Modeling and Analysis of Multi-Line Orders in Multi-Tote Storage and Retrieval Autonomous Mobile Robot Systems

TL;DR

This work addresses the challenge of efficiently processing multi-line orders in multi-tote storage and retrieval RMFS systems by developing a shared-token, multi-class semi-open queueing network (SOQN) that accommodates general distributions of line counts per order, captured by $N_o$. The model is analyzed with approximate mean value analysis (AMVA) and validated against discrete-event simulation, yielding high accuracy across key metrics such as order throughput time $THT$ and resource utilizations. It examines the impact of tote buffer capacity $C$, the number of robots $N_r$, and tote retrieval policies (closest retrieval vs random), finding that a closest retrieval policy can reduce the required robots by about $12.5\%$ at the same arrival rate, and that larger $C$ reduces trips nonlinearly with diminishing returns. The results support rapid, pre-deployment planning and resource optimization for tailored warehouses, and point to future work on congestion effects, multi-deep shelves, and dwell-point policies to further enhance performance.

Abstract

As warehouses are emphasizing space utilization and the ability to handle multi-line orders, multi-tote storage and retrieval (MTSR) autonomous mobile robot systems, where robots directly retrieve totes from high shelves, are becoming increasingly popular. This paper presents a novel shared-token, multi-class, semi-open queueing network model to account for multi-line orders with general distribution forms in MTSR systems. The numerical results obtained from solving the SOQN model are validated against discrete-event simulation, with most key performance metrics demonstrating high accuracy. In our experimental setting, results indicate a 12.5% reduction in the minimum number of robots needed to satisfy a specific order arrival rate using the closest retrieval sequence policy compared with the random policy. Increasing the number of tote buffer positions on a robot can greatly reduce the number of robots required in the warehouse.

Figures (5)

• Figure 1: The MTSR autonomous mobile robot system, where robots directly pick multiple totes from vertical storage shelves hairoboticsHaiPickSystem.
• Figure 2: Top view of an MTSR system layout, where WS symbolizes the workstation for retrieving goods from arriving totes or replenishing them with goods, CS denotes charging station.
• Figure 3: The shared-token, multi-class semi-open queueing network is constructed based on the MTSR system operation process.
• Figure 4: A small warehouse layout with unidirectional paths has three workstations on the west, south, and east sides of the warehouse, with the charging station located at the top.
• Figure 5: Under both CR and random tote retrieval policies, we compare: (a) Robot utilization and order throughput time with varying numbers of robots in the system. (b) Robot utilization and order throughput time with varying buffer positions. (c) Minimum number of robots needed to maintain system stability and corresponding order throughput time with varying average order arrival rate.