Automated Guided Vehicle (AGV)-based order picking (OP) systems, also known as Robotic Mobile Fulfilment Systems, continues to receive attention in industry and academia since their introduction as Kiva systems. A key component of AGV-based OP systems is the ‘robots’ (or AGVs) that pick up the ‘pods’ and transport them to the appropriate pick station (PS), where a picker picks the items ordered by customers. The performance of such systems depends on the shape of the forward area (FA) and the number of AGVs, which in turn depends on the time it takes an AGV to retrieve a pod. To aid system designers, we explore alternative shapes for the FA and we derive closed-form expressions for the expected AGV travel distances under two possible order assignment rules. Under the random assignment rule, an order is assigned to any PS with equal probability. Under the closest assignment rule, the order is assigned to the closest PS. We also examine the impact of alternative PS configurations for different shapes of the FA. The results offer valuable insights concerning expected travel distances under alternative design configurations. The results would also be useful when building design and performance evaluation models for AGV-based OP systems.

基于自动导引车 (AGV) 的订单拣选 (OP) 系统，也称为机器人移动履行系统，自作为 Kiva 系统推出以来一直受到工业界和学术界的关注。基于 AGV 的 OP 系统的一个关键组件是“机器人”（或 AGV），它们拾取“吊舱”并将它们运送到适当的拣货站 (PS)，拣货员在那里拣选客户订购的物品。此类系统的性能取决于前方区域 (FA) 的形状和 AGV 的数量，而这又取决于 AGV 检索吊舱所需的时间。为了帮助系统设计人员，我们探索了 FA 的替代形状，并在两种可能的顺序分配规则下推导出了预期 AGV 行驶距离的封闭式表达式。在随机分配规则下，一个订单以相等的概率分配给任何 PS。在最近分配规则下，订单分配给最近的 PS。我们还研究了替代 PS 配置对不同形状 FA 的影响。结果提供了有关替代设计配置下预期行驶距离的宝贵见解。在为基于 AGV 的 OP 系统构建设计和性能评估模型时，这些结果也很有用。