The advent of e-commerce and omnichannel retailing has sparked renewed interest in picker routing in warehouses. This paper presents two significant methodological advances in this well-established field. First, it is a well-known fact that the parallel-aisle layout of warehouses, as opposed to general graphs, allows for polynomial-time solutions of the Traveling Salesman Problem. We show that the parallel-aisle structure can also be exploited when pickers are tasked with visiting storage positions associated with specific due dates. We establish that picker routing in warehouses, subject to soft due date constraints, is a binary NP-hard problem. We also present an exact branch-and-bound algorithm with pseudo-polynomial time complexity. This algorithm effectively solves instances with up to 60 picking positions and five cross aisles within a few seconds while guaranteeing optimality. Second, for even larger pick lists, we demonstrate the successful integration of our algorithm into a real-time framework. This approach allows us to avoid extended solution times that would otherwise delay the picker’s departure, without compromising the quality of the solution. To illustrate the practical relevance of these two methodological innovations, we apply our routing algorithm to the context of pick-from-store omnichannel retailing. By assigning due dates to critical products, we significantly reduce stockout occurrences for online customers. These stockouts occur when the stock level, initially deemed sufficient to confirm an online order, is depleted by walk-in customers before the picker reaches the relevant shelf.

中文翻译：

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面向到期日期的拣货员路由、高效的精确解决方案算法及其在商店拣选全渠道零售中的应用


电子商务和全渠道零售的出现激发了人们对仓库拣货员路线的新兴趣。本文提出了这个成熟领域的两个重要方法学进展。首先，众所周知的事实是，与一般图形相反，仓库的平行通道布局允许对旅行推销员问题进行多项式时间解。我们表明，当拣选员的任务是访问与特定到期日相关的存储位置时，也可以利用平行通道结构。我们确定仓库中的拣货员路由（受软到期日约束）是一个二进制 NP-hard 问题。我们还提出了一种具有伪多项式时间复杂度的精确分支定界算法。该算法可在几秒钟内有效解决具有多达 60 个拣选位置和 5 个交叉通道的实例，同时保证最佳性。其次，对于更大的选择列表，我们展示了将我们的算法成功集成到实时框架中。这种方法使我们能够避免延长求解时间，否则会延迟拣选员的离开，而不会影响求解的质量。为了说明这两项方法创新的实际相关性，我们将路由算法应用于从商店拣选全渠道零售的上下文中。通过为关键产品分配到期日，我们显著减少了在线客户的缺货情况。当最初被认为足以确认在线订单的库存水平在拣货员到达相关货架之前被步入式顾客耗尽时，就会发生这些缺货。