Introducing Combi-Stations in Robotic Mobile Fulfilment Systems: A Queueing-Theory-Based Efficiency Analysis

TL;DR

The paper addresses the bottleneck of order picking in warehouse automation by evaluating combi-stations within Robotic Mobile Fulfilment Systems (RMFS) using queueing theory. It models RMFS as a semi-open queueing network with backordering (SOQN-BO) and applies a structured approximation framework to estimate the order turnover time, decomposing it into external-queue waiting and inner-network processing. The main contributions are (i) a detailed SOQN-BO formulation for RMFS with two-station types and with combi-stations, (ii) a practical approximation method based on modified loss systems, Norton’s theorem, and Little’s law, and (iii) numerical results showing that combi-stations can reduce the required number of robots by one to reach stability and can decrease average turnover time by up to about 64% at the same robot count, validated against SimPy simulations. The findings offer actionable guidance for warehouse designers: adopting combi-stations can accelerate fulfillment and reduce capital and operational costs, with demonstrated potential for improved throughput in e-commerce logistics. Further work is suggested to explore scalability to larger RMFS deployments.

Abstract

In the era of digital commerce, the surge in online shopping and the expectation for rapid delivery have placed unprecedented demands on warehouse operations. The traditional method of order fulfilment, where human order pickers traverse large storage areas to pick items, has become a bottleneck, consuming valuable time and resources. Robotic Mobile Fulfilment Systems (RMFS) offer a solution by using robots to transport storage racks directly to human-operated picking stations, eliminating the need for pickers to travel. This paper introduces combi-stations, a novel type of station that enables both item picking and replenishment, as opposed to traditional separate stations. We analyse the efficiency of combi-stations using queueing theory and demonstrate their potential to streamline warehouse operations. Our results suggest that combi-stations can reduce the number of robots required for stability and significantly reduce order turnover time, indicating a promising direction for future warehouse automation.

Figures (7)

• Figure 1: The picking and replenishment processes of two RMFS systems.
• Figure 2: An SOQN with backordering and external queue otten2019numRobot.
• Figure 3: RMFS with two-station types modelled as an SOQN-BO.
• Figure 4: RMFS with combi-stations modelled as an SOQN-BO.
• Figure 5: Overview of the solution approach developed in otten2019numRobot. We use the same colour for parts that we change in a single approximation step. (This figure is a slight modification of otten2019numRobot.