An exact approach to the restricted block relocation problem based on a new integer programming formulation

Abstract

This study addresses the block(s) relocation problem (BRP), also known as the container relocation problem. This problem considers individually retrieving blocks piled up in tiers according to a predetermined order. When the block to be retrieved next is not at the top, we have to relocate the blocks above it because we can access only the topmost blocks. The objective is to retrieve all the blocks with the smallest number of relocations. In this study, a novel exact algorithm is proposed for the restricted BRP, a class of the problem where relocatable blocks are restricted. The proposed algorithm computes lower and upper bounds iteratively by solving the corresponding integer programming problems until the optimality gap is reduced to zero. The novelty of the algorithm lies in the formulations based on complete and truncated relocation sequences of the individual blocks. We examine the effectiveness of the proposed algorithm through computational experiments for benchmark instances from the literature. In particular, we report that, for the first time, all the instances with up to 100 blocks are solved to proven optimality.