Abstract
To minimize bunker fuel consumption, ship captains choose suitable speed and heading to take advantage of ocean currents, wind, and wave when routing a ship between two ports. Conventional approaches discretize the space and time and then apply dynamic programming to find the optimal speed and heading of a ship at each time. Nevertheless, the resulting solution to the discretized problem may not converge to the optimal solution to the original continuous problem, even when the sizes of the discretization grids approach 0. To overcome this deficiency, we propose an improved dynamic programming approach. The novelty of the improved method lies in that we repeatedly re-discretize the space in both controlled and random manners to obtain better solutions. The improved dynamic programming approach provides significantly better solutions than the conventional approaches.
References
Bell, M.G.H., Liu, X., Angeloudis, P., Fonzone, A., Hosseinloo, S.H.: A frequency-based maritime container assignment model. Transp. Res. Part B 45(8), 1152–1161 (2011)
Bell, M.G.H., Liu, X., Rioult, J., Angeloudis, P.: A cost-based maritime container assignment model. Transp. Res. Part B 58, 58–70 (2013)
Fagerholt, K., Heimdal, S., Loktu, A.: Shortest path in the presence of obstacles: an application to ocean shipping. J. Oper. Res. Soc. 683–688 (2000)
Fagerholt, K., Hvattum, L.M., Johnsen, T.A.V., Korsvik, J.E.: Routing and scheduling in project shipping. Ann. Oper. Res. 207(1), 67–81 (2013)
Fagerholt, K., Laporte, G., Norstad, I.: Reducing fuel emissions by optimizing speed on shipping routes. J. Oper. Res. Soc. 61(3), 523–529 (2010)
Halvorsen-Weare, E.E., Fagerholt, K.: Routing and scheduling in a liquefied natural gas shipping problem with inventory and berth constraints. Ann. Oper. Res. 203(1), 167–186 (2013)
Haversine: Haversine formula. Wikipedia. (2014). http://en.wikipedia.org/wiki/Haversine_formula
Hvattum, L.M., Norstad, I., Fagerholt, K., Laporte, G.: Analysis of an exact algorithm for the vessel speed optimization problem. Networks 62(2), 132–135 (2013)
Lo, H.K., McCord, M.R.: Routing through dynamic ocean currents: general heuristics and empirical results in the gulf stream region. Transp. Res. Part B 29(2), 109–124 (1995)
Lo, H.K., McCord, M.R., Wall, C.K.: Value of ocean current information for strategic routing. Eur. J. Oper. Res. 55(2), 124–135 (1991)
Norstad, I., Fagerholt, K., Laporte, G.: Tramp ship routing and scheduling with speed optimization. Transp. Res. Part C 19(5), 853–865 (2011)
Ronen, D.: The effect of oil price on containership speed and fleet size. J. Oper. Res. Soc. 62(1), 211–216 (2011)
Wang, S., Meng, Q., Liu, Z.: Containership scheduling with transit-time-sensitive container shipment demand. Transp. Res. Part B 54, 68–83 (2013)
Zhen, L., Wang, K.: A stochastic programming model for multi-product oriented multi-channel component replenishment. Computers Oper. Res. 60, 79–90 (2015)
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Wang, S. A note on ship routing between ports. Optim Lett 11, 217–223 (2017). https://doi.org/10.1007/s11590-016-1000-1
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DOI: https://doi.org/10.1007/s11590-016-1000-1