Inventory-routing problems: Review, challenges, and innovations

We present a comprehensive review of the Inventory-Routing Problem (IRP), synthesizing the main variants, clarifying their methodological foundations, and outlining promising directions for future research relevant to both researchers and practitioners in logistics and supply chain management. We describe the IRP using arc- and path-based formulations, then propose a systematic categorization framework through four categories: (i) structural variants, (ii) application-oriented variants, (iii) additional modeling considerations, and (iv) objectives. This framework provides a structured perspective on the evolution of IRP variants in the literature. We highlight how IRP applications span diverse sectors, reflecting the variety of operational contexts. Moreover, we categorize and examine existing exact or heuristic solution approaches, compare these methods by mapping them to relevant IRP variants, review benchmark instances, evaluate how algorithm performance evolves as instance size increases, while summarizing computational outcomes on standard benchmark sets. We emphasize emerging research developments, including the use of the Internet of Things and electric vehicles, as well as the application of machine learning and artificial intelligence to manage the computational complexity of high-dimensional data in IRP.