A Two-Stage Heuristic Framework for Joint Order-Rack Scheduling in Robotic Mobile Fulfillment Systems

Robotic mobile fulfillment systems (RMFS) employ mobile robots to deliver movable racks to workstations for order picking. Their efficiency depends on coupled decisions on order allocation, order sequencing, and rack service scheduling, yet joint optimization is computationally expensive at scale. This paper proposes a two-stage heuristic framework to minimize total rack-to-workstation travel distance. During Stage I, orders are allocated by stock keeping unit (SKU) similarity and candidate racks are filtered to shrink the search space. Then during Stage II, workstation order sequences are improved via simulated annealing, beam search and lightweight postoptimization. Experiments over 30 parameter settings, each averaged over 50 independently generated random instances, show that the proposed framework achieves a 36.2% overall reduction in travel distance and a 79.3% overall reduction in runtime compared with a reproduced MIP-heuristic baseline, showing its effectiveness for offline decision-block order-rack scheduling.