A Study on the Dynamic Programming-based Algorithm for the Dual-spreader Quay Crane Scheduling

Abstract

As economies of scale in container transport are maximized with the introduction of mega container ships, ports and terminals are also making great efforts to prepare for an increase in their capacities. One example of such efforts is the use of a new type of quay crane that can simultaneously lift more than one container at a time. This quay crane can lift one or more containers depending on its lifting mode. However, scheduling of this crane is more complicated than scheduling of existing quay cranes because it is necessary to consider the weight limit of containers to be lifted, and the set-up time required for changing the lifting mode. Previous study has already mentioned the importance of this problem and suggested solutions for it, but since there are not many, verification of various approaches is necessary. This paper addresses the scheduling problem of dual-spreader quay crane that can lift up-to two containers at a time. We propose a Markov decision process (MDP) model for the problem. In order to reduce the computation time required to obtain a solution, instead of applying dynamic programming, we propose a heuristic that only considers a subset of states and transition functions used for searching solutions. Since this heuristic does not consider all possible states and transition functions, it cannot guarantee that an optimal solution is derived. However, as confirmed through experiments, it finds a solution close to the optimal solution for relatively small-sized instances. And, for larger-sized instances, while commercial software did not find an optimal solution for one hour, this heuristic can find a solution. Moreover, the solution from the proposed heuristic has better quality than the solution found by commercial software for one hour.