A Lagrangian heuristic for determining the speed and bunkering port of a ship

This study addresses the problem of determining the ship speed and bunkering ports in a ship route. All of the previous research has investigated the ship speed optimization issues by assuming that the ship navigates at constant speed or by ignoring the bunkering port decision. In this study, the problem of determining the variable speed and bunkering port is formulated mathematically with a nonlinear program in order to minimize the bunker fuel, ship time costs, and carbon tax imposed on greenhouse gas emissions. This study then provides a Lagrangian heuristic by deriving a property for a relaxed problem. The performance of the heuristic is evaluated and analysed using the data obtained from the literature, real practice and random generation.