Inventory allocation to robotic mobile-rack and picker-to-part warehouses at minimum order-splitting and replenishment costs

A novel part-to-picker warehouse with robotic mobile racks is spreading recently because of its advantages in picking multi-item e-commerce orders. However, warehouse managers may suffer the situation that the new warehouse and an old one coexist in a distribution center. Due to their respective capacities, any warehouse cannot hold all the stock keeping units (SKUs). How to allocate SKUs to the two warehouses is an important decision. It has a significant influence on the cost of combining the SKUs that have to be picked from two warehouses for customer orders. The problem is formulated by using an innovative virtual-warehouse-based idea, the NP-hardness of the problem is proved, and a hybrid algorithm by alternating between the large neighborhood search and local search is developed. Some effective data-driven strategies are proposed to improve the most time-consuming modules of the algorithm. Extensive case studies are conducted and good performances of the algorithm are shown when it is compared with the MIP solver on small-sized cases, and an adapted tabu search and a simulated annealing algorithm on large-sized real-world cases. The sensitivity analyses on key parameters of the problem are made and related managerial insights are obtained.