Integer Programming for Multi-Robot Planning: A Column Generation Approach

In this paper, we tackle multi-robot planning (MRP), which aims to route a fleet of robots in a warehouse so as to achieve the maximum reward in a limited amount of time, while not having the robots collide and obeying the constraints of individual robots. In MRP, individual robots may make multiple trips over a given time window and may carry multiple items on each trip. We optimize the efficiency of the warehouse, not the makespan, since we expect new orders to be continuously added. Our contributions are that (1) we adapt the integer linear programming (ILP) formulation and column generation (CG) approach for (prize collecting) vehicle routing (Desrochers et al. 1992, Stenger et al. 2013) to MRP and (2) adapt the seminal work of (Boland et al. 2017) to permit efficient optimization by avoiding consideration of every time increment. Routing problems for a fleet of robots in a warehouse are often treated as Multi-Agent Pathfinding problems (MAPF) (Stern et al. 2019).