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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
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    References listed on IDEAS

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    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.
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