New formulations and solutions for the strategic berth template problem

This paper develops new formulations for the Strategic Berth Template Problem, which combines strategic and operational decisions for medium-term berth planning of a given set of cyclically calling ships. The strategic decisions determine the ship calls that will be served, whereas the operational ones establish the berth template that will be applied in a cyclic fashion in the planning horizon. The proposed formulations use binary variables that classify served ships depending on whether or not their service starts in their arrival cycle or in the next one. This helps modeling the problem, since a closed linear expression can be obtained for the waiting times. Constraints imposing that the availability of the berths is respected at each time period can be derived by defining additional binary variables pointing to the starting service times of the served ships. Aggregating such variables over all berths leads to a relaxed formulation, which can be solved in remarkably small computing times. Furthermore, the solution of an auxiliary subproblem produces feasible solutions to the original problem as well as a simple optimality check. Disaggregating the initial service time variables for the different berths leads to a valid formulation. Numerical results from extensive computational tests over a set of benchmark instances from the literature are presented and analyzed. The obtained results assess the excellent performance of the proposed formulations, which outperform existing ones.