Modeling Single Picker Routing Problems in Classical and Modern Warehouses

TL;DR

This paper introduces a new compact mathematical model for the single picker routing problem in warehouses, extending it to modern settings and demonstrating its efficiency and practical benefits through numerical studies.

Contribution

A novel compact formulation for SPRP that avoids classical constraints and extends to modern warehouse configurations, outperforming existing models in computational efficiency.

Findings

The new model solves large instances quickly.

Decoupling picker and cart can significantly reduce costs.

Additional end depots have limited impact on costs.

Abstract

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.