Order batching problems in parallel-aisle order picking systems with larger-than-bin orders

Order batching facilitates order picking by merging orders into single vehicle trips. Filling orders with a total volume larger than a vehicle’s bin capacity, however, requires binning into multiple suborders, a procedure that influences batching performance by altering both the number of suborders and the routes for each suborder. This paper introduces the binning and batching problem (BBP) in an order picking system with pick support vehicles. To minimize the weighted sum of the number of bins and the total travel distance, we propose a binning and batching model (BBM) based on a mixed-integer programming (MIP) and an MIP-based heuristic for large-scale BBPs. Our heuristic obtains near-optimal solutions by the tight lower bound in the problems. A comparison of the heuristic and lower bound shows optimal gaps between 1.38 and 9.21% in a parallel-aisle system for 250–1000 orders. We demonstrate that the heuristic achieves the shortest travel distance for a large number of orders when the number of bins varies within a reasonable range.