Efficient routing in robotic movable fulfillment systems with integer programming: A rolling horizon and heuristic approach

This paper addresses an integrated rack assignment and robot routing problem arising in robotic movable fulfillment systems (RMFS). This NP-hard planning task goes beyond current literature by simultaneously optimizing movable rack selection and multi-agent collision-free path finding, rather than decomposing them. A mixed integer programming (MIP) model with a new level-space-time network representation is proposed, jointly considering reusable racks, robot-rack pairings, storage repositioning, and collision avoidance. To improve computational efficiency, a fast rolling horizon heuristic and greedy algorithm are developed. Extensive experiments demonstrate that the integrated method's solutions can improve by 30 % upon conventional decomposed approaches. Intriguing test cases reveal the model, suggesting non-intuitive robot carryover policies that are unfound by separate selection and routing methods. This indicates potential optimization benefits from explicitly coordinating task assignment, scheduling, and routing decisions in complex automated warehousing systems. The rolling horizon heuristic solutions approach optimality with much greater efficiency than directly solving one large MIP, validating its practical value. This research provides useful integrated modeling insights, efficient solution algorithms, and decision support for efficiently controlling next-generation robotic movable fulfillment systems.