Rack retrieval and repositioning optimization problem in robotic mobile fulfillment systems

Robotic mobile fulfillment systems provide a new solution for e-commerce retailers to fulfill customers’ orders, wherein racks are moved by mobile robots to workstations so pickers can retrieve the purchased products. While such automated parts-to-picker systems can save on labor costs, they raise new operational challenges. In this paper, we investigate the rack storage and robot assignment to racks problem during order processing. We formulate this problem with the goal of minimizing the makespan of the system. Based on a rolling horizon framework and the simulated annealing method, we develop a matheuristic decomposition approach, which involves the solution of a special axial 3-index assignment problem in each stage to solve the problem. We test the performance of the proposed method for both large-scale cases based on a real-world dataset and small-scale instances generated synthetically. Computational results demonstrate the good performance of the proposed approach.