Efficient Order Batching Optimization Using Seed Heuristics and the Metropolis Algorithm

Abstract

Order Picking in warehouses is often optimized using a method known as Order Batching, which means that one vehicle can be assigned to pick a batch of several orders at a time. There exists a rich body of research on Order Batching Problem (OBP) optimization, but one area which demands more attention is computational efficiency, especially for optimization scenarios where warehouses have unconventional layouts and vehicle capacity configurations. Due to the NP-hard nature of the OBP, computational cost for optimally solving large instances is often prohibitive. In this paper, we compare the performance of two approximate optimizers designed for maximum computational efficiency. The first optimizer, Single Batch Iterated (SBI), is based on a Seed Algorithm, and the second, Metropolis Batch Sampling (MBS), is based on a Metropolis algorithm. Trade-offs in memory and CPU-usage and generalizability of both algorithms is analyzed and discussed. Existing benchmark datasets are used to evaluate the optimizers on various scenarios. On smaller instances, we find that both optimizers come within a few percentage points of optimality at minimal CPU-time. For larger instances, we find that solution improvement continues throughout the allotted time but at a rate which is difficult to justify in many operational scenarios. SBI generally outperforms MBS and this is mainly attributed to the large search space and the latter’s failure to efficiently cover it. The relevance of the results within Industry 4.0 era warehouse operations is discussed.