  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.
