Modeling Single Picker Routing Problems in Classical and Modern Warehouses

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.