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Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem

Author

Listed:
  • Agostinho Agra

    (Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

  • Marielle Christiansen

    (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway)

  • Alexandrino Delgado

    (Cape Verde University, CP 163 Mindelo, Cape Verde)

Abstract

We consider a short sea fuel oil distribution problem occurring in the archipelago at Cape Verde. Here, an oil company is responsible for the routing and scheduling of ships between the islands such that the demand for various fuel oil products is satisfied during the planning horizon. Inventory management considerations are taken into account at the demand side but not at the supply side. The ports have restricted opening hours each day, so multiple time windows are considered. In contrast to the ships in many other studies within ship routing and scheduling, ships here spend considerable time in the ports compared to at sea. Hence, the time in port is modeled in detail by incorporating both a variable (un)loading time and a setup time for loading different products in the same ports. A mathematical model of the problem is presented and it includes a combined continuous and discrete time horizon because of the multiple time windows and a daily varying consumption rate of the various products in the different ports. We discuss several strategies to improve the proposed model, such as tightening bounds, using extended formulations, and including valid inequalities. The computational study shows that the real problem can be solved to optimality within reasonable time by the use of improved formulations based on a combination of such strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:1:p:108-124
    DOI: 10.1287/trsc.1120.0416
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    References listed on IDEAS

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    4. Roar Grønhaug & Marielle Christiansen & Guy Desaulniers & Jacques Desrosiers, 2010. "A Branch-and-Price Method for a Liquefied Natural Gas Inventory Routing Problem," Transportation Science, INFORMS, vol. 44(3), pages 400-415, August.
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    1. 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.
    2. Archetti, Claudia & Speranza, M. Grazia & Boccia, Maurizio & Sforza, Antonio & Sterle, Claudio, 2020. "A branch-and-cut algorithm for the inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 282(3), pages 886-895.
    3. Kirschstein, Thomas, 2018. "Rail transportation planning in the chemical industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 112(C), pages 142-160.
    4. Agostinho Agra & Marielle Christiansen & Lars Magnus Hvattum & Filipe Rodrigues, 2018. "Robust Optimization for a Maritime Inventory Routing Problem," Transportation Science, INFORMS, vol. 52(3), pages 509-525, 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. 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.
    7. 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.
    8. De, Arijit & Choudhary, Alok & Turkay, Metin & Tiwari, Manoj K., 2021. "Bunkering policies for a fuel bunker management problem for liner shipping networks," European Journal of Operational Research, Elsevier, vol. 289(3), pages 927-939.
    9. Jørgen Bjaarstad Nikolaisen & Sofie Smith Vågen & Peter Schütz, 2023. "Solving a maritime inventory routing problem under uncertainty using optimization and simulation," Computational Management Science, Springer, vol. 20(1), pages 1-27, December.
    10. 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.
    11. Zelda B. Zabinsky & Pattamon Dulyakupt & Shabnam Zangeneh-Khamooshi & Cao Xiao & Pengbo Zhang & Seksan Kiatsupaibul & Joseph A. Heim, 2020. "Optimal collection of medical specimens and delivery to central laboratory," Annals of Operations Research, Springer, vol. 287(1), pages 537-564, April.
    12. Katrin Heßler & Stefan Irnich, 2021. "Partial Dominance in Branch-Price-and-Cut for the Basic Multi-Compartment Vehicle-Routing Problem," Working Papers 2115, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    13. Ostermeier, Manuel & Henke, Tino & Hübner, Alexander & Wäscher, Gerhard, 2021. "Multi-compartment vehicle routing problems: State-of-the-art, modeling framework and future directions," European Journal of Operational Research, Elsevier, vol. 292(3), pages 799-817.
    14. Ioannis Fragkos & Bert De Reyck, 2016. "Improving the Maritime Transshipment Operations of the Noble Group," Interfaces, INFORMS, vol. 46(3), pages 203-217, April.
    15. 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.
    16. Miranda, Pablo A. & Blazquez, Carola A. & Vergara, Rodrigo & Weitzler, Sebastian, 2015. "A novel methodology for designing a household waste collection system for insular zones," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 227-247.
    17. 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.
    18. Li, Feng & Yang, Dong & Wang, Shuaian & Weng, Jinxian, 2019. "Ship routing and scheduling problem for steel plants cluster alongside the Yangtze River," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 198-210.
    19. Christiansen, Marielle & Fagerholt, Kjetil & Rachaniotis, Nikolaos P. & Stålhane, Magnus, 2017. "Operational planning of routes and schedules for a fleet of fuel supply vessels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 163-175.

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