A pareto simulated annealing for the integrated problem of berth and quay crane scheduling at maritime container terminals with multiple objectives and stochastic arrival times of vessels

Abstract

Efficient planning and scheduling of operations at congested seaside container terminals are issues of extreme importance because of the ever growing worldwide demand for container shipments. In this paper, the two main problems of berth and quay crane scheduling are integrated in a novel mathematical model. It is assumed that the arrival times of vessels are stochastic and can take any value that exists within a specific interval. The presented model includes three objectives. They are the minimisation of weighted deviations from the target berthing locations and times as well as departure delays. In the first solution attempt, an $$\epsilon $$-constraint method is used which employs an exact solver. Since the problem has high complexity and cannot be solved in large scales with an exact solver, a Pareto Simulated Annealing (PSA) algorithm is designed for it. It is proved that this metaheuristic can provide better non-dominated solutions in much shorter times compared to the $$\epsilon $$-constraint approach. Furthermore, the advantage of integrating the berth and quay crane scheduling is examined by comparing the results with the case that these two problems are processed separately.