Optimization under Uncertainty for Ambulance Location-Allocation

• Autores: Imanol Gago Carro
• Directores de la Tesis: María Merino Maestre (dir. tes.), Unai Aldasoro Marcellan (codir. tes.)
• Lectura: En la Universidad del País Vasco - Euskal Herriko Unibertsitatea ( España ) en 2025
• Idioma: inglés
• Programa de doctorado: Programa de Doctorado en Matemáticas y Estadística por la Universidad de La Laguna; la Universidad de Oviedo; la Universidad de Zaragoza; la Universidad del País Vasco/Euskal Herriko Unibertsitatea y la Universidad Pública de Navarra
• Menciones:
  • Internacional
• Calificación: Sobresaliente Cum Laude
• Materias:
  • Matemáticas
• Enlaces
  • Tesis en acceso abierto en: ADDI
• Resumen

  • This thesis studies the strategic planning of Emergency Medical Services (EMS) by modeling the location and allocation of ambulances under conditions of uncertainty and with multiple objectives. Using the Basque public EMS as a real-world case study, we utilize historical databases to model the uncertainty that is gradually introduced into the proposed models. In this way, we estimate stochastic travel times using adjusted distributions (in particular, BCCG), with a clustering process and GAM. As a first model, we propose a two-stage 0-1 stochastic MILP to evaluate relocation and expansion policies, balancing overall efficiency and equity between regions. The model incorporates spatiotemporal uncertainty of emergencies and a response time penalty at various intervals. Second, we formulate a hierarchical compromise model: first, coverage is maximized, and then the average response time, resource adequacy, and equity (using CVaR) are jointly improved. To address large-scale cases, we extend the Branch-and-Fix Coordination matheuristic to handle constraints between scenarios. This model incorporates a new uncertain component: ambulance travel times. Third, we develop a distributionally robust optimization framework to protect against poorly specified travel time distributions and compare it with stochastic and robust optimization. A discrete-event simulation model shows that DRO solutions better align design and operation. Overall, the thesis bridges the gap between theory and practice by using realistic data, scalable algorithms, and rigorous validation.