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Routing Container Ships Using Lagrangean Relaxation and Decomposition


  • Krishan Rana

    (The University of Toledo, Toledo, Ohio 43606)

  • R. G. Vickson

    (University of Waterloo, Waterloo, Ontario, Canada N2L 3G1)


International shipping is a multibillon dollar business and shipping companies may expect large benefits from improving the routing and scheduling processes of their ships. In this paper, we describe a container-ship routing scenario in which a shipping company provides services to a network of ports. We formulate a mathematical programming model that maximizes total profit (i.e., revenue minus operating costs) for multiple ships and determines: (a) the optimal sequence of ports of call for each ship, (b) the number of trips each ship makes in a planning horizon, and (c) the amount of cargo transported between any two ports by each ship. The model contains discrete, 0–1 and continuous variables, and nonlinear complicating constraints. The multiple container ship model is quite different from those of vehicle routing and traveling salesman problems. We use a decomposition method for the model as well as for the network in order to solve the problem. Several problems on 10- to 20-port networks are solved and the results presented.

Suggested Citation

  • Krishan Rana & R. G. Vickson, 1991. "Routing Container Ships Using Lagrangean Relaxation and Decomposition," Transportation Science, INFORMS, vol. 25(3), pages 201-214, August.
  • Handle: RePEc:inm:ortrsc:v:25:y:1991:i:3:p:201-214
    DOI: 10.1287/trsc.25.3.201

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    Cited by:

    1. Chen, Tzu-Li & Cheng, Chen-Yang & Chen, Yin-Yann & Chan, Li-Kai, 2015. "An efficient hybrid algorithm for integrated order batching, sequencing and routing problem," International Journal of Production Economics, Elsevier, vol. 159(C), pages 158-167.
    2. Yadong Wang & Qiang Meng & Haibo Kuang, 2019. "Intercontinental Liner Shipping Service Design," Transportation Science, INFORMS, vol. 53(2), pages 344-364, March.
    3. Berit D. Brouer & J. Fernando Alvarez & Christian E. M. Plum & David Pisinger & Mikkel M. Sigurd, 2014. "A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design," Transportation Science, INFORMS, vol. 48(2), pages 281-312, May.
    4. Zhao, Hui & Hu, Hao & Lin, Yisong, 2016. "Study on China-EU container shipping network in the context of Northern Sea Route," Journal of Transport Geography, Elsevier, vol. 53(C), pages 50-60.
    5. Brouer, Berit Dangaard & Desaulniers, Guy & Pisinger, David, 2014. "A matheuristic for the liner shipping network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 42-59.
    6. Marielle Christiansen, 1999. "Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem," Transportation Science, INFORMS, vol. 33(1), pages 3-16, February.
    7. Alfandari, Laurent & Davidović, Tatjana & Furini, Fabio & Ljubić, Ivana & Maraš, Vladislav & Martin, Sébastien, 2019. "Tighter MIP models for Barge Container Ship Routing," Omega, Elsevier, vol. 82(C), pages 38-54.
    8. Qiang Meng & Shuaian Wang & Henrik Andersson & Kristian Thun, 2014. "Containership Routing and Scheduling in Liner Shipping: Overview and Future Research Directions," Transportation Science, INFORMS, vol. 48(2), pages 265-280, May.
    9. Chen, Kang & Chen, Dongxu & Sun, Xueshan & Yang, Zhongzhen, 2016. "Container Ocean-transportation System Design with the factors of demand fluctuation and choice inertia of shippers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 267-281.
    10. Richa Agarwal & Özlem Ergun, 2008. "Ship Scheduling and Network Design for Cargo Routing in Liner Shipping," Transportation Science, INFORMS, vol. 42(2), pages 175-196, May.
    11. Harilaos N. Psaraftis, 2019. "Ship routing and scheduling: the cart before the horse conjecture," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(1), pages 111-124, March.
    12. Qiang Meng & Tingsong Wang, 2010. "A chance constrained programming model for short-term liner ship fleet planning problems," Maritime Policy & Management, Taylor & Francis Journals, vol. 37(4), pages 329-346, July.
    13. Zhongzhen Yang & Haiping Shi & Kang Chen & Hongli Bao, 2014. "Optimization of container liner network on the Yangtze River," Maritime Policy & Management, Taylor & Francis Journals, vol. 41(1), pages 79-96, January.
    14. Manuel Herrera & Per J. Agrell & Casiano Manrique-de-Lara-Peñate & Lourdes Trujillo, 2017. "Vessel capacity restrictions in the fleet deployment problem: an application to the Panama Canal," Annals of Operations Research, Springer, vol. 253(2), pages 845-869, June.
    15. Wang, Yadong & Meng, Qiang & Jia, Peng, 2019. "Optimal port call adjustment for liner container shipping routes," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 107-128.
    16. Berit Dangaard Brouer & Christian Vad Karsten & David Pisinger, 2017. "Optimization in liner shipping," 4OR, Springer, vol. 15(1), pages 1-35, March.
    17. Reinhardt, Line Blander & Pisinger, David & Sigurd, Mikkel M. & Ahmt, Jonas, 2020. "Speed optimizations for liner networks with business constraints," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1127-1140.
    18. Berit Dangaard Brouer & Christian Vad Karsten & David Pisinger, 2018. "Optimization in liner shipping," Annals of Operations Research, Springer, vol. 271(1), pages 205-236, December.

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