Order sequencing, tote scheduling, and robot routing optimization in multi-tote storage and retrieval autonomous mobile robot systems

This study explores a novel multi-tote storage and retrieval autonomous mobile robot system, where multi-tote autonomous mobile robots transport totes (or ‘SKU bins’) for order picking. We investigate the joint optimisation problem of order sequencing, tote scheduling, and robot routing in a single workstation equipped with the capacity to accommodate multiple order bins and parallel totes. The inbound and outbound streams of SKUs stored in totes are crucial for order picking at the workstation, as they jointly affect the picking performance efficiency through synchronization with the order sequence. To address this synchronization problem, we formulate a Mixed-Integer Linear Programming (MILP) model and propose a two-stage hybrid heuristic combining a variable neighbourhood search (VNS) algorithm and a refinement model. This model further improves the VNS solution with partially fixed SKU inbound stream and problem-tailored inequalities. Our numerical studies highlight the superior performance of the proposed hybrid heuristic, where the VNS solution surpasses the benchmark VNS-Simplified by a significant margin of 14%. The rearrangement process enhances the VNS performance by reducing 33.8% of SKU revisits. We also offer managerial insights, suggesting that the maximum number of order bins and parallel totes, exhibit boundary points where adding capacity yields limited marginal improvements.