Efficient order consolidation in warehouses: The product-to-order-assignment problem in warehouses with sortation systems

To improve picking performance, many warehouses apply order batching and/or zoning in their picking areas. The former policy collects multiple customer orders jointly on a picker tour to increase picking density, and the latter partitions the picking area into smaller zones to enable a parallel order processing. Both picking policies require an additional consolidation stage, where bins filled with partial orders arriving from multiple zones are sorted according to customer orders. To connect both stages, a conveyor system is applied on which the picked products, each being a piece of a specific Stock Keeping Unit (SKU), move from the picking area toward the consolidation stage. If multiple pieces of the product sequence, approaching the consolidation area on the conveyor, refer to the same SKU, these products are interchangeable among customer orders, and our product-to-order assignment problem arises: Given a product sequence where each product refers to some SKU, we assign products to customer orders, such that demands are fulfilled and order-related objectives, e.g., the sum of completion times, are optimized. We investigate different objectives for this very basic optimization task and show that some problem versions are solvable in polynomial time, whereas others turn out to be NP-hard. Furthermore, we provide exact and heuristic solution approaches. By applying these algorithms in a comprehensive simulation study, we show that our product-to-order assignment problem can be an impactful lever to improve consolidation performance.