Extension of the dominance properties for the unrestricted block relocation problem

The block (container) relocation problem is an optimization problem that typically arises in container terminals. Its objective is to minimize the number of relocation operations necessary for retrieving all blocks (containers) stacked in tiers according to a given order. In our previous study, we considered the unrestricted version of the problem where no restriction is imposed on relocatable blocks, and proposed two dominance properties for it. However, they considered only two successive operations. The purpose of this study is to extend them for any two operations. They enable us to improve the efficiency of the branch-and-bound algorithm for the problem, which will be verified by numerical experiment.