IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v6y2025i2d10.1007_s43069-025-00454-9.html
   My bibliography  Save this article

Fractional Programming-Based Heuristic: An Efficient Method for Marine Inventory Routing Problem

Author

Listed:
  • Mohammad Nasir Yarahmadi

    (Amirkabir University of Technology (Tehran Polytechnic))

  • Seyed Ali MirHassani

    (Amirkabir University of Technology (Tehran Polytechnic))

  • Farnaz Hooshmand

    (Amirkabir University of Technology (Tehran Polytechnic))

Abstract

This study investigates a specific category of Marine Inventory Routing Problems (MIRPs), which involves the supply and demand management of a port inventory under vessel routing constraints. MIRP is typically formulated as mixed-integer linear programming models which present computational challenges when employing existing solvers. To address the computational difficulties of the MIRP, researchers have explored numerous approximation, decomposition, and heuristic approaches to generate effective and practical solutions. Given that the feasibility pump method (FPM) can find feasible solutions for MILP models, this paper seeks to adopt a recently addressed version of FPM to find feasible solutions for MIRP. We refer to our approach as a heuristic method based on fractional programming (HBFP) and, through computational experiments, show its superiority over the FPM when tackling large-scale instances of MIRP.

Suggested Citation

  • Mohammad Nasir Yarahmadi & Seyed Ali MirHassani & Farnaz Hooshmand, 2025. "Fractional Programming-Based Heuristic: An Efficient Method for Marine Inventory Routing Problem," SN Operations Research Forum, Springer, vol. 6(2), pages 1-19, June.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00454-9
    DOI: 10.1007/s43069-025-00454-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-025-00454-9
    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/s43069-025-00454-9?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

    for a different version of it.

    References listed on IDEAS

    as
    1. M. N. Yarahmadi & S. A. MirHassani & F. Hooshmand, 2023. "A heuristic method to find a quick feasible solution based on the ratio programming," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    2. Dimitri J. Papageorgiou & Ahmet B. Keha & George L. Nemhauser & Joel Sokol, 2014. "Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 825-847, November.
    3. Bilgen, Bilge & Ozkarahan, Irem, 2007. "A mixed-integer linear programming model for bulk grain blending and shipping," International Journal of Production Economics, Elsevier, vol. 107(2), pages 555-571, June.
    4. Sonia Cafieri & Claudia D’Ambrosio, 2018. "Feasibility pump for aircraft deconfliction with speed regulation," Journal of Global Optimization, Springer, vol. 71(3), pages 501-515, July.
    5. Al-Khayyal, Faiz & Hwang, Seung-June, 2007. "Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model," European Journal of Operational Research, Elsevier, vol. 176(1), pages 106-130, January.
    6. David Sacramento & Christine Solnon & David Pisinger, 2020. "Constraint Programming and Local Search Heuristic: a Matheuristic Approach for Routing and Scheduling Feeder Vessels in Multi-terminal Ports," SN Operations Research Forum, Springer, vol. 1(4), pages 1-33, December.
    7. Kristin Uggen & Marte Fodstad & Vibeke Nørstebø, 2013. "Using and extending fix-and-relax to solve maritime inventory routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 355-377, July.
    8. Nikolaos Charalambopoulos & Andreas C. Nearchou, 2021. "Ship Routing Using Genetic Algorithms," SN Operations Research Forum, Springer, vol. 2(3), pages 1-26, September.
    9. AGRA, Agostinho & ANDERSSON, Henrik & CHRISTIANSEN, Marielle & WOLSEY, Laurence A., 2013. "A maritime inventory routing problem: discrete time formulations and valid inequalities," LIDAM Reprints CORE 2584, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Dimitri J. Papageorgiou & Myun-Seok Cheon & George Nemhauser & Joel Sokol, 2015. "Approximate Dynamic Programming for a Class of Long-Horizon Maritime Inventory Routing Problems," Transportation Science, INFORMS, vol. 49(4), pages 870-885, November.
    11. YongJin Kim & YunChol Jong & JinWon Yu, 2021. "A parametric solution method for a generalized fractional programming problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 971-989, December.
    12. Faramroze G. Engineer & Kevin C. Furman & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "A Branch-Price-and-Cut Algorithm for Single-Product Maritime Inventory Routing," Operations Research, INFORMS, vol. 60(1), pages 106-122, February.
    13. Miller, David M., 1987. "An interactive, computer-aided ship scheduling system," European Journal of Operational Research, Elsevier, vol. 32(3), pages 363-379, December.
    14. Marielle Christiansen, 1999. "Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem," Transportation Science, INFORMS, vol. 33(1), pages 3-16, February.
    15. Amir Saeed Nikkhah Qamsari & Seyyed-Mahdi Hosseini-Motlagh & Seyed Farid Ghannadpour, 2022. "A column generation approach for an inventory routing problem with fuzzy time windows," Operational Research, Springer, vol. 22(2), pages 1157-1207, April.
    16. Awi Federgruen & Paul Zipkin, 1984. "A Combined Vehicle Routing and Inventory Allocation Problem," Operations Research, INFORMS, vol. 32(5), pages 1019-1037, October.
    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. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    2. Hemmati, Ahmad & Hvattum, Lars Magnus & Christiansen, Marielle & Laporte, Gilbert, 2016. "An iterative two-phase hybrid matheuristic for a multi-product short sea inventory-routing problem," European Journal of Operational Research, Elsevier, vol. 252(3), pages 775-788.
    3. Papageorgiou, Dimitri J. & Nemhauser, George L. & Sokol, Joel & Cheon, Myun-Seok & Keha, Ahmet B., 2014. "MIRPLib – A library of maritime inventory routing problem instances: Survey, core model, and benchmark results," European Journal of Operational Research, Elsevier, vol. 235(2), pages 350-366.
    4. Agostinho Agra & Marielle Christiansen & Kristine S. Ivarsøy & Ida Elise Solhaug & Asgeir Tomasgard, 2017. "Combined ship routing and inventory management in the salmon farming industry," Annals of Operations Research, Springer, vol. 253(2), pages 799-823, June.
    5. Mutlu, Fatih & Msakni, Mohamed K. & Yildiz, Hakan & Sönmez, Erkut & Pokharel, Shaligram, 2016. "A comprehensive annual delivery program for upstream liquefied natural gas supply chain," European Journal of Operational Research, Elsevier, vol. 250(1), pages 120-130.
    6. Nooshin Heidari & Ahmad Hemmati, 2023. "An ALNS-based matheuristic algorithm for a multi-product many-to-many maritime inventory routing problem," Computational Management Science, Springer, vol. 20(1), pages 1-23, December.
    7. Xu, Dongyang & Li, Kunpeng & Zou, Xuxia & Liu, Ling, 2017. "An unpaired pickup and delivery vehicle routing problem with multi-visit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 218-247.
    8. Agra, Agostinho & Christiansen, Marielle & Delgado, Alexandrino & Simonetti, Luidi, 2014. "Hybrid heuristics for a short sea inventory routing problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 924-935.
    9. Dimitri J. Papageorgiou & Myun-Seok Cheon & George Nemhauser & Joel Sokol, 2015. "Approximate Dynamic Programming for a Class of Long-Horizon Maritime Inventory Routing Problems," Transportation Science, INFORMS, vol. 49(4), pages 870-885, November.
    10. Kristin Uggen & Marte Fodstad & Vibeke Nørstebø, 2013. "Using and extending fix-and-relax to solve maritime inventory routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 355-377, July.
    11. Mingyu Li & Peter Schütz, 2020. "Planning Annual LNG Deliveries with Transshipment," Energies, MDPI, vol. 13(6), pages 1-24, March.
    12. Agra, Agostinho & Christiansen, Marielle & Wolsey, Laurence, 2022. "Improved models for a single vehicle continuous-time inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 297(1), pages 164-179.
    13. Archetti, Claudia & Christiansen, Marielle & Grazia Speranza, M., 2018. "Inventory routing with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 268(1), pages 314-324.
    14. Fokkema, Jan Eise & Land, Martin J. & Coelho, Leandro C. & Wortmann, Hans & Huitema, George B., 2020. "A continuous-time supply-driven inventory-constrained routing problem," Omega, Elsevier, vol. 92(C).
    15. Pietro Tiaraju Giavarina dos Santos & Denis Borenstein, 2025. "Combined cargo allocation and multi-ship routing and scheduling problem: application in the fertilizer industry," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 29-55, April.
    16. Mingyu Li & Kjetil Fagerholt & Peter Schütz, 2023. "Maritime inventory routing with transshipment: the case of Yamal LNG," Flexible Services and Manufacturing Journal, Springer, vol. 35(1), pages 269-294, March.
    17. Jørgen Glomvik Rakke & Henrik Andersson & Marielle Christiansen & Guy Desaulniers, 2015. "A New Formulation Based on Customer Delivery Patterns for a Maritime Inventory Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 384-401, May.
    18. Agostinho Agra & Marielle Christiansen & Alexandrino Delgado, 2013. "Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem," Transportation Science, INFORMS, vol. 47(1), pages 108-124, February.
    19. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    20. Harmen W. Bouma & Ruud H. Teunter, 2016. "The routed inventory pooling problem with multiple lateral transshipments," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3523-3533, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00454-9. 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.