Assigning orders and pods to picking stations in a multi-level robotic mobile fulfillment system

This paper addresses the operational planning problem of assigning orders and pods (i.e., mobile shelves) to picking stations in a multi-level robotic mobile fulfillment system (RMFS), which deals with two issues: deciding on which picking station handles which order, and from which pods to pick the ordered items, considering the limited storage capacity of the pods. Due to the relatively poor space utilization of single-level RMFS warehouses, such systems are often spread over multiple floors in practice. Therefore, we explicitly consider multi-level warehouse layouts with isolated levels (or zones) where a pod can only be brought to a station if both of them are on the same level. We optimize the problem with regard to a multi-criteria objective function that consists of three workload-oriented objectives: we aim to balance the total workload among all pickers, minimize the total order-consolidation effort for the packers, and the pod movement effort for the mobile robots. After formalizing the planning problem as a multi-objective optimization problem, we provide two mixed-integer linear programming models. Additionally, we propose a matheuristic that reduces the model size to the desired granularity so that realistically sized problem instances can be solved within less than four minutes of computation time. Moreover, we derive some managerial insights, such as the impact of the number of warehouse levels and picking waves on the objective values. We find evidence that running the RMFS warehouse in a multi-level facility can substantially compromise the consolidation effort at packing stations since it leads to a higher number of split orders. Furthermore, splitting the planning horizon into multiple short waves can lead to a higher number of pod-to-station assignments and, thus, to a raised pod-movement workload for mobile robots.