IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v45y2023i1d10.1007_s10878-022-00944-0.html
   My bibliography  Save this article

Approximation algorithms for some extensions of the maximum profit routing problem

Author

Listed:
  • Bogdan Armaselu

Abstract

In this paper, we consider extensions of the Maximum-Profit Public Transportation Route Planning Problem, or simply Maximum-Profit Routing Problem (MPRP), introduced in Armaselu and Daescu (Approximation algorithms for the maximum profit pick-up problem with time windows and capacity constraint, 2016. arXiv:1612.01038 , Interactive assisting framework for maximum profit routing in public transportation in smart cities, PETRA, 13–16, 2017). Specifically, we consider MPRP with Time-Variable Supply (MPRP-VS), in which the quantity $$q_i(t)$$ q i ( t ) supplied at site i is linearly increasing in time t, as opposed to the original MPRP problem, where the quantity is constant in time. For MPRP-VS, our main result is a $$5.5 \log {T} (1 + \epsilon ) \left( 1 + \frac{1}{1 + \sqrt{m}}\right) ^2$$ 5.5 log T ( 1 + ϵ ) 1 + 1 1 + m 2 approximation algorithm, where T is the latest time window and m is the number of vehicles used. We also study the MPRP with Multiple Vehicles per Site, in which a site may be visited by a vehicle multiple times, which can have 2 flavors: with quantities fixed in time (MPRP-M), and with time-variable quantities (MPRP-MVS). Our algorithmic solution to MPRP-VS can also improve upon the MPRP algorithm in Armaselu and Daescu (2017) under certain conditions. In addition, we simulate the MPRP-VS algorithm on a few benchmark, real-world, and synthetic instances.

Suggested Citation

  • Bogdan Armaselu, 2023. "Approximation algorithms for some extensions of the maximum profit routing problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-22, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00944-0
    DOI: 10.1007/s10878-022-00944-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-022-00944-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-022-00944-0?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. Christos H. Papadimitriou & Mihalis Yannakakis, 1993. "The Traveling Salesman Problem with Distances One and Two," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 1-11, February.
    2. Marshall L. Fisher & Kurt O. Jörnsten & Oli B. G. Madsen, 1997. "Vehicle Routing with Time Windows: Two Optimization Algorithms," Operations Research, INFORMS, vol. 45(3), pages 488-492, June.
    3. Michael Drexl, 2012. "Synchronization in Vehicle Routing---A Survey of VRPs with Multiple Synchronization Constraints," Transportation Science, INFORMS, vol. 46(3), pages 297-316, August.
    Full references (including those not matched with items on IDEAS)

    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. E Duman & M H Ozcelik & A N Ceranoglu, 2005. "A TSP (1,2) application arising in cable assembly shops," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 642-648, June.
    2. Niels Agatz & Paul Bouman & Marie Schmidt, 2018. "Optimization Approaches for the Traveling Salesman Problem with Drone," Transportation Science, INFORMS, vol. 52(4), pages 965-981, August.
    3. Timo Gschwind & Stefan Irnich, 2012. "Effective Handling of Dynamic Time Windows and Synchronization with Precedences for Exact Vehicle Routing," Working Papers 1211, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    5. Ren, Xuan & Froger, Aurélien & Jabali, Ola & Liang, Gongqian, 2024. "A competitive heuristic algorithm for vehicle routing problems with drones," European Journal of Operational Research, Elsevier, vol. 318(2), pages 469-485.
    6. Yanchao Liu, 2019. "A Progressive Motion-Planning Algorithm and Traffic Flow Analysis for High-Density 2D Traffic," Transportation Science, INFORMS, vol. 53(6), pages 1501-1525, November.
    7. Arda, Yasemin & Cattaruzza, Diego & François, Véronique & Ogier, Maxime, 2024. "Home chemotherapy delivery: An integrated production scheduling and multi-trip vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 317(2), pages 468-486.
    8. Liu, Fuh-Hwa Franklin & Shen, Sheng-Yuan, 1999. "A route-neighborhood-based metaheuristic for vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 118(3), pages 485-504, November.
    9. Nuraiman, Dian & Ozlen, Melih & Hearne, John, 2020. "A spatial decomposition based math-heuristic approach to the asset protection problem," Operations Research Perspectives, Elsevier, vol. 7(C).
    10. Raeesi, Ramin & Zografos, Konstantinos G., 2020. "The electric vehicle routing problem with time windows and synchronised mobile battery swapping," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 101-129.
    11. Meyer, Anne & Amberg, Boris, 2018. "Transport concept selection considering supplier milk runs – An integrated model and a case study from the automotive industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 147-169.
    12. Chase Murray & Mark Karwan, 2013. "A branch‐and‐bound‐based solution approach for dynamic rerouting of airborne platforms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 141-159, March.
    13. Ruf, Moritz & Cordeau, Jean-François, 2021. "Adaptive large neighborhood search for integrated planning in railroad classification yards," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 26-51.
    14. Bhoopalam, Anirudh Kishore & Agatz, Niels & Zuidwijk, Rob, 2018. "Planning of truck platoons: A literature review and directions for future research," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 212-228.
    15. Goel, Asvin & Meisel, Frank, 2013. "Workforce routing and scheduling for electricity network maintenance with downtime minimization," European Journal of Operational Research, Elsevier, vol. 231(1), pages 210-228.
    16. Klumpp, Matthias & Neukirchen, Thomas & Jäger, Stefanie, 2016. "Logistikqualifikation und Gamification: Der wissenschaftliche und fachpraktische Ansatz des Projektes MARTINA," ild Schriftenreihe 51, FOM Hochschule für Oekonomie & Management, Institut für Logistik- & Dienstleistungsmanagement (ild).
    17. 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.
    18. Li, Jiliu & Qin, Hu & Baldacci, Roberto & Zhu, Wenbin, 2020. "Branch-and-price-and-cut for the synchronized vehicle routing problem with split delivery, proportional service time and multiple time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    19. Federico Della Croce, 2016. "MP or not MP: that is the question," Journal of Scheduling, Springer, vol. 19(1), pages 33-42, February.
    20. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2015. "Branch-and-Price for the Active-Passive Vehicle-Routing Problem," Working Papers 1513, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    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:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00944-0. 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.