New exact methods for the time-invariant berth allocation and quay crane assignment problem

Abstract

Efficient management of operations in seaport container terminals has become a critical issue, due to the increase in maritime traffic and the strong competition between ports. In this paper we focus on two seaside operational problems: the Berth Allocation Problem and the Quay Crane Assignment Problem, which are considered in an integrated way. For the continuous BACAP problem with time-invariant crane assignment we propose a new mixed integer linear model in which the vessels can be moored at any position on the quay, not requiring any quay discretization. The model is enhanced by adding several families of valid inequalities. The resulting model is able to solve instances with up to 50 vessels and outperforms other recently published proposals. In a second part, the model is extended to include the assignment of specific cranes to each vessel: the BACASP. This assignment ensures that the handling of each vessel can be carried out without disruptions, thus producing solutions that can be applied in practice. We also propose an iterative procedure for the BACASP in which the BACAP model is solved, and whenever its solution is not feasible for the BACASP, specific constraints are added until an optimal solution for the BACASP is found. Additionally, a branch-and-cut algorithm is proposed based on the cuts used in the iterative procedure. The computational study on several classes of test instances shows that problems with up to 40 vessels can be solved to optimality.