  In this paper, we study the one-shot and lifelong versions of the Target
Assignment and Path Finding problem in automated sortation centers, where each
agent needs to constantly assign itself a sorting station, move to its assigned
station without colliding with obstacles or other agents, wait in the queue of
that station to obtain a parcel for delivery, and then deliver the parcel to a
sorting bin. The throughput of such centers is largely determined by the total
idle time of all stations since their queues can frequently become empty. To
address this problem, we first formalize and study the one-shot version that
assigns stations to a set of agents and finds collision-free paths for the
agents to their assigned stations. We present efficient algorithms for this
task based on a novel min-cost max-flow formulation that minimizes the total
idle time of all stations in a fixed time window. We then demonstrate how our
algorithms for solving the one-shot problem can be applied to solving the
lifelong problem as well. Experimentally, we believe to be the first
researchers to consider real-world automated sortation centers using an
industrial simulator with realistic data and a kinodynamic model of real
robots. On this simulator, we showcase the benefits of our algorithms by
demonstrating their efficiency and effectiveness for up to 350 agents.
