Fast delivery is one of the most popular services in e-commerce retail. It consists in shipping the items ordered on-line in short times. Customer orders in this segment come with deadlines, and respecting this latter is pivotal to ensure a high service quality. The most time-consuming process in the warehouse is order picking. It consists in regrouping orders into batches, assigning those batches to order pickers, sequencing the batches assigned to each order picker such that the orders deadlines are satisfied, and the picking time is minimized. To speed up the order picking operations, e-commerce warehouses implement new logistical practices. In this paper, we study the impact of splitting the orders (assigning the orderlines of an order to multiple pickers). We thus generalize the integrated orders batching, batch scheduling, and picker routing problem by allowing the orders splitting and propose a route first-schedule second heuristic to solve the problem. In the routing phase, the heuristic divides the orders into clusters and constructs the picking tours that retrieve the orderlines of each cluster using a split-based procedure. In the scheduling phase, the constructed tours are assigned to pickers such that the orders deadlines are satisfied using a constraint programming formulation. On a publicly available benchmark, we compare our results against a state-of-the-art iterated local search algorithm designed for the non-splitting version of the problem. Results show that splitting the customer orders using our algorithm reduces the picking time by 30% on average with a maximum reduction of 60%.

快速交货是电子商务零售中最受欢迎的服务之一。它包括在短时间内运送在线订购的物品。该细分市场的客户订单有截止日期，尊重后者对于确保高服务质量至关重要。仓库中最耗时的过程是订单拣选。它包括将订单重新分组为批次，将这些批次分配给订单拣货员，对分配给每个订单拣货员的批次进行排序，以满足订单截止日期，并最大限度地减少拣货时间。为了加快订单拣选操作，电子商务仓库实施了新的物流实践。在本文中，我们研究拆分订单（将一个订单的订单行分配给多个拣货员）的影响。因此，我们概括了集成的订单批处理、批量调度、和拣货员路由问题通过允许订单拆分并提出路由优先调度第二启发式来解决问题。在路由阶段，启发式将订单划分为集群，并使用基于拆分的过程构建检索每个集群的订单行的拣货路线。在调度阶段，将构建的行程分配给拣货员，以便使用约束规划公式满足订单截止日期。在公开可用的基准测试中，我们将我们的结果与为该问题的非分裂版本设计的最先进的迭代局部搜索算法进行比较。结果表明，使用我们的算法拆分客户订单平均减少了 30% 的拣货时间，最大减少了 60%。