The storage location assignment and picker routing problem: A generic branch-cut-and-price algorithm

The Storage Location Assignment Problem (SLAP) and the Picker Routing Problem (PRP) have received significant attention in the literature due to their pivotal role in the performance of the Order Picking (OP) activity, the most resource-intensive process of warehousing logistics. The two problems are traditionally considered at different decision-making levels: tactical for the SLAP, and operational for the PRP. However, this paradigm has been challenged by the emergence of modern practices in e-commerce warehouses, where decisions are more dynamic. This shift makes the integrated problem, called the Storage Location Assignment and Picker Routing Problem (SLAPRP), pertinent to consider. Scholars have investigated several variants of the SLAPRP, including different warehouse layouts and routing policies. Nevertheless, the available computational results suggest that each variant requires an ad-hoc formulation. Moreover, achieving a complete integration of the two problems, where the routing is solved optimally, remains out of reach for commercial solvers, even on trivial instances. In this paper, we propose an exact solution framework that addresses a broad class of variants of the SLAPRP, including all the previously existing ones. This paper proposes a Branch-Cut-and-Price framework based on a novel formulation with an exponential number of variables, which is strengthened with a novel family of non-robust valid inequalities. We have developed an ad-hoc branching scheme to break symmetries and maintain the size of the enumeration tree manageable. Computational experiments show that our framework can effectively solve medium-sized instances of several SLAPRP variants and outperforms the state-of-the-art methods from the literature.