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Integer Programming Methods for a Vessel Scheduling Problem

Author

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  • Leif H. Appelgren

    (Salén Shipping Companies, Stockholm, Sweden)

Abstract

In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53--68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem.

Suggested Citation

  • Leif H. Appelgren, 1971. "Integer Programming Methods for a Vessel Scheduling Problem," Transportation Science, INFORMS, vol. 5(1), pages 64-78, February.
    • Handle: RePEc:inm:ortrsc:v:5:y:1971:i:1:p:64-78
    DOI: 10.1287/trsc.5.1.64
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    Cited by:

    1. Ricardo Gatica & Pablo Miranda, 2011. "Special Issue on Latin-American Research: A Time Based Discretization Approach for Ship Routing and Scheduling with Variable Speed," Networks and Spatial Economics, Springer, vol. 11(3), pages 465-485, September.
    2. Nikiforos A. Papadakis & Anastassios N. Perakis, 1989. "A nonlinear approach to the multiorigin, multidestination fleet deployment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 515-528, August.
    3. Wang, Xiubin & Regan, Amelia C., 2002. "Local truckload pickup and delivery with hard time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 97-112, February.
    4. Jahn, Carlos & Kersten, Wolfgang & Ringle, Christian M. (ed.), 2019. "Digital Transformation in Maritime and City Logistics: Smart Solutions for Logistics," Proceedings of the Hamburg International Conference of Logistics (HICL), Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management, volume 28, number 28.
    5. Hennig, F. & Nygreen, B. & Christiansen, M. & Fagerholt, K. & Furman, K.C. & Song, J. & Kocis, G.R. & Warrick, P.H., 2012. "Maritime crude oil transportation – A split pickup and split delivery problem," European Journal of Operational Research, Elsevier, vol. 218(3), pages 764-774.
    6. Bredström, David & Rönnqvist, Mikael, 2006. "Supply Chain Optimization in Pulp Distribution using a Rolling Horizon Solution Approach," Discussion Papers 2006/17, Norwegian School of Economics, Department of Business and Management Science.
    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. Marshall L. Fisher & Moshe B. Rosenwein, 1989. "An interactive optimization system for bulk‐cargo ship scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 27-42, February.
    9. 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.
    10. Shih, Li-Hsing, 1997. "Planning of fuel coal imports using a mixed integer programming method," International Journal of Production Economics, Elsevier, vol. 51(3), pages 243-249, September.
    11. Zhang, Ruiyou & Lu, Jye-Chyi & Wang, Dingwei, 2014. "Container drayage problem with flexible orders and its near real-time solution strategies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 235-251.
    12. Said El Noshokaty, 2017. "Shipping Optimisation Systems (SOS): tramp optimisation perspective," Journal of Shipping and Trade, Springer, vol. 2(1), pages 1-36, December.
    13. Meng, Qiang & Wang, Shuaian & Lee, Chung-Yee, 2015. "A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 1-19.
    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. Hee-Su Hwang & Siriwat Visoldilokpun & Jay M. Rosenberger, 2008. "A Branch-and-Price-and-Cut Method for Ship Scheduling with Limited Risk," Transportation Science, INFORMS, vol. 42(3), pages 336-351, August.
    16. Rizvanolli, Anisa & Haupt, Alexander & Müller, Peter Marvin & Dornemann, Jorin, 2019. "Fleet based schedule optimisation for product tanker considering shipʼs stability," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Jahn, Carlos & Kersten, Wolfgang & Ringle, Christian M. (ed.), Digital Transformation in Maritime and City Logistics: Smart Solutions for Logistics. Proceedings of the Hamburg International Conference of Logistics, volume 28, pages 395-426, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    17. Marielle Christiansen & Kjetil Fagerholt & David Ronen, 2004. "Ship Routing and Scheduling: Status and Perspectives," Transportation Science, INFORMS, vol. 38(1), pages 1-18, February.
    18. Zolfagharinia, Hossein & Haughton, Michael A., 2017. "Operational flexibility in the truckload trucking industry," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 437-460.
    19. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.

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