Facility Location Problems determine optimal locations for facilities (warehouses, plants, service centers) to minimize total costs while satisfying demand. The uncapacitated facility location problem (UFLP): given n customers and m potential facility sites with fixed opening costs fⱼ and service costs cᵢⱼ, decide which facilities to open and how to assign customers. Objective: minimize Σⱼ fⱼyⱼ + Σᵢ Σⱼ cᵢⱼxᵢⱼ where yⱼ ∈ {0,1} indicates if facility j opens. Variants include: capacitated facility location, p-median problem, p-center problem, and hub location. Solution methods: Lagrangian relaxation, branch and bound, and various heuristics. Applications in supply chain design, emergency services, and telecommunications.