Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals

In this work, we focus on the integrated planning of the following problems faced within the context of seaside operations at container terminals: berth allocation, quay crane assignment, and quay crane scheduling. First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment problems called BACAP. Then we extend it by incorporating the crane scheduling problem as well, which is named BACASP. Although the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality, only small instances for BACASP can be solved optimally. To be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a postprocessing algorithm. We also develop a cutting plane algorithm for the case where this condition is not satisfied. This algorithm solves BACAP repeatedly by adding cuts generated from the optimal solutions at each trial until the aforementioned condition holds.