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Minimal Time Vessel Routing in a Time-Dependent Environment

Author

Listed:
  • Anastassios N. Perakis

    (The University of Michigan, Ann Arbor, Michigan 48109)

  • Nikiforos A. Papadakis

    (The University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We examine the two-dimensional minimal time routing problem for a vessel traveling from an origin to several ordered destination points. The sailing space is characterized by time-dependent routing properties. The controls are the power setting and the heading. For the vessel performance model, we prove that the optimal power setting always takes its upper permissible value. Moreover, appropriate first variation considerations result in local optimality conditions which, combined with global boundary conditions, form the framework of our “broken extremal” approach. The algorithmic implementation of the methodologies developed is also discussed. In particular, we emphasize that if the departure time from the origin location is known, the problem becomes much easier than the one with unspecified departure time. Elliptical bounds for the optimal state evolution are derived, significantly reducing the dimensionality of the problem. Finally, we present numerical examples based on the above methodologies.

Suggested Citation

  • Anastassios N. Perakis & Nikiforos A. Papadakis, 1989. "Minimal Time Vessel Routing in a Time-Dependent Environment," Transportation Science, INFORMS, vol. 23(4), pages 266-276, November.
    • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:4:p:266-276
    DOI: 10.1287/trsc.23.4.266
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    Cited by:

    1. Bektaş, Tolga & Ehmke, Jan Fabian & Psaraftis, Harilaos N. & Puchinger, Jakob, 2019. "The role of operational research in green freight transportation," European Journal of Operational Research, Elsevier, vol. 274(3), pages 807-823.
    2. Lo, Hong K. & McCord, Mark R., 1995. "Routing through dynamic ocean currents: General heuristics and empirical results in the gulf stream region," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 109-124, April.
    3. Meng, Qiang & Du, Yuquan & Wang, Yadong, 2016. "Shipping log data based container ship fuel efficiency modeling," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 207-229.
    4. Shuaian Wang & Dan Zhuge & Lu Zhen & Chung-Yee Lee, 2021. "Liner Shipping Service Planning Under Sulfur Emission Regulations," Transportation Science, INFORMS, vol. 55(2), pages 491-509, March.
    5. Irina S. Dolinskaya, 2012. "Optimal path finding in direction, location, and time dependent environments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 325-339, August.
    6. Irina S. Dolinskaya & Marina A. Epelman & Esra Şişikoğlu Sir & Robert L. Smith, 2016. "Parameter-Free Sampled Fictitious Play for Solving Deterministic Dynamic Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 631-655, May.
    7. Lo, Hong K. & McCord, Mark R., 1998. "Adaptive ship routing through stochastic ocean currents: general formulations and empirical results," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 547-561, September.

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