In the digital age, coordinating robots and humans is critical in e-commerce warehousing. Motivated by observed industrial practices, this study presents a queueing theory based analytical model to investigate the planning issue of robot-human coordination in a parts-to-picker warehousing system. The critical planning decisions involve finding the optimal number of robots in the warehouse, the expected number of robots at essential locations of the warehouse, and performance analysis of the order picking system. A distinctive feature of this study is the conceptualization of a human factor called perceived workload (which depends on the number of robots) in the order picking planning model for efficient order fulfillment. Our analyses interestingly suggest that deploying more robots in warehouses with a parts-to-picker system does not necessarily increase the warehousing system’s performance; instead, a trade-off exists. Additionally, the workload-dependent service rate significantly influences the robots queueing in front of the order picking station (internal queue) and the synchronization station (external queue) in the warehouse. More importantly, this work contributes to the design of a human-centric work environment for parts-to-picker order fulfillment system.

在数字时代，协调机器人和人类在电子商务仓储中至关重要。受观察到的工业实践的启发，本研究提出了一个基于排队论的分析模型，以研究零件到拣选机仓储系统中机器人与人协调的规划问题。关键的规划决策涉及寻找仓库中机器人的最佳数量、仓库重要位置的机器人预期数量以及订单拣选系统的性能分析。这项研究的一个显着特点是将称为感知工作量的人为因素概念化（这取决于机器人的数量）在订单拣选计划模型中以实现高效的订单履行。我们的分析有趣地表明，在具有零件到拣选系统的仓库中部署更多机器人并不一定会提高仓储系统的性能；相反，存在权衡。此外，依赖于工作量的服务率显着影响在仓库中订单拣选站（内部队列）和同步站（外部队列）前排队的机器人。更重要的是，这项工作有助于为零件到拣选订单履行系统设计以人为中心的工作环境。