IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v166y2022icp143-182.html
   My bibliography  Save this article

Rich arc routing problem in city logistics: Models and solution algorithms using a fluid queue-based time-dependent travel time representation

Author

Listed:
  • Lu, Jiawei
  • Nie, Qinghui
  • Mahmoudi, Monirehalsadat
  • Ou, Jishun
  • Li, Chongnan
  • Zhou, Xuesong Simon

Abstract

City logistics, as an essential component of the city operation system, aims at managing the complex flow of goods and services from providers to customers efficiently. Delays associated with peak-period traffic congestion exists in both large and small metropolitan areas. As many of the service tasks in city logistics are needed to be performed during peak hours, operators of urban management movement should consider reducing the total trip time and delay when designing service plans. Equally important, the congestion impact of service vehicles to other road users should also be considered. In this paper, we focus on formulating and solving rich arc routing problems (RARPs) in city logistics with a congested urban environment. We highlight the needs of embedding a structurally parsimonious time-dependent travel time model in RARP for producing high-quality and practically useful solutions. A fluid queue model based analytical approach is presented for link travel time calibration in the form of polynomial arrival rate functions. Accordingly, system-wide (societal) impact of vehicles routing is analytically derived and incorporated into the RARP models which enables traffic managers to systematically consider operation costs and societal impacts when designing routing policies in real-life city logistics applications. Additionally, we develop two new representation schemes for time-dependent travel time modeling in RARPs, including a discretized time-expanded representation scheme and a nonlinear polynomial representation scheme. Three modeling approaches for RARPs are proposed, with different perspectives of capturing time-dependent travel time and formulating problem-specific constraints. With a real-life sprinkler truck routing problem as the representative example of RARP, we develop two efficient exact solution algorithms, including a Lagrangian relaxation-based method and a branch-and-price based method. The latter one is embedded with an enhanced parallel branch-and-bound algorithm. Extensive numerical experiments are conducted based on real-world networks and traffic flow data to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Lu, Jiawei & Nie, Qinghui & Mahmoudi, Monirehalsadat & Ou, Jishun & Li, Chongnan & Zhou, Xuesong Simon, 2022. "Rich arc routing problem in city logistics: Models and solution algorithms using a fluid queue-based time-dependent travel time representation," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 143-182.
    • Handle: RePEc:eee:transb:v:166:y:2022:i:c:p:143-182
    DOI: 10.1016/j.trb.2022.10.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261522001709
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2022.10.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yao, Yu & Van Woensel, Tom & Veelenturf, Lucas P. & Mo, Pengli, 2021. "The consistent vehicle routing problem considering path consistency in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 21-44.
    2. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    3. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2018. "The time-dependent pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 1-24.
    4. Li, Zhi-Chun & Huang, Hai-Jun & Yang, Hai, 2020. "Fifty years of the bottleneck model: A bibliometric review and future research directions," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 311-342.
    5. Lawrence D. Bodin & Samuel J. Kursh, 1978. "A Computer-Assisted System for the Routing and Scheduling of Street Sweepers," Operations Research, INFORMS, vol. 26(4), pages 525-537, August.
    6. Said Dabia & Stefan Ropke & Tom van Woensel & Ton De Kok, 2013. "Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 47(3), pages 380-396, August.
    7. Martinelli, Rafael & Pecin, Diego & Poggi, Marcus, 2014. "Efficient elementary and restricted non-elementary route pricing," European Journal of Operational Research, Elsevier, vol. 239(1), pages 102-111.
    8. Andres Figliozzi, Miguel, 2012. "The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 616-636.
    9. Juan-Pablo Riquelme-Rodríguez & Michel Gamache & André Langevin, 2014. "Periodic capacitated arc-routing problem with inventory constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(12), pages 1840-1852, December.
    10. Donati, Alberto V. & Montemanni, Roberto & Casagrande, Norman & Rizzoli, Andrea E. & Gambardella, Luca M., 2008. "Time dependent vehicle routing problem with a multi ant colony system," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1174-1191, March.
    11. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
    12. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    13. Laoucine Kerbache & T. van Woensel & N. Vandaele & Herbert Peremans, 2008. "Vehicle routing with dynamic travel times: A queueing approach," Post-Print hal-00465127, HAL.
    14. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    15. Belieres, Simon & Hewitt, Mike & Jozefowiez, Nicolas & Semet, Frédéric, 2021. "A time-expanded network reduction matheuristic for the logistics service network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    16. Stefan Irnich & Daniel Villeneuve, 2006. "The Shortest-Path Problem with Resource Constraints and k -Cycle Elimination for k (ge) 3," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 391-406, August.
    17. Chen, Huey-Kuo & Hsueh, Che-Fu & Chang, Mei-Shiang, 2006. "The real-time time-dependent vehicle routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 42(5), pages 383-408, September.
    18. Luke Marshall & Natashia Boland & Martin Savelsbergh & Mike Hewitt, 2021. "Interval-Based Dynamic Discretization Discovery for Solving the Continuous-Time Service Network Design Problem," Transportation Science, INFORMS, vol. 55(1), pages 29-51, 1-2.
    19. Zhang, Yongxiang & Peng, Qiyuan & Yao, Yu & Zhang, Xin & Zhou, Xuesong, 2019. "Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 344-379.
    20. Thibaut Vidal & Rafael Martinelli & Tuan Anh Pham & Minh Hoàng Hà, 2021. "Arc Routing with Time-Dependent Travel Times and Paths," Transportation Science, INFORMS, vol. 55(3), pages 706-724, May.
    21. Hamza Ben Ticha & Nabil Absi & Dominique Feillet & Alain Quilliot & Tom Woensel, 2021. "The Time-Dependent Vehicle Routing Problem with Time Windows and Road-Network Information," SN Operations Research Forum, Springer, vol. 2(1), pages 1-25, March.
    22. Huang, Yixiao & Zhao, Lei & Van Woensel, Tom & Gross, Jean-Philippe, 2017. "Time-dependent vehicle routing problem with path flexibility," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 169-195.
    23. Xiao, Yiyong & Konak, Abdullah, 2016. "The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 88(C), pages 146-166.
    24. Diego Cattaruzza & Nabil Absi & Dominique Feillet & Jesús González-Feliu, 2017. "Vehicle routing problems for city logistics," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 51-79, March.
    25. Ziliaskopoulos, Athanasios K. & Mahmassani, Hani S., 1996. "A note on least time path computation considering delays and prohibitions for intersection movements," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 359-367, October.
    26. Mourao, Maria Candida & Amado, Ligia, 2005. "Heuristic method for a mixed capacitated arc routing problem: A refuse collection application," European Journal of Operational Research, Elsevier, vol. 160(1), pages 139-153, January.
    27. Van Woensel, T. & Kerbache, L. & Peremans, H. & Vandaele, N., 2008. "Vehicle routing with dynamic travel times: A queueing approach," European Journal of Operational Research, Elsevier, vol. 186(3), pages 990-1007, May.
    28. Shang, Pan & Li, Ruimin & Guo, Jifu & Xian, Kai & Zhou, Xuesong, 2019. "Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 135-167.
    29. O. Jabali & T. Van Woensel & A. de Kok & C. Lecluyse & H. Peremans, 2009. "Time-dependent vehicle routing subject to time delay perturbations," IISE Transactions, Taylor & Francis Journals, vol. 41(12), pages 1049-1066.
    30. Natashia Boland & Mike Hewitt & Luke Marshall & Martin Savelsbergh, 2017. "The Continuous-Time Service Network Design Problem," Operations Research, INFORMS, vol. 65(5), pages 1303-1321, October.
    31. Bernhard Fleischmann & Martin Gietz & Stefan Gnutzmann, 2004. "Time-Varying Travel Times in Vehicle Routing," Transportation Science, INFORMS, vol. 38(2), pages 160-173, May.
    32. Tagmouti, Mariam & Gendreau, Michel & Potvin, Jean-Yves, 2007. "Arc routing problems with time-dependent service costs," European Journal of Operational Research, Elsevier, vol. 181(1), pages 30-39, August.
    33. Chryssi Malandraki & Mark S. Daskin, 1992. "Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms," Transportation Science, INFORMS, vol. 26(3), pages 185-200, August.
    34. Benjamin Dussault & Bruce Golden & Edward Wasil, 2014. "The downhill plow problem with multiple plows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(10), pages 1465-1474, October.
    35. Scherr, Yannick Oskar & Hewitt, Mike & Neumann Saavedra, Bruno Albert & Mattfeld, Dirk Christian, 2020. "Dynamic discretization discovery for the service network design problem with mixed autonomous fleets," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 164-195.
    36. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    37. Jean-François Cordeau, 2006. "A Branch-and-Cut Algorithm for the Dial-a-Ride Problem," Operations Research, INFORMS, vol. 54(3), pages 573-586, June.
    38. Vu, Duc Minh & Hewitt, Mike & Vu, Duc D., 2022. "Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery," European Journal of Operational Research, Elsevier, vol. 302(3), pages 831-846.
    39. Remy Spliet & Said Dabia & Tom Van Woensel, 2018. "The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 52(2), pages 261-276, March.
    40. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    41. Tom van Woensel & Laoucine Kerbache & Herbert Peremans & Nico Vandaele, 2007. "A Queueing Framework for Routing Problems with Time-dependent Travel Times," Post-Print hal-00465130, HAL.
    42. Carey, Malachy & Humphreys, Paul & McHugh, Marie & McIvor, Ronan, 2014. "Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 90-104.
    43. Mourao, M. Candida & Almeida, M. Teresa, 2000. "Lower-bounding and heuristic methods for a refuse collection vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 121(2), pages 420-434, March.
    44. Yao, Yu & Zhu, Xiaoning & Dong, Hongyu & Wu, Shengnan & Wu, Hailong & Carol Tong, Lu & Zhou, Xuesong, 2019. "ADMM-based problem decomposition scheme for vehicle routing problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 156-174.
    45. Ghali, M. O. & Smith, M. J., 1995. "A model for the dynamic system optimum traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 29(3), pages 155-170, June.
    46. Tong, Lu & Zhou, Xuesong & Miller, Harvey J., 2015. "Transportation network design for maximizing space–time accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 555-576.
    47. Mahmoudi, Monirehalsadat & Zhou, Xuesong, 2016. "Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 19-42.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tingting Li & Shejun Deng & Caoye Lu & Yong Wang & Huajun Liao, 2023. "Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation," Sustainability, MDPI, vol. 15(22), pages 1-16, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    2. Verbeeck, C. & Sörensen, K. & Aghezzaf, E.-H. & Vansteenwegen, P., 2014. "A fast solution method for the time-dependent orienteering problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 419-432.
    3. Said Dabia & Stefan Ropke & Tom van Woensel & Ton De Kok, 2013. "Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 47(3), pages 380-396, August.
    4. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2018. "The time-dependent pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 1-24.
    5. Pan, Binbin & Zhang, Zhenzhen & Lim, Andrew, 2021. "Multi-trip time-dependent vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 291(1), pages 218-231.
    6. Guo, Feng & Wei, Qu & Wang, Miao & Guo, Zhaoxia & Wallace, Stein W., 2023. "Deep attention models with dimension-reduction and gate mechanisms for solving practical time-dependent vehicle routing problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    7. Diego Cattaruzza & Nabil Absi & Dominique Feillet & Jesús González-Feliu, 2017. "Vehicle routing problems for city logistics," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 51-79, March.
    8. Nicolas Rincon-Garcia & Ben J. Waterson & Tom J. Cherrett, 2018. "Requirements from vehicle routing software: perspectives from literature, developers and the freight industry," Transport Reviews, Taylor & Francis Journals, vol. 38(1), pages 117-138, January.
    9. Rifki, Omar & Chiabaut, Nicolas & Solnon, Christine, 2020. "On the impact of spatio-temporal granularity of traffic conditions on the quality of pickup and delivery optimal tours," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    10. Gmira, Maha & Gendreau, Michel & Lodi, Andrea & Potvin, Jean-Yves, 2021. "Tabu search for the time-dependent vehicle routing problem with time windows on a road network," European Journal of Operational Research, Elsevier, vol. 288(1), pages 129-140.
    11. Andres Figliozzi, Miguel, 2012. "The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 616-636.
    12. Sun, Peng & Veelenturf, Lucas P. & Dabia, Said & Van Woensel, Tom, 2018. "The time-dependent capacitated profitable tour problem with time windows and precedence constraints," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1058-1073.
    13. Hamza Ben Ticha & Nabil Absi & Dominique Feillet & Alain Quilliot & Tom Woensel, 2021. "The Time-Dependent Vehicle Routing Problem with Time Windows and Road-Network Information," SN Operations Research Forum, Springer, vol. 2(1), pages 1-25, March.
    14. Rincon-Garcia, Nicolas & Waterson, Ben & Cherrett, Tom J. & Salazar-Arrieta, Fernando, 2020. "A metaheuristic for the time-dependent vehicle routing problem considering driving hours regulations – An application in city logistics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 429-446.
    15. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    16. Schmidt, Carise E. & Silva, Arinei C.L. & Darvish, Maryam & Coelho, Leandro C., 2023. "Time-dependent fleet size and mix multi-depot vehicle routing problem," International Journal of Production Economics, Elsevier, vol. 255(C).
    17. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    18. Lecluyse, Christophe & Sörensen, Kenneth & Peremans, Herbert, 2013. "A network-consistent time-dependent travel time layer for routing optimization problems," European Journal of Operational Research, Elsevier, vol. 226(3), pages 395-413.
    19. Yao, Yu & Van Woensel, Tom & Veelenturf, Lucas P. & Mo, Pengli, 2021. "The consistent vehicle routing problem considering path consistency in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 21-44.
    20. Vu, Duc Minh & Hewitt, Mike & Vu, Duc D., 2022. "Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery," European Journal of Operational Research, Elsevier, vol. 302(3), pages 831-846.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:166:y:2022:i:c:p:143-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.