A linearized approach for liner ship fleet planning with demand uncertainty

In this paper, we focus on the liner Ship fleet planning (LSFP) with cargo demand uncertainty. The LSFP aims to determine which type of ships and how many of them are needed, and how to deploy and operate these ships. We first propose a mixed integer nonlinear programming model for the LSFP by taking into account cargo shipment demand uncertainty. We find that the fuel consumption cost of a ship can be approximated by a linear function with respect to its cruising speed, and we then proceed to build a mixed integer linear programming model that can approximate the originally proposed nonlinear programming model. The mixed integer programming model can be thus effectively solved by some optimization solvers. Finally, numerical examples are carried out to assess the linearized approach.