Scheduling optimization of hybrid multi-deep robotic mobile fulfillment systems

Under the combined pressures of expanding logistics scale, escalating delivery urgency, and rising costs, modern warehouses are being reengineered for space-efficient storage and time-optimized operations. To balance storage density with picking efficiency in robotic mobile fulfillment systems (RMFS), a hybrid multi-deep storage strategy is proposed, employing single-deep storage for high-frequency items and multi-deep storage for low-frequency items. This paper presents a detailed analysis of hybrid multi-deep RMFS. A mixed-integer programming model is formulated to characterize the interrelated decisions of order batching, picking station allocation, pod selection, and robot task assignment. The model incorporates practical considerations such as remaining inventory in each pod and unidirectional aisles. To enhance system efficiency, two novel strategies are proposed: a reverse temporary storage strategy and a robot collaborative task bundling allocation. Subsequently, a multiple Markov chain simulated annealing algorithm is developed to solve the model. Finally, numerical experiments demonstrate that the hybrid multi-deep layout increases storage density by 11.77% compared to single-deep configurations, while incurring a 5.13% increase in average order picking time and a 3.24% increase in average picking time for orders consisting solely of high-frequency items. This indicates that the hybrid multi-deep RMFS significantly enhances storage density with minimal operational trade-offs.