To meet today’s ambitious order throughput targets, many distribution centers, especially those operated by online retailers, apply batching and zoning in their picker-to-parts warehouses. These order retrieval policies improve the pick density per tour by unifying multiple customer orders to larger pick lists and allow a parallelization of the picking process among multiple zones, respectively. The price for this is an additional consolidation stage, where picked products must be sorted according to customer orders, typically with the help of a sortation conveyor. In this context, we treat the loop sorter scheduling problem, which is defined as follows. Once a wave of orders, picked concurrently in multiple zones, has been inducted onto a closed-loop sorter, we have to assign the products that refer to the same stock keeping units (SKUs) to orders and orders to packing lanes, where they are prepared for shipping. Furthermore, we have to decide on the sequence in which the orders are channeled into their packing lanes. Our aim is to minimize the makespan until all orders of the current wave are readily sorted. We formulate the loop sorter scheduling problem, investigate computational complexity, and derive suitable solution algorithms. One important finding of our computational study is that simple priority rules, which are frequently applied in real-world warehouses and previous research, waste significant optimization potential.

中文翻译：

---

仓库中的订单整合：循环分拣机调度问题

为了满足当今雄心勃勃的订单吞吐量目标，许多配送中心，尤其是由在线零售商运营的配送中心，在其拣选员到零件仓库中应用批处理和分区。这些订单检索策略通过将多个客户订单统一到更大的拣选列表来提高每次巡检的拣选密度，并分别允许多个区域之间的拣选过程并行化。这样做的代价是额外的整合阶段，必须根据客户订单对拣选的产品​​进行分类，通常借助分类输送机。在这种情况下，我们处理循环排序器调度问题，其定义如下。一旦在多个区域同时分拣的一波订单被引入闭环分拣机，我们就必须将涉及相同库存单位 (SKU) 的产品分配给订单，并将订单分配给包装通道，它们所在的位置准备运输。此外，我们必须决定订单进入包装通道的顺序。我们的目标是最小化完工时间，直到当前波次的所有订单都已轻松排序。我们制定循环排序机调度问题，研究计算复杂性，并得出合适的解决算法。我们的计算研究的一个重要发现是，在现实世界的仓库和之前的研究中经常应用的简单优先级规则浪费了巨大的优化潜力。