Mathematical models for the berth allocation problem in dry bulk terminals

Port terminals processing large cargo vessels play an important role in bulk material supply chains. This paper addresses the question of how to allocate vessels to a location on a berth and the sequence in which the vessels should be processed in order to minimize delays. An important consideration in the berth allocation is the presence of tidal constraints that limit the departure of fully loaded vessels from the terminal. We show how the berth allocation problem can be modeled as an integer program and discuss a number of ways to tighten the formulation in order to make it computationally tractable. In addition, a two‐phase method is developed for solving these problems. Empirical computational results demonstrate an order of magnitude improvement in performance. The two new approaches can solve significantly larger instances, producing faster solutions for small instances and much tighter bounds for large instances.