Abstract The joint order batching and picker routing problem (JOBPRP) is a promising approach to minimize the order picking travel distance in a picker-to-parts warehouse environment. In this paper, we show that the JOBPRP can be modelled as a clustered vehicle routing problem (CluVRP), a variant of the capacitated VRP in which customers are grouped into clusters. To solve this cluster-based model of the JOBPRP, we apply a two-level variable neighborhood search (2level-VNS) metaheuristic, previously developed for the CluVRP, and study which adaptations are required for it to perform efficiently in a warehouse environment. Additionally, we evaluate if the Hausdorff distance used as an approximation for the clusters’ proximity in the CluVRP, performs equally well when determining closeness between pick orders in a warehouse. We compare the performance of the Hausdorff-based batching criterion to the cumulative minimal aisles visited-criterion, known as a well-performing batching metric in rectangular warehouses with parallel aisles. The 2level-VNS performs well compared to state-of-the-art algorithms specifically developed for the order batching problem (OBP) in a single-block warehouse. A multi-start VNS remains slightly superior to our approach. Concerning the Hausdorff distance, we conclude that in most experiments, the minimum-aisles criterion retains a better fit in the warehouse context.

中文翻译：

---

联合订单批处理和拣货员路由问题：建模并解决为聚类车辆路由问题

摘要 联合订单批处理和拣货员路由问题（JOBPRP）是一种在拣货员到零件仓库环境中最小化订单拣选旅行距离的有前途的方法。在本文中，我们展示了 JOBPRP 可以建模为集群车辆路由问题 (CluVRP)，这是一种将客户分组到集群中的有能力 VRP 的变体。为了解决这个基于集群的 JOBPRP 模型，我们应用了先前为 CluVRP 开发的两级变量邻域搜索 (2level-VNS) 元启发式，并研究需要哪些适应才能使其在仓库环境中有效执行。此外，我们评估了用作 CluVRP 中集群接近度的近似值的 Hausdorff 距离在确定仓库中拣货订单之间的接近度时是否表现得同样好。我们将基于 Hausdorff 的批处理标准的性能与累积最小通道访问标准进行比较，该标准被称为具有平行通道的矩形仓库中性能良好的批处理指标。与专为单块仓库中的订单批处理问题 (OBP) 开发的最先进算法相比，2level-VNS 表现良好。多启动 VNS 仍然略优于我们的方法。关于 Hausdorff 距离，我们得出结论，在大多数实验中，最小通道标准更适合仓库环境。与专为单块仓库中的订单批处理问题 (OBP) 开发的最先进算法相比，2level-VNS 表现良好。多启动 VNS 仍然略优于我们的方法。关于 Hausdorff 距离，我们得出结论，在大多数实验中，最小通道标准更适合仓库环境。与专为单块仓库中的订单批处理问题 (OBP) 开发的最先进算法相比，2level-VNS 表现良好。多启动 VNS 仍然略优于我们的方法。关于 Hausdorff 距离，我们得出结论，在大多数实验中，最小通道标准更适合仓库环境。