The Storage Location Assignment and Picker Routing Problem: A Generic Branch-Cut-and-Price Algorithm

TL;DR

This paper introduces a comprehensive exact algorithm for the joint optimization of storage location assignment and picker routing in warehouses, effectively solving various complex variants and outperforming existing methods.

Contribution

It presents a novel Branch-Cut-and-Price framework with a new formulation and inequalities, capable of solving a broad class of SLAPRP variants efficiently.

Findings

Effectively solves medium-sized instances of SLAPRP variants.

Outperforms state-of-the-art methods in computational experiments.

Handles diverse warehouse layout and routing policy variants.

Abstract

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 storage decisions are more dynamic and are made at an operational level, making the integration of the SLAP and PRP pertinent to consider. Despite its practical significance, the joint optimization of both operations, called the Storage Location Assignment and Picker Routing Problem (SLAPRP), has received limited attention. 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. 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.