IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v20y2020i2d10.1007_s11067-019-09492-3.html
   My bibliography  Save this article

Multi-Trip Time-Dependent Vehicle Routing Problem with Soft Time Windows and Overtime Constraints

Author

Listed:
  • Ampol Karoonsoontawong

    (King Mongkut’s University of Technology Thonburi)

  • Puntipa Punyim

    (King Mongkut’s University of Technology Thonburi)

  • Wanvara Nueangnitnaraporn

    (Transportation Engineer, Systra MVA (Thailand) Limited)

  • Vatanavongs Ratanavaraha

    (Suranaree University of Technology)

Abstract

The multi-trip time-dependent vehicle routing problem with soft time windows and overtime constraints (MT-TDVRPSTW-OT) is considered in this paper. The modified hierarchical multi-objective formulation and the equivalent single-objective formulation are proposed. The iterative multi-trip tour construction and improvement (IMTTCI) procedure and the single-trip tour counterpart procedure with post-processing greedy heuristic (ISTTCI-GH) are proposed to solve the problem. These procedures are based on the ruin and recreate principle, and consider trade-offs among cost components (vehicle usage, number of early/late soft time window occurrences, transport distance, transport time, overtime and early/late soft time window penalty costs) in the search process. From the computational experiment, the IMTTCI procedure outperforms the existing efficient insertion heuristic with 42.09% improvement in number of vehicles and 24.30% improvement in travel time for the constant-speed multi-trip vehicle routing problem with hard time windows and shift time limits, a special case of MT-TDVRPSTW-OT problem, on all problem instances. For the MT-TDVRPSTW-OT problem, the ISTTCI-GH and the IMTTCI outperform the ISTTCI on all problem groups by 43.21% and 69.44% in the number of vehicles (the primary objective), respectively. The IMTTCI outperforms the ISTTCI-GH in number of vehicles by 51.07%, but takes 42.83% longer CPU time than the ISTTCI-GH. The performance of IMTTCI in terms of the primary objective improves with the increase of mean speed as well as the increase of time window width and planning horizon across all customer configuration types, tighter/looser time windows, shorter/longer planning horizon and various time-dependent travel speed profiles. The sensitivity analysis of different problem parameters is performed. The complexity analysis of the proposed procedures shows that the proposed procedures are solvable in polynomial time, and from the computational results the relationships between the CPU time and problem size confirm this. For the MT-VRPSTW-OT, a mixed integer program and the special case of MT-TDVRPSTW-OT, on 12-customer instances, the proposed IMTTCI algorithm yields the average optimality gap of 1.35% with the average CPU time of 0.66 seconds, whereas the GAMS/CPLEX solver yields the average optimality gap of 0.83% with the average CPU time of 256.39 seconds. The proposed IMTTCI algorithm yields only 0.52% greater optimality gap but 388 times faster CPU time than the commercial solver.

Suggested Citation

  • Ampol Karoonsoontawong & Puntipa Punyim & Wanvara Nueangnitnaraporn & Vatanavongs Ratanavaraha, 2020. "Multi-Trip Time-Dependent Vehicle Routing Problem with Soft Time Windows and Overtime Constraints," Networks and Spatial Economics, Springer, vol. 20(2), pages 549-598, June.
    • Handle: RePEc:kap:netspa:v:20:y:2020:i:2:d:10.1007_s11067-019-09492-3
    DOI: 10.1007/s11067-019-09492-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-019-09492-3
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-019-09492-3?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. Malandraki, Chryssi & Dial, Robert B., 1996. "A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 90(1), pages 45-55, April.
    2. Lahyani, Rahma & Khemakhem, Mahdi & Semet, Frédéric, 2015. "Rich vehicle routing problems: From a taxonomy to a definition," European Journal of Operational Research, Elsevier, vol. 241(1), pages 1-14.
    3. Brandao, Jose & Mercer, Alan, 1997. "A tabu search algorithm for the multi-trip vehicle routing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 100(1), pages 180-191, July.
    4. Diego Cattaruzza & Nabil Absi & Dominique Feillet, 2016. "Vehicle routing problems with multiple trips," 4OR, Springer, vol. 14(3), pages 223-259, September.
    5. François, Véronique & Arda, Yasemin & Crama, Yves & Laporte, Gilbert, 2016. "Large neighborhood search for multi-trip vehicle routing," European Journal of Operational Research, Elsevier, vol. 255(2), pages 422-441.
    6. 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.
    7. Christophe Duhamel & Jean-Yves Potvin & Jean-Marc Rousseau, 1997. "A Tabu Search Heuristic for the Vehicle Routing Problem with Backhauls and Time Windows," Transportation Science, INFORMS, vol. 31(1), pages 49-59, February.
    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. Éric Taillard & Philippe Badeau & Michel Gendreau & François Guertin & Jean-Yves Potvin, 1997. "A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows," Transportation Science, INFORMS, vol. 31(2), pages 170-186, May.
    10. 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.
    11. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    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. Alexis Robbes & Yannick Kergosien & Virginie André & Jean-Charles Billaut, 2022. "Efficient heuristics to minimize the total tardiness of chemotherapy drug production and delivery," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 785-820, September.

    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. Tao Zhang & W. Art Chaovalitwongse & Yuejie Zhang, 2014. "Integrated Ant Colony and Tabu Search approach for time dependent vehicle routing problems with simultaneous pickup and delivery," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 288-309, July.
    2. 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.
    3. 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.
    4. M. Alinaghian & M. Ghazanfari & N. Norouzi & H. Nouralizadeh, 2017. "A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization," Networks and Spatial Economics, Springer, vol. 17(4), pages 1185-1211, December.
    5. W Maden & R Eglese & D Black, 2010. "Vehicle routing and scheduling with time-varying data: A case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 515-522, March.
    6. 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.
    7. 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.
    8. 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).
    9. Liu, Yiming & Roberto, Baldacci & Zhou, Jianwen & Yu, Yang & Zhang, Yu & Sun, Wei, 2023. "Efficient feasibility checks and an adaptive large neighborhood search algorithm for the time-dependent green vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 310(1), pages 133-155.
    10. Tan, K.C. & Chew, Y.H. & Lee, L.H., 2006. "A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 855-885, August.
    11. 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.
    12. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    13. Daqing Wu & Chenxiang Wu, 2022. "Research on the Time-Dependent Split Delivery Green Vehicle Routing Problem for Fresh Agricultural Products with Multiple Time Windows," Agriculture, MDPI, vol. 12(6), pages 1-28, May.
    14. Tikani, Hamid & Setak, Mostafa & Demir, Emrah, 2021. "A risk-constrained time-dependent cash-in-transit routing problem in multigraph under uncertainty," European Journal of Operational Research, Elsevier, vol. 293(2), pages 703-730.
    15. Jose Carlos Molina & Ignacio Eguia & Jesus Racero, 2018. "An optimization approach for designing routes in metrological control services: a case study," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 924-952, December.
    16. 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.
    17. 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.
    18. Yiming Liu & Yang Yu & Yu Zhang & Roberto Baldacci & Jiafu Tang & Xinggang Luo & Wei Sun, 2023. "Branch-Cut-and-Price for the Time-Dependent Green Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 14-30, January.
    19. Sébastien Mouthuy & Florence Massen & Yves Deville & Pascal Van Hentenryck, 2015. "A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows," Transportation Science, INFORMS, vol. 49(2), pages 223-238, May.
    20. Baals, Julian & Emde, Simon & Turkensteen, Marcel, 2023. "Minimizing earliness-tardiness costs in supplier networks—A just-in-time truck routing problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 707-741.

    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:kap:netspa:v:20:y:2020:i:2:d:10.1007_s11067-019-09492-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.