A lagrangian relaxation based heuristic for the static berth allocation problem using the cutting plane method

One of the important seaside operations problems that received a lot of attention in the literature is the assignment of quay space and service time to vessels that have to be unloaded and loaded at a terminal. This problem is commonly referred to as the Berth Allocation Problem (BAP). Different approaches exist in the literature for the berth allocation problem (BAP). Some of those approaches consider static arrival of vessels, so called the static berth allocation problem (SBAP), while other approaches consider dynamic arrival of vessels, called the dynamic berth allocation problem (DBAP). Approaches also differ in the layout used for the quay. In this paper we study one of the SBAP models presented in literature. Since the SBAP is a non-deterministic polynomial-time (NP) problem, we applied a Lagrangian Relaxation heuristic technique with the application of cutting plane method on our problem. We coded the cutting plane method in Matlab, and ran it on different instances of the problem. In most of the cases that we studied, our solution technique converged to an optimal solution.