Fleet routing and scheduling problem based on constraints of chance

Tramp shipping transport is an important part of ocean transportation. However, facing the spot market with many uncertain conditions, it is not easy for fleet operators to plan vessel's routes and schedule in the later period time, especially considering the situation that loading time window for a lot of cargoes has strong randomness. This article designed a linear programming model with chance constraints for the time window of loading cargo. Before the optimization, a survey for the waiting time of ships for berths is carried out in some of the ports with large export volume. Combined with the degree of acceptance how long ship owners can wait for the berth, the uncertain time window constraints can be transformed into deterministic constraints. The model is solved by column generation optimization technique. The model and algorithm are verified by a case of Panamax bulker fleet planning in real market. The results show that the model and the algorithm proposed in the article can well work on large-scale problem and can achieve good precision. Also, via sensitivity analysis, we provide decision makers good reference to balance profit and risks coming from randomness.