  The standard single picker routing problem (SPRP) seeks the cost-minimal tour
to collect a set of given articles in a rectangular single-block warehouse with
parallel picking aisles and a dedicated storage policy, i.e, each SKU is only
available from one storage location in the warehouse. We present a compact
formulation that forgoes classical subtour elimination constraints by directly
exploiting two of the properties of an optimal picking tour used in the dynamic
programming algorithm of Ratliff and Rosenthal (1983). We extend the
formulation to three important settings prevalent in modern e-commerce
warehouses: scattered storage, decoupling of picker and cart, and multiple end
depots. In numerical studies, our formulation outperforms existing standard
SPRP formulations from the literature and proves able to solve large instances
within short runtimes. Realistically sized instances of the three problem
extensions can also be solved with low computational effort. We find that
decoupling of picker and cart can lead to substantial cost savings depending on
the speed and capacity of the picker when traveling alone, whereas additional
end depots have rather limited benefits in a single-block warehouse.
