Tramp ship routing and scheduling with speed optimization

Tramp shipping companies are committed to transport a set of contracted cargoes and try to derive additional revenue from carrying optional spot cargoes. Traditionally, models for ship routing and scheduling problems are based on fixed speed and a given fuel consumption rate for each ship. However, in real life a ship's speed is variable within an interval, and fuel consumption per time unit can be approximated by a cubic function of speed. Here we present the tramp ship routing and scheduling problem with speed optimization, where speed on each sailing leg is introduced as a decision variable. We present a multi-start local search heuristic to solve this problem. To evaluate each move in the local search we have to determine the optimal speed for each sailing leg of a given ship route. To do this we propose two different algorithms. Extensive computational results show that the solution method solves problems of realistic size and that taking speed into consideration in tramp ship routing and scheduling significantly improves the solutions.