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A New Formulation Based on Customer Delivery Patterns for a Maritime Inventory Routing Problem

Author

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  • Jørgen Glomvik Rakke

    (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, 7491 Trondheim, Norway)

  • Henrik Andersson

    (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, 7491 Trondheim, Norway)

  • Marielle Christiansen

    (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, 7491 Trondheim, Norway)

  • Guy Desaulniers

    (Department of Mathematics and Industrial Engineering, École Polytechnique and GERAD, Montréal, Québec H3C 3A7, Canada)

Abstract

In this paper we address a maritime inventory routing problem encountered by one of the world’s largest producers of liquefied natural gas (LNG). The producer is responsible for the LNG inventories at the liquefaction plant, the loading port with a limited number of berths, and the routing and scheduling of a heterogeneous fleet of LNG ships. In addition, the producer has to fulfill a set of long-term contracts to customers all around the world. The producer’s goal is to create a minimum-cost long-term delivery program that respects the long-term contracts while maximizing revenue from selling LNG in the spot market. We introduce a new formulation for this problem arising from a novel decomposition scheme based on delivery patterns. To solve this formulation, we develop an exact branch-price-and-cut algorithm. Computational results show that this new formulation provides much tighter lower bounds than the only known mixed integer programming (MIP) formulation for this problem. Furthermore, on a set of 27 benchmark instances, the proposed branch-price-and-cut method clearly outperforms a commercial MIP solver applied to the existing MIP model.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:384-401
    DOI: 10.1287/trsc.2013.0503
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    References listed on IDEAS

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    1. Marielle Christiansen & Bjorn Nygreen, 1998. "A method for solving ship routing problemswith inventory constraints," Annals of Operations Research, Springer, vol. 81(0), pages 357-378, June.
    2. Elin Halvorsen-Weare & Kjetil Fagerholt, 2013. "Routing and scheduling in a liquefied natural gas shipping problem with inventory and berth constraints," Annals of Operations Research, Springer, vol. 203(1), pages 167-186, March.
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    5. 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.
    6. 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.
    7. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
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    Cited by:

    1. Ghiami, Yousef & Demir, Emrah & Van Woensel, Tom & Christiansen, Marielle & Laporte, Gilbert, 2019. "A deteriorating inventory routing problem for an inland liquefied natural gas distribution network," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 45-67.
    2. Liu, Baoli & Li, Zhi-Chun & Wang, Yadong, 2023. "A branch-and-price heuristic algorithm for the bunkering operation problem of a liquefied natural gas bunkering station in the inland waterways," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 145-170.
    3. 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.
    4. 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.
    5. Di Wu & Xuejun Ji & Fang Xiao & Shijie Sheng, 2022. "A Location Inventory Routing Optimisation Model and Algorithm for a Remote Island Shipping Network considering Emergency Inventory," Sustainability, MDPI, vol. 14(10), pages 1-22, May.
    6. Yazdani, Majid & Aouam, Tarik, 2023. "Shipment planning and safety stock placement in maritime supply chains with stochastic demand and transportation times," International Journal of Production Economics, Elsevier, vol. 263(C).
    7. Koza, David Franz & Ropke, Stefan & Boleda Molas, Anna, 2017. "The liquefied natural gas infrastructure and tanker fleet sizing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 99(C), pages 96-114.
    8. 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.

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