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

Solving the unit-load pre-marshalling problem in block stacking storage systems with multiple access directions