Hub location problems with asymmetric allocation
Hub location problems are central to optimizing logistics, telecommunications, and transportation networks by consolidating flows through strategically placed hubs. While existing models assume symmetric allocation, where hubs handle incoming and outgoing flows uniformly, real-world applications often require asymmetric handling of origins and destinations. This paper introduces the Asymmetric Hub Location Problem ((r,s)-AHLP), a novel framework where origins and destinations may connect to hubs under distinct allocation limits (r and s, respectively). We then focus on the (1,p)-AHLP variant, where origins are single-assigned and destinations are multi-assigned, motivated by applications in humanitarian logistics and global supply chains (e.g., UN relief networks, e-commerce fulfillment). We propose two integer programming formulations: A four-index adaptation of classical models and a new compact three-index formulation. The latter reduces the size while improving effectiveness, supported by valid inequalities and decomposition techniques. The computational study, performed on standard datasets commonly used in hub location literature, demonstrates the high effectiveness and efficiency of the proposed solution methodology. Our work presents a robust methodological framework for the (1,p)-AHLP, significantly expanding the applicability of hub location theory to asymmetric flow contexts and providing a foundation for future studies on complex multi-level hub network design.