Extension of the dominance properties for the unrestricted block relocation problem

Abstract

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.

A Study on the Block Relocation Problem: Lower Bound Derivations and Strong Formulations

“…In addition to the lower bound, Tanaka and Mizuno [28] propose two dominance properties associated with optimal solutions to reduce solution space. Their result is further complemented by two new dominance properties presented in Tanaka [29].…”

“…In addition to their focus on the restricted BRP, Zhu et al [9] also develop IDA algorithms for the unrestricted BRP. By using their derived dominance properties, Tanaka and Mizuno [28] and [29] develop some strengthened B&B algorithms in the search tree. Together with a new lower bound, the B&B algorithms are further improved in Tanaka and Mizuno [26].…”