A Flow Model to the Order Picking Problem

Order picking is one of the most critical operations in warehouse logistics, particularly in the context of e-Commerce, where speed and accuracy are paramount. This paper addresses the Order Picking in Waves problem, where a subset of customer orders is grouped for simultaneous collection to optimize operational efficiency. We propose a novel mathematical formulation based on network flow and introduce constraints that ensure the feasibility of selected order groups. Our objective is to maximize the average number of items picked per aisle, thereby reducing unnecessary traversal and improving productivity. We compare our flow-based formulation with a standard integer programming approach, highlighting its advantages in capturing item-aisle dependencies. Computational experiments in real-world-inspired instances demonstrate that our model produces high-quality solutions and supports a two-phase algorithm that efficiently finds the optimal number of aisles required. These results provide valuable insights for warehouse managers seeking to streamline order fulfillment operations in complex environments.