Constraint Models for the Container Pre-Marshaling Problem

The container pre-marshaling problem (PMP) is an important optimization problem that arises in terminals where containers are stacked in bays before they are collected by vessels. However, if a due container is stacked underneath other containers, it is blocked, and additional relocations are necessary to retrieve the container from the bay, which can cause significantly delays. To avoid this effect, the PMP is concerned with finding a minimal number of container movements that result in a container bay without blocked containers. In this paper, we introduce a Constraint Programming (CP) formulation of the PMP and propose a specialized search heuristic that attempts to try out the most promising moves first. Furthermore, we present a robust variant of the problem that considers the uncertainty of the arrival time of collecting vessels. We show how the robust PMP can be very naturally formulated using CP and give some preliminary results in an experimental evaluation.