Block stacking storage systems are highly adaptable warehouse systems with
low investment costs. With multiple, deep lanes they can achieve high storage
densities, but accessing some unit loads can be time-consuming. The unit-load
pre-marshalling problem sorts the unit loads in a block stacking storage system
in off-peak time periods to prepare for upcoming orders. The goal is to find a
minimum number of unit-load moves needed to sequence a storage bay in ascending
order based on the retrieval priority group of each unit load. In this paper,
we present two solution approaches for determining the minimum number of
unit-load moves. We show that for storage bays with one access direction, it is
possible to adapt existing, optimal tree search procedures and lower bound
heuristics from the container pre-marshalling problem. For multiple access
directions, we develop a novel, two-step solution approach based on a network
flow model and an A* algorithm with an adapted lower bound that is applicable
in all scenarios. We further analyze the performance of the presented solutions
in computational experiments for randomly generated problem instances and show
that multiple access directions greatly reduce both the total access time of
unit loads and the required sorting effort