Container ship stowage problem: complexity and connection to the coloring of circle graphs

This paper deals with a stowage plan for containers in a container ship. Since the approach to the containers on board the ship is only from above, it is often the case that containers have to be shifted. Shifting is defined as the temporary removal from and placement back of containers onto a stack of containers. Our aim is to find a stowage plan that minimizes the shifting cost. We show that the shift problem is NP-complete. We also show a relation between the stowage problem and the coloring of circle graphs problem. Using this relation we slightly improve Ungerʹs upper bound on the coloring number of circle graphs.