A variable neighborhood search approach to solve the order batching problem with heterogeneous pick devices

In this paper, we discuss the order batching problem in manual order picking systems. In such systems, order pickers move through a warehouse to collect items that are requested by customers. Customer orders have to be grouped into picking orders of limited size to ensure that the total length of the picker tours to collect all items is minimized. Motivated by real-world restrictions, we assume that the pick devices are heterogeneous, i.e., it is not necessarily possible to transport each customer order with each device. Since the order batching problem is NP-hard, we propose both serial and parallel versions of a variable neighborhood search (VNS) scheme to tackle large-sized problem instances in a reasonable amount of time. Moreover, the VNS scheme is hybridized with a set partitioning problem formulation. Based on computational experiments, we show that the proposed VNS scheme is a very fast approach that is able to provide solutions for benchmark instances with homogeneous pick devices that are of comparable quality or even partly superior to the best performing approaches from the literature. New benchmark instances for heterogeneous pick devices are proposed. High-quality solutions are obtained for these instances. We also consider large-scale problem instances from a real-world e-commerce warehouse. The VNS scheme outperforms the heuristic applied for order batching in this warehouse. Moreover, we demonstrate that a warehouse setup with heterogeneous pick devices is highly beneficial with respect to operating cost savings.