Berth scheduling for container terminals by using a sub-gradient optimization technique

A method for establishing a berth schedule consisting of berthing times and berthing positions of containerships in port container terminals is addressed in this paper. Each vessel requires a specific amount of space on the berth during a predetermined length of time for unloading and loading containers. The berth schedule must be constructed in a way to satisfy requests from carriers on berthing times and minimize handling efforts during ship operation. A mixed integer program is formulated for the berth-scheduling problem, which can be solved using a commercial package. In order to overcome the computational load of the mixed integer program, the formulation is converted into another integer linear program in which the solution space of the berth and the time is discretized. A Lagrangean relaxation model of the discretized model is solved using a sub-gradient optimization technique. Results of a numerical experiment are provided and discussed.