Sorting multibay block stacking storage systems

Autonomous mobile robots (AMRs) are increasingly used to automate operations in intralogistics. One crucial feature of AMRs is their availability, allowing them to operate 24/7. This work addresses the multibay unit load pre-marshalling problem, which extends pre-marshalling from a single bay to larger warehouse configurations with multiple bays. Pre-marshalling leverages off-peak time intervals to sort a block stacking warehouse in anticipation of future orders. These larger warehouse configurations require not only the minimization of the number of moves but also the consideration of distance or time when making sorting decisions. Our proposed solution for the multibay unit load pre-marshalling problem is based on our two-step approach that first determines the access direction for each stack and then finds a sequence of moves to sort the warehouse. In addition to adapting the existing approach that integrates a network flow model and an extended A* algorithm, we additionally present an exact constraint programming approach for the second stage of the problem-solving process. The results demonstrate that the presented solution approach effectively enhances the access time of unit loads and reduces the sorting effort for block stacking warehouses with multiple bays.