxxx
Zhao & Zengxxx
Szeto & Wuxx
Hadas & Shnaidermanxxx
Baskaran & Krishnaiahxxx
Tilahun & Ongxx
Liu et al.xx
Zhang et al.xx
Wang et al.xx
Erankix
Ibarra-Rojas et al.xxx
Avila et al.xxxxxxxx
AuthorsFrequencyTransfer nodesBunching nodesCostMultimodalUncertain DemandMultiperiodIntegration
Chen et al.xxx
Chakrobortyxxx
Zhao & Zengxxx
Szeto & Wuxx
Hadas & Shnaidermanxxx
Baskaran & Krishnaiahxxx
Tilahun & Ongxx
Liu et al.xx
Zhang et al.xx
Wang et al.xx
Erankix
Ibarra-Rojas et al.xxx
Avila et al.xxxxxxxx
Table 2.  Characteristics of instances
ParameterLow levelHigh level
Routes820
Periods212
Segments10150
Sync. nodes212
Headways5-105-20
ParameterLow levelHigh level
Routes820
Periods212
Segments10150
Sync. nodes212
Headways5-105-20
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