As a new type of part-to-picker storage system, the double-deep multi-tier shuttle system has been developed rapidly in the e-commerce industry because of its high flexibility, large storage capacity, and robustness. The system consists of a multi-tier shuttle sub-system that controls horizontal movement and a lift sub-system that manages vertical movement. The combination of shuttles and lifts, instead of a stacker crane in conventional automated storage and retrieval system, undertakes inbound/outbound tasks. Because of the complex structure and numerous equipment of the system, task scheduling has become a major difficulty in the outbound operation of the double-deep multi-tier shuttle system. Figuring out methods to improve the overall efficiency of task scheduling operations is the focus of current system application enterprises. This paper introduces the task scheduling problem for the shuttle system. Inspired from workshop production scheduling problems, we minimize the total time of a batch of retrieval tasks as the objective function, applying the modified Simulated Annealing Algorithms (SAAs) to solve the task scheduling problem. In conclusion, we verified the proposed model and the algorithm efficiency, using case studies.

The shuttle-based storage and retrieval system (SBS/RS) is composed of a shuttle sub-system that is responsible for horizontal movements and a lift sub-system that is responsible for vertical movements. As the combination of the two sub-systems yields high flexibility, low operating cost and large storage capacity, SBS/RS is becoming more and more popular, but also raises managerial issue of how to coordinate the shuttle and the lift. Based on its operational processes, this study models the tier-to-tier SBS/RS system as a semi-open queuing network (SOQN). By removing or adding the synchronization nodes, the SOQN is further transformed into two different closed queuing networks (CQNs), and applies the approximate mean value analysis (AMVA) algorithm to solve the model and estimate its performance. The system performance is measured by the utilization of shuttles, the utilization of lift, and the task cycle time, under various design configurations. Simulation is carried out to validate the effectiveness of the analytical model and algorithm. Compared with the simulation results, the established semi-open queuing network can accurately estimate task cycle time for different rack configurations. The proposed solution method can help to identify the optimal number of shuttles and guide the design of the SBS/RS system.INDEX TERMS Automated warehouses, shuttle-based storage and retrieval systems, semi-open queuing network, analytical and numerical modeling, optimization, performance analysis.