Crane scheduling for end-of-aisle picking: Complexity and efficient solutions based on the vehicle routing problem

To relieve human order pickers from unproductive walking through a warehouse, parts-to-picker systems deliver demanded stock keeping units (SKUs) toward picking workstations. In a wide-spread parts-to-picker setup, a crane-operated automated storage and retrieval system (ASRS) delivers bins with demanded SKUs toward an end-of-aisle picking workstation and returns them back into the rack once the picks are completed. We consider the scheduling of the crane that operates subsequent dual commands. Each dual command combines a retrieval request for another SKU bin demanded at the picking workstation with a storage request, where a bin that has already been processed and passed through the bin buffer is returned to its dedicated storage position in the ASRS. This system setup in general and the resulting crane scheduling problem in particular have been an active field of research for more than 30 years. We add the following contributions to this stream of research: We finally prove that the crane scheduling problem is strongly NP-hard. Furthermore, we show that, although only a single vehicle (namely, the crane) is applied, the problem is equivalent to the traditional vehicle routing problem (VRP). This opens the rich arsenal of very efficient VRP solvers, which substantially outperform existing tailor-made algorithms from the literature.