-
Previous Article
Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted gegenbauer integral pseudospectral method
- JIMO Home
- This Issue
-
Next Article
Ebola model and optimal control with vaccination constraints
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 |
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.
Mathematics Subject Classification:
Primary: 90C11; Secondary: 90-08.
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. |
| [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. |
| [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. |
| [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. Daraio, D. Marco, F. Di Costa, C. Leporelli, G. 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. |
| [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. |
| [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. |
| [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. Linzhong, Y. Juhua, M. Haibo, L. 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. |
| [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. |
| [17] |
F. Perez, T. 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. |
| [19] |
T. Rasmussen, M. Anderson, O. 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. Shangyao, C. 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. Sun, Z. 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. |
| [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. |
| [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. |
| [25] |
I. Verbas, C. Frei, H. 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. Wang, X. 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. |
| [28] |
J. Zhang, T. 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. |
| [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. |
| [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. |
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. |
| [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. |
| [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. |
| [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. Daraio, D. Marco, F. Di Costa, C. Leporelli, G. 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. |
| [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. |
| [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. |
| [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. Linzhong, Y. Juhua, M. Haibo, L. 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. |
| [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. |
| [17] |
F. Perez, T. 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. |
| [19] |
T. Rasmussen, M. Anderson, O. 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. Shangyao, C. 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. Sun, Z. 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. |
| [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. |
| [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. |
| [25] |
I. Verbas, C. Frei, H. 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. Wang, X. 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. |
| [28] |
J. Zhang, T. 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. |
| [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. |
| [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. |
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
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
| Authors | Frequency | Transfer nodes | Bunching nodes | Cost | Multimodal | Uncertain Demand | Multiperiod | Integration |
| Chen et al. | x | x | x | |||||
| Chakroborty | x | x | x | |||||
| Zhao & Zeng | x | x | x | |||||
| Szeto & Wu | x | x | ||||||
| Hadas & Shnaiderman | x | x | x | |||||
| Baskaran & Krishnaiah | x | x | x | |||||
| Tilahun & Ong | x | x | ||||||
| Liu et al. | x | x | ||||||
| Zhang et al. | x | x | ||||||
| Wang et al. | x | x | ||||||
| Eranki | x | |||||||
| Ibarra-Rojas et al. | x | x | x | |||||
| Avila et al. | x | x | x | x | x | x | x | x |
| Authors | Frequency | Transfer nodes | Bunching nodes | Cost | Multimodal | Uncertain Demand | Multiperiod | Integration |
| Chen et al. | x | x | x | |||||
| Chakroborty | x | x | x | |||||
| Zhao & Zeng | x | x | x | |||||
| Szeto & Wu | x | x | ||||||
| Hadas & Shnaiderman | x | x | x | |||||
| Baskaran & Krishnaiah | x | x | x | |||||
| Tilahun & Ong | x | x | ||||||
| Liu et al. | x | x | ||||||
| Zhang et al. | x | x | ||||||
| Wang et al. | x | x | ||||||
| Eranki | x | |||||||
| Ibarra-Rojas et al. | x | x | x | |||||
| Avila et al. | x | x | x | x | x | x | x | x |
Table 2.
Characteristics of instances
| Parameter | Low level | High level |
| Routes | 8 | 20 |
| Periods | 2 | 12 |
| Segments | 10 | 150 |
| Sync. nodes | 2 | 12 |
| Headways | 5-10 | 5-20 |
| Parameter | Low level | High level |
| Routes | 8 | 20 |
| Periods | 2 | 12 |
| Segments | 10 | 150 |
| Sync. nodes | 2 | 12 |
| Headways | 5-10 | 5-20 |
| [1] |
Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1235-1259. doi: 10.3934/jimo.2018202 |
| [2] |
Min He. On continuity in parameters of integrated semigroups. Conference Publications, 2003, 2003 (Special) : 403-412. doi: 10.3934/proc.2003.2003.403 |
| [3] |
Zhongbao Zhou, Ximei Zeng, Helu Xiao, Tiantian Ren, Wenbin Liu. Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1493-1515. doi: 10.3934/jimo.2018106 |
| [4] |
Peng Zhang, Yongquan Zeng, Guotai Chi. Time-consistent multiperiod mean semivariance portfolio selection with the real constraints. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1663-1680. doi: 10.3934/jimo.2020039 |
| [5] |
Angel Angelov, Marcus Wagner. Multimodal image registration by elastic matching of edge sketches via optimal control. Journal of Industrial & Management Optimization, 2014, 10 (2) : 567-590. doi: 10.3934/jimo.2014.10.567 |
| [6] |
Mikko Kaasalainen. Multimodal inverse problems: Maximum compatibility estimate and shape reconstruction. Inverse Problems & Imaging, 2011, 5 (1) : 37-57. doi: 10.3934/ipi.2011.5.37 |
| [7] |
José M. Amigó, Ángel Giménez. Formulas for the topological entropy of multimodal maps based on min-max symbols. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3415-3434. doi: 10.3934/dcdsb.2015.20.3415 |
| [8] |
Jingni Guo, Junxiang Xu, Zhenggang He, Wei Liao. Research on cascading failure modes and attack strategies of multimodal transport network. Journal of Industrial & Management Optimization, 2022, 18 (1) : 397-410. doi: 10.3934/jimo.2020159 |
| [9] |
Miriam Kiessling, Sascha Kurz, Jörg Rambau. The integrated size and price optimization problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 669-693. doi: 10.3934/naco.2012.2.669 |
| [10] |
Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky, Viktor Tkachenko, Serhiy Yanchuk. Frequency locking of modulated waves. Discrete & Continuous Dynamical Systems, 2011, 31 (3) : 847-875. doi: 10.3934/dcds.2011.31.847 |
| [11] |
Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1187-1198. doi: 10.3934/dcdss.2019082 |
| [12] |
Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial & Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581 |
| [13] |
Juan J. Nieto, M. Victoria Otero-Espinar, Rosana Rodríguez-López. Dynamics of the fuzzy logistic family. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 699-717. doi: 10.3934/dcdsb.2010.14.699 |
| [14] |
Natalia Skripnik. Averaging of fuzzy integral equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1999-2010. doi: 10.3934/dcdsb.2017118 |
| [15] |
Purnima Pandit. Fuzzy system of linear equations. Conference Publications, 2013, 2013 (special) : 619-627. doi: 10.3934/proc.2013.2013.619 |
| [16] |
İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics & Games, 2021, 8 (3) : 267-275. doi: 10.3934/jdg.2021010 |
| [17] |
Peng Zhang. Multiperiod mean semi-absolute deviation interval portfolio selection with entropy constraints. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1169-1187. doi: 10.3934/jimo.2016067 |
| [18] |
Editorial Office. RETRACTION: Peng Zhang, Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 2019, 15 (2) : 537-564. doi: 10.3934/jimo.2018056 |
| [19] |
Sanyi Tang, Lansun Chen. Modelling and analysis of integrated pest management strategy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 759-768. doi: 10.3934/dcdsb.2004.4.759 |
| [20] |
Jia Shu, Jie Sun. Designing the distribution network for an integrated supply chain. Journal of Industrial & Management Optimization, 2006, 2 (3) : 339-349. doi: 10.3934/jimo.2006.2.339 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]