Velocity-based rack storage location assignment for the unidirectional robotic mobile fulfillment system

Nowadays, the robotic mobile fulfillment system (RMFS) has been increasingly used by online retailers. Compared with traditional picker-to-parts warehouses, the racks of RMFS do not have to return to the same location after picking, thus we can dynamically change their locations, which brings great potential to efficiently fulfill orders. Aiming at minimizing the sum of rack travel distances, the key question is how to reassign a rack to an unoccupied storage location after picking items from the rack. However, the issue involves two challenges for unidirectional RMFS, one is that huge differences may exist between the classical Manhattan distance estimation and the actual distance for the unidirectional aisles in RMFS, and the other one is that we need to account for the frequency of rack moving for multi-item orders. We thus first propose closed-form formulas to optimally estimate the cycle travel distance for each rack. Then, by overcoming the repeated counting issue for multi-item orders, we propose a novel SKU (Stock Keeping Units)-correlation-based algorithm to choose high-velocity racks, which can better fulfill multi-item orders. Finally, embedding the cycle travel distance and SKU-correlation-based velocity, we propose a Velocity-based Rack Storage Location Assignment method (VRSLA) to solve the rack storage location assignment problem by assigning high-velocity racks to the nearest storage locations. Collaborating with a large online retailer in China, we demonstrate the performance of VRSLA by using both small-scale and large-scale datasets. The computational results show that VRSLA not only can achieve near-best solutions compared with an integer programming model solved by Gurobi, but also outperforms four state-of-the-art assignment methods in literature (random, velocity-based class, shortest path, and sale-based) by reducing the rack travel distance up to 43.32%. We also found that the stronger the correlation between SKUs on the racks or the larger the size of the RMFS, the shorter the rack travel distance by the proposed VRSLA method.