AIRO Young Dissertation Award

Facility location problems are pivotal in both academic research and practical applications across various sectors. This thesis underscores the importance of such problems within the telecommunications (TLC) sector, given the crucial role TLC plays in modern society. The advent of 5G technology has posed new challenges in meeting network quality standards, demanding sophisticated mathematical optimization techniques. Indeed, a growing demand for service and an increasing signal interference leading to service degradation are expected. Traditional network design formulations suffer from numerical issues and are limited in their applicability to large-scale practical scenarios due to slow resolution processes and unreliable solutions. In the more general context of service and coverage networks, similar urgencies exist: there is a requirement for high-quality service alongside an increasing demand for service. Hence, there is a need to address system congestion to meet service requirements. However, this topic is poorly explored in the literature, and data uncertainty is not taken into account, resulting in unreliable deterministic solutions. Driven by these complexities, this thesis makes two significant contributions addressing two distinct network design problems: one specific to the telecommunications sector and the other broadly applicable to service and communications networks, with the aim of developing solution approaches that are both theoretically robust and practically viable. The first contribution focuses on the location of transmitters, which are the facilities enabling wireless connections, to meet service coverage requirements. We addressed the drawbacks of traditional formulations from a modeling point of view, improving the modeling of service quality constraints, proposing valid cutting planes, constraints aggregation, and various presolve operations. Our proposals prove effective, allowing us to achieve optimality in large-scale scenarios within solution times aligning well with planning windows. The second contribution concerns the introduction of a novel location problem allowing for partial coverage that considers both the minimization of congestion and the protection from uncertainty in customer demand. We provide mathematical formulations to this problem and propose Benders decomposition approaches to solve it, also introducing a cut-strengthening technique to efficiently deal with the degeneracy of the Benders subproblem. Our tailored approach outperforms Gurobi on adapted instances from the literature.