The rapid growth of e-commerce has increased the demand for efficient order picking systems in large warehouses. To improve throughput performance, many facilities deploy autonomous mobile robots (AMRs) to assist human pickers. Warehouse throughput critically depends on the choice of human-robot collaboration policy. This study focuses on two popular policies: the swarm policy, in which pickers switch between AMRs while picking, and the system-directed policy, in which a picker completes an order with a single AMR. An analytical framework is developed to evaluate these policies. We model the swarm policy as a closed queuing network with a synchronization station, and we derive closed-form expressions for its steady-state probabilities and throughput given load-dependent service rates. The service rates of the network nodes are estimated by Monte Carlo simulation, accounting for stochastic travel times, varying order sizes, item allocation strategies, matching rules, and warehouse layouts. The analytical predictions are validated against detailed discrete-event simulations, with average relative errors below 2% in 12,000 instances. The results indicate that the swarm policy generally provides higher throughput than the system-directed policy, with gains increasing in the AMR-to-picker count and speed ratios. The system-directed policy is more effective when AMR and picker speeds are similar, the orders are large, and there is a limited number of AMRs. Managerial insights are provided to guide policy choice.

Funding: This research is part of the Sharehouse Project, which was cofinanced and supported by the Dutch Research Council NWO, the Dutch Ministry of I&W, the Taskforce for Applied Research SIA, the Dutch Topsector Logistics, and TKI Dinalog [Project 439.18.452].