Flow-Based Task Assignment for Large-Scale Online Multi-Agent Pickup and Delivery

We study the problem of online Multi-Agent Pickup and Delivery (MAPD), where a team of agents must repeatedly serve dynamically appearing tasks on a shared map. Existing online methods either rely on simple heuristics, which result in poor decisions, or employ complex reasoning, which suffers from limited scalability under real-time constraints. In this work, we focus on the task assignment subproblem and formulate it as a minimum-cost flow over the environment graph. This eliminates the need for pairwise distance computations and allows agents to be simultaneously assigned to tasks and routed toward them. The resulting flow network also supports efficient guide path extraction to integrate with the planner and accelerates planning under real-time constraints. To improve solution quality, we introduce two congestion-aware edge cost models that incorporate real-time traffic estimates. This approach supports real-time execution and scales to over 20000 agents and 30000 tasks within 1-second planning time, outperforming existing baselines in both computational efficiency and assignment quality.