The warehouse reshuffling problem with swap moves and time limit

In this paper, we study the warehouse reshuffling problem, where pallets in a storage have to be rearranged in an efficient way. A high-bay warehouse with an automated storage and retrieval system is considered, which is equipped with a twin shuttle stacker crane. This twin shuttle is designed to perform swap moves, where the pallet at a storage location is swapped with the pallet currently loaded on the stacker crane. We study a new problem variant, where the time for reshuffling is limited, and the desired assignment of pallets to storage locations is not given as input. The objective is to store the frequently accessed pallets closely to the input/output-point to keep the warehouse operations efficient. After proposing necessary and sufficient optimality conditions for assignments of pallets to storage locations, we present algorithms to deal with the time limit. Moreover, we prove NP-hardness of two special cases, introduce lower bound procedures, several construction heuristics and a simulated annealing algorithm. Finally, we present computational results on randomly generated instances based on a real-world company setting.