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A Branch-Price-and-Cut Algorithm for Single-Product Maritime Inventory Routing

Author

Listed:
  • Faramroze G. Engineer

    (School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, New South Wales 2308, Australia)

  • Kevin C. Furman

    (ExxonMobil Research and Engineering Company, Annandale, New Jersey 08801)

  • George L. Nemhauser

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Martin W. P. Savelsbergh

    (School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, New South Wales 2308, Australia)

  • Jin-Hwa Song

    (ExxonMobil Research and Engineering Company, Annandale, New Jersey 08801)

Abstract

A branch-price-and-cut algorithm is developed for a complex maritime inventory-routing problem with varying storage capacities and production/consumption rates at facilities. The resulting mixed-integer pricing problem is solved exactly and efficiently using a dynamic program that exploits certain “extremal” characteristics of the pricing problem. The formulation is tightened by using the problem's boundary conditions in preprocessing and to restrict the set of columns that are produced by the pricing problem. Branching schemes and cuts are introduced that can be implemented efficiently and that preserve the structure of the pricing problem. Some of the cuts are inspired by the capacity cuts known for the vehicle-routing problem, whereas others specifically target fractional solutions brought about by individual vessels “competing” for limited inventory at load ports and limited storage capacity at discharge ports. The branch-price-and-cut approach solves practically sized problems motivated by the operations of an oil company to optimality, and it provides reasonable bounds for larger instances.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:1:p:106-122
    DOI: 10.1287/opre.1110.0997
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Song, Ruidian & Zhao, Lei & Van Woensel, Tom & Fransoo, Jan C., 2019. "Coordinated delivery in urban retail," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 122-148.
    3. 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.
    4. 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.
    5. Guy Desaulniers & Jørgen G. Rakke & Leandro C. Coelho, 2016. "A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem," Transportation Science, INFORMS, vol. 50(3), pages 1060-1076, August.
    6. Henrik Andersson & Marielle Christiansen & Guy Desaulniers, 2016. "A new decomposition algorithm for a liquefied natural gas inventory routing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 564-578, January.
    7. Abdalrahman Algendi & Sebastián Urrutia & Lars Magnus Hvattum, 2023. "Optimizing production levels in maritime inventory routing with load-dependent speed optimization," Flexible Services and Manufacturing Journal, Springer, vol. 35(1), pages 111-141, March.
    8. 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.
    9. Hu, Weihong & Toriello, Alejandro & Dessouky, Maged, 2018. "Integrated inventory routing and freight consolidation for perishable goods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 548-560.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Cho, Jaeyoung & Lim, Gino J. & Kim, Seon Jin & Biobaku, Taofeek, 2018. "Liquefied natural gas inventory routing problem under uncertain weather conditions," International Journal of Production Economics, Elsevier, vol. 204(C), pages 18-29.
    15. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.

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