Convex formulation of the maritime fleet size and mix problem considering battery electric ships

This paper focuses on the problem of determining a minimum-cost fleet of battery electric ships for a given liner shipping operation. The problem is strongly nonlinear and includes integer decision variables, which make it intractable for most real-world instances. The conventional approach in the literature is to formulate a linear approximation by restricting available ship types to a small number of predetermined alternatives. Contrary to the conventional linearization approach, this paper models the nonlinearities directly. We show that the nonlinearities have a hidden convex form uncovered by changes of variables. Computational experiments show that our convex formulation achieves 15.1% lower fleet cost on average and reduces solve time by at least 10 × compared to the linear formulation. The solve time advantage is attributed to the elimination of binary variables for ship type selection. Our implementation is available at https://github.com/ajritari/cvxfleet .