Finding an Optimal Assignment of Berths Containers to Storage Areas in Port Terminals: Formulation, Complexity and Case Study

In order to reduce the congestion of ships in ports, two strategic interrelated scheduling problems need to be considered simultaneously. The firstis the Ships Assignment to Berths problem known by the Berth Allocation Problem (BAP) that seeks to reduce the time during which ships stay in ports. This objective is known in the scheduling theory by the flow time. We use a simple known rule called SPT to obtain a solution to the BAP. Even though this method is highly efficient and provides an optimal solution, it is applied on the assumption that all ships are ready for assignment at time zero. The second problem, whose modeling and resolution are the main contributions of this paper, attempts to reach an optimal Assignment of Ship containers to the Storage areas (SSA). The focus of this paper is twofold: First, it studies the assignment of ships to berths in a way that minimizes ships' stay time in the port. Second, it examines the optimization of the traveling time and containers dispersion while satisfying the storage capacities in the seaport container terminals. Worth noting is that the output of the first problem is used as one of the inputs to the second problem. In order to address the SSA problem, a Mixed Integer Linear Program model is developed. The program is illustrated with an example and the resolution time results for different high instances are presented. Besides, the complexity of the SSA problem is established by reducing the Numerical Matching with Target Sum Problems where all ship containers are allocated to the same storage area.