Optimal ice routing of a ship with icebreaker assistance

Offshore development and growing prospects of commercial shipping in the Arctic pose the challenge of optimal ship routing in ice. Route selection in spatially distributed ice conditions significantly affects the voyage time and determines the efficiency of shipping. Most of the applied methods of ice routing solve the problem of a single vessel route selection without considering icebreaker support. At the same time, the real practice of ice navigation is closely connected with icebreaker assistance. It allows reducing the voyage time and fuel consumption, while having additional costs for icebreaker services. Such opposite trends set an optimization task that has not been studied in detail before. In this article, we presented the formulation of a Single Vessel and Icebreaker Assisted Ice Routing optimization problem in non-stationary ice conditions. We considered the icebreaker assistance as an integral part of the overall route optimization problem, and used the economic criterion to optimize both ship route and amount of icebreaker involvement. The article contains the adapted mathematical formulations of classical graph-based and wave-based routing problems in order to consider icebreaker assistance. To prove the practical applicability of these formulations, we developed special subject-oriented research software and implemented there both graph-based (Dijkstra, A*) and the wave-based ice routing methods. Using this developments, we conducted several case studies and made the analysis of strengthens and weaknesses of the alternative routing methods in case of ice operation. The results of the study may serve an additional step to the practical implementation of ice routing technologies and planning of icebreaker resources.