Model and heuristic for berth allocation in tidal bulk ports with stock level constraints

We consider the problem of allocating berth positions for vessels in tidal bulk port terminals. A berth is defined as a specific location alongside a quay where a ship loader is available for loading or unloading vessels, accommodating only one vessel at a time. In tidal ports, draft conditions depend on high tide conditions, since available depth at low tide is not adequate for the movement of ships. Some port terminals are associated with important transnational enterprises which maintain strong control over the stock level of their goods. Since the stock level sometimes depends on a continuous process of consumption or production of minerals, the decision to load or unload vessels must consider the amount of the bulk cargo stored in the port yards. Therefore, a basic criterion for decision making is to give priority to the vessels related to the most critical mineral stock level. A second basic criterion is to decide what sequence of vessels reduces the overall demurrage within a given planning horizon. This paper presents an integer linear programming model based on the transportation problem to represent the Berth Allocation Problem in Tidal Bulk ports with Stock level conditions (BAPTBS). Problem instances are solved by a commercial solver and by a Simulated Annealing-based algorithm (SA). The SA employs a problem-specific heuristic, becoming a valid alternative for finding out good solutions for difficult instances.