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Modelling path flows for a combined ship routingand inventory management problem

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  • Marielle Christiansen
  • Bjørn Nygreen

Abstract

We consider a combined time constrained ship routing and inventory managementproblem. A fleet of ships transports a single product between production and consumptionharbours. The transporter has the responsibility for keeping the stock level within its limitsat all actual harbours, and there should be no need to stop the production at any harboursdue to missing transportation possibilities. The number of arrivals to each harbour and thequantities loaded and discharged at each arrival are determined by the continuous productionrates at the harbours, the stock limits and the actual ships visiting the harbours. We use apath flow formulation for this planning problem, and generate paths for each ship includinginformation about the geographical route, the load quantity and start time at each harbourarrival. In addition, we generate paths for each harbour including information about thenumber of arrivals to the harbour, the load quantity and start time at each harbour arrival.We emphasise the formulation of the path generation problems which are subproblems inthe total planning problem. The generated paths appear as columns in a path flow problemwhich corresponds to a master problem. We use a column generation approach to solve thecontinuous problem. The solution is made integer optimal by branch-and-bound. Computationalresults indicate that a path flow formulation and an optimisation based solutionapproach work for real instances of the planning problem. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Marielle Christiansen & Bjørn Nygreen, 1998. "Modelling path flows for a combined ship routingand inventory management problem," Annals of Operations Research, Springer, vol. 82(0), pages 391-413, August.
  • Handle: RePEc:spr:annopr:v:82:y:1998:i:0:p:391-413:10.1023/a:1018979107222
    DOI: 10.1023/A:1018979107222
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    Cited by:

    1. 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.
    2. Sayarshad, Hamid R. & Gao, H. Oliver, 2018. "A non-myopic dynamic inventory routing and pricing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 83-98.
    3. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "The Fixed-Charge Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 578-596, November.
    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.
    5. Marielle Christiansen & Kjetil Fagerholt & David Ronen, 2004. "Ship Routing and Scheduling: Status and Perspectives," Transportation Science, INFORMS, vol. 38(1), pages 1-18, February.
    6. G Brønmo & M Christiansen & B Nygreen, 2007. "Ship routing and scheduling with flexible cargo sizes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1167-1177, September.
    7. H Gunnarsson & M Rönnqvist & D Carlsson, 2006. "A combined terminal location and ship routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 928-938, August.
    8. 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.
    9. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    10. 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.
    11. Marielle Christiansen, 1999. "Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem," Transportation Science, INFORMS, vol. 33(1), pages 3-16, February.
    12. 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.
    13. 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.
    14. Persson, Jan A. & Gothe-Lundgren, Maud, 2005. "Shipment planning at oil refineries using column generation and valid inequalities," European Journal of Operational Research, Elsevier, vol. 163(3), pages 631-652, June.
    15. 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.
    16. Kevin C. Furman & Jin-Hwa Song & Gary R. Kocis & Michael K. McDonald & Philip H. Warrick, 2011. "Feedstock Routing in the ExxonMobil Downstream Sector," Interfaces, INFORMS, vol. 41(2), pages 149-163, April.
    17. Alejandro Toriello & George Nemhauser & Martin Savelsbergh, 2010. "Decomposing inventory routing problems with approximate value functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 718-727, December.
    18. Brønmo, Geir & Nygreen, Bjørn & Lysgaard, Jens, 2010. "Column generation approaches to ship scheduling with flexible cargo sizes," European Journal of Operational Research, Elsevier, vol. 200(1), pages 139-150, January.
    19. Ann Campbell, 2006. "The Vehicle Routing Problem with Demand Range," Annals of Operations Research, Springer, vol. 144(1), pages 99-110, April.
    20. Gschwind, Timo, 2015. "A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 60-71.
    21. 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.
    22. 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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