EXPRESS: Robotic Mobile Fulfillment Systems: Strategies for Pod Selection and Scheduling

Robotic mobile fulfillment (RMF) systems automate storage and transportation within fulfillment centers while still relying on human pickers. We focus on two key performance metrics in these systems, aiming to minimize overall completion time (OCT) as the primary objective and the number of required robots (NRR) as a secondary objective. We investigate two interrelated operational problems influencing these metrics: (i) pod selection, which involves choosing the mobile racks for item picking, and (ii) pod scheduling, which entails assigning these racks to pickers and determining the picking sequence. We first explore the pod scheduling problem independently, providing theoretical results. This stand-alone problem is NP-hard with at least two pickers when minimizing OCT and remains NP-hard with even one picker when minimizing NRR. The NRR objective introduces a novel optimization problem structure, contributing to scheduling theory even beyond the RMF context. We demonstrate that a simple but effective scheduling rule is asymptotically optimal for minimizing OCT with multiple pickers. For NRR minimization with a single picker, we derive theoretical performance bounds for two sequencing rules. When incorporating the pod selection problem, we focus on two approaches: (i) sequential and (ii) integrated pod selection and scheduling. The sequential approach handles pod selection first, then pod scheduling, while the integrated approach addresses both problems simultaneously within a single formulation to minimize OCT. Computational experiments using e-commerce order data reveal that the sequential approach achieves significantly faster and constant computation times, with a mean OCT similar to that of the integrated approach. We also find that our sequencing rules can reduce mean NRR by 13% to 28% without affecting OCT, compared to the case where no such rules are used. The sequential approach for OCT minimization and the proposed sequencing rules for NRR minimization are scalable to large systems with any picker count. Our experiments also explore the changes in OCT and NRR values with varying numbers of pickers. These results guide managers in assigning the desired number of pickers for a target OCT and inform managers about the average NRR they can expect for the chosen picker count.