IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v284y2020i3p906-919.html
   My bibliography  Save this article

Exact algorithms for the multi-pickup and delivery problem with time windows

Author

Listed:
  • Aziez, Imadeddine
  • Côté, Jean-François
  • Coelho, Leandro C.

Abstract

In the multi-pickup and delivery problem with time windows (MPDPTW) a set of vehicles must be routed to satisfy a set of client requests between given origins and destinations. A request is composed of several pickups of different items, followed by a single delivery at the client location. This paper introduces two new formulations for the MPDPTW, the 2-index formulation, and the asymmetric representatives formulation. In addition, we also present an existing 3-index formulation for this problem and improve it by means of several preprocessing and valid inequalities. We solve the problem exactly via a branch-and-cut algorithm. We introduce several families of valid inequalities to strengthen the LP relaxations of the proposed formulations. Computational results are reported on different types of instances to firstly highlight the advantage of adding different families of valid inequalities then to compare the performance of the different formulations presented in this paper. While the heuristic and exact algorithms of the literature prove optimality for 16 instances containing up to 50 nodes, we prove optimality for 41 instances for cases containing up to 100 nodes from the existing benchmark set.

Suggested Citation

  • Aziez, Imadeddine & Côté, Jean-François & Coelho, Leandro C., 2020. "Exact algorithms for the multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 284(3), pages 906-919.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:3:p:906-919
    DOI: 10.1016/j.ejor.2020.01.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720300771
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.01.040?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. Goeke, Dominik, 2019. "Granular tabu search for the pickup and delivery problem with time windows and electric vehicles," European Journal of Operational Research, Elsevier, vol. 278(3), pages 821-836.
    2. Savelsbergh, M. W. P., 1990. "An efficient implementation of local search algorithms for constrained routing problems," European Journal of Operational Research, Elsevier, vol. 47(1), pages 75-85, July.
    3. Roberto Baldacci & Enrico Bartolini & Aristide Mingozzi, 2011. "An Exact Algorithm for the Pickup and Delivery Problem with Time Windows," Operations Research, INFORMS, vol. 59(2), pages 414-426, April.
    4. Naccache, Salma & Côté, Jean-François & Coelho, Leandro C., 2018. "The multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 269(1), pages 353-362.
    5. 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.
    6. Letchford, Adam N. & Salazar-González, Juan-José, 2016. "Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 251(1), pages 74-84.
    7. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    8. Bettinelli, Andrea & Cacchiani, Valentina & Crainic, Teodor Gabriel & Vigo, Daniele, 2019. "A Branch-and-Cut-and-Price algorithm for the Multi-trip Separate Pickup and Delivery Problem with Time Windows at Customers and Facilities," European Journal of Operational Research, Elsevier, vol. 279(3), pages 824-839.
    9. Antonio Alonso-Ayuso & Paolo Detti & Laureano Escudero & M. Ortuño, 2003. "On Dual Based Lower Bounds for the Sequential Ordering Problem with Precedences and Due Dates," Annals of Operations Research, Springer, vol. 124(1), pages 111-131, November.
    10. The Jin Ai & Voratas Kachitvichyanukul, 2009. "A Particle Swarm Optimisation for Vehicle Routing Problem with Time Windows," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 6(4), pages 519-537.
    11. Escudero, L. F., 1988. "An inexact algorithm for the sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 37(2), pages 236-249, November.
    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. Li, Siqiao & Zhu, Xiaoning & Shang, Pan & Li, Tianqi & Liu, Wenqian, 2023. "Optimizing a shared freight and passenger high-speed railway system: A multi-commodity flow formulation with Benders decomposition solution approach," Transportation Research Part B: Methodological, Elsevier, vol. 172(C), pages 1-31.
    2. Côté, Jean-François & Alves de Queiroz, Thiago & Gallesi, Francesco & Iori, Manuel, 2023. "A branch-and-regret algorithm for the same-day delivery problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    3. Dessouky, Maged M & Hu, Shichun, 2021. "Dynamic Routing for Ride-Sharing," Institute of Transportation Studies, Working Paper Series qt6qq8r7hz, Institute of Transportation Studies, UC Davis.
    4. Kohar, Amit & Jakhar, Suresh Kumar & Agarwal, Yogesh K., 2023. "Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    5. Zhen, Lu & Baldacci, Roberto & Tan, Zheyi & Wang, Shuaian & Lyu, Junyan, 2022. "Scheduling heterogeneous delivery tasks on a mixed logistics platform," European Journal of Operational Research, Elsevier, vol. 298(2), pages 680-698.
    6. Arslan, A.M. & Agatz, N.A.H. & Srour, F.J., 2023. "Model Formulations for Pickup and Delivery Problems in Designated Driver Services," ERIM Report Series Research in Management ERS-2023-004-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Qin Song, 2023. "Semi-Open Multi-Distribution Center Path Planning with Time Windows," Sustainability, MDPI, vol. 15(6), pages 1-14, March.

    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. Naccache, Salma & Côté, Jean-François & Coelho, Leandro C., 2018. "The multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 269(1), pages 353-362.
    2. Schulz, Arne & Pfeiffer, Christian, 2024. "Using fixed paths to improve branch-and-cut algorithms for precedence-constrained routing problems," European Journal of Operational Research, Elsevier, vol. 312(2), pages 456-472.
    3. Sophie N. Parragh & Jorge Pinho de Sousa & Bernardo Almada-Lobo, 2015. "The Dial-a-Ride Problem with Split Requests and Profits," Transportation Science, INFORMS, vol. 49(2), pages 311-334, May.
    4. Guo, Jiaqi & Long, Jiancheng & Xu, Xiaoming & Yu, Miao & Yuan, Kai, 2022. "The vehicle routing problem of intercity ride-sharing between two cities," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 113-139.
    5. Cherkesly, Marilène & Gschwind, Timo, 2022. "The pickup and delivery problem with time windows, multiple stacks, and handling operations," European Journal of Operational Research, Elsevier, vol. 301(2), pages 647-666.
    6. Bolor Jargalsaikhan & Ward Romeijnders & Kees Jan Roodbergen, 2021. "A Compact Arc-Based ILP Formulation for the Pickup and Delivery Problem with Divisible Pickups and Deliveries," Transportation Science, INFORMS, vol. 55(2), pages 336-352, March.
    7. Cherkesly, Marilène & Desaulniers, Guy & Irnich, Stefan & Laporte, Gilbert, 2016. "Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks," European Journal of Operational Research, Elsevier, vol. 250(3), pages 782-793.
    8. Schaumann, Sarah K. & Bergmann, Felix M. & Wagner, Stephan M. & Winkenbach, Matthias, 2023. "Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics," European Journal of Operational Research, Elsevier, vol. 311(1), pages 88-111.
    9. Aziez, Imadeddine & Côté, Jean-François & Coelho, Leandro C., 2022. "Fleet sizing and routing of healthcare automated guided vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 161(C).
    10. Mahmoudi, Monirehalsadat & Chen, Junhua & Shi, Tie & Zhang, Yongxiang & Zhou, Xuesong, 2019. "A cumulative service state representation for the pickup and delivery problem with transfers," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 351-380.
    11. Zhang, Li & Liu, Zhongshan & Yu, Bin & Long, Jiancheng, 2024. "A ridesharing routing problem for airport riders with electric vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    12. Si, Jinhua & He, Fang & Lin, Xi & Tang, Xindi, 2024. "Vehicle dispatching and routing of on-demand intercity ride-pooling services: A multi-agent hierarchical reinforcement learning approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    13. Andrew Lim & Zhenzhen Zhang & Hu Qin, 2017. "Pickup and Delivery Service with Manpower Planning in Hong Kong Public Hospitals," Transportation Science, INFORMS, vol. 51(2), pages 688-705, May.
    14. 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.
    15. 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.
    16. Liu, Mengyang & Luo, Zhixing & Lim, Andrew, 2015. "A branch-and-cut algorithm for a realistic dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 267-288.
    17. Bongiovanni, Claudia & Kaspi, Mor & Geroliminis, Nikolas, 2019. "The electric autonomous dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 436-456.
    18. Michael Drexl, 2021. "On the one-to-one pickup-and-delivery problem with time windows and trailers," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 1115-1162, September.
    19. Ali Mehsin Alyasiry & Michael Forbes & Michael Bulmer, 2019. "An Exact Algorithm for the Pickup and Delivery Problem with Time Windows and Last-in-First-out Loading," Transportation Science, INFORMS, vol. 53(6), pages 1695-1705, November.
    20. Boshuai Zhao & Kai Wang & Wenchao Wei & Roel Leus, 2024. "The Dial-a-Ride Problem with Limited Pickups per Trip," Papers 2408.07602, arXiv.org, revised Aug 2024.

    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:ejores:v:284:y:2020:i:3:p:906-919. 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/locate/eor .

    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.