Integration of returns and decomposition of customer orders in e-commerce warehouses

In picker-to-parts warehouses, order picking is a cost- and labor-intensive operation that must be designed efficiently. It comprises the construction of order batches and the associated order picker routes, and the assignment and sequencing of those batches to multiple order pickers. The ever-increasing competitiveness among e-commerce companies has made the joint optimization of this order picking process inevitable. Inspired by the large number of product returns and the many but small-sized customer orders, we address a new integrated order picking process problem. We integrate the restocking of returned products into regular order picking routes and we allow for the decomposition of customer orders so that multiple batches may contain products from the same customer order. We thereby generalize the existing models on order picking processing. We provide Mixed Integer Programming (MIP) formulations and a tailored adaptive large neighborhood search heuristic that, amongst others, exploits these MIPs. We propose a new set of practically-sized benchmark instances, consisting of up to 5547 to be picked products and 2491 to be restocked products. On those large-scale instances, we show that integrating the restocking of returned products into regular order picker routes results in cost-savings of 10 to 15%. Allowing for the decomposition of the customer orders' products results in cost savings of up to 44% compared to not allowing this. Finally, we show that on average cost-savings of 17.4% can be obtained by using our ALNS instead of heuristics typically used in practice.