Integrated Laycan and Berth Allocation Problem

Handling vessels within the agreed time limits at a port with an optimal exploitation of its quays plays an important role in the improvement of port effectiveness as it reduces the stay time of vessels and avoid the payment of contractual penalties to shipowners due to the overrun of laytimes. In this paper, we propose a mixed zero-one linear model for a new problem called the integrated Laycan and Berth Allocation Problem with dynamic vessel arrivals in a port with multiple continuous quays. The model aims, first, to achieve an optimal berth plan that reduces the late departures of chartered vessels by maximizing the difference between their despatch money and demurrage charges, considering water depth and maximum waiting time constraints and the productivity that depends on berth positions and, second, to propose laycans for new vessels to charter. Only one binary variable is used to determine the spatiotemporal allocations of vessels and the spatiotemporal constraints of the problem are covered by a disjunctive constraint. An illustrative example and several numerical tests are provided.