| In this thesis, we generalize a set of facility location models within a two-stage robust optimization framework by assuming each demand is only known to lie within a continuous and bounded uncertainty region. Our approach involves discretizing each uncertainty region into a set of finite scenarios, each of which represents a potential location where the demand may be realized. We show that the gap between the optimal values of the theorized continuous uncertainty problem and our discretized model can be bounded by a function of the granularity of the discretization. We then propose a solution technique based on row-and-column generation, and compare its performance with existing solution methods. Lastly, we apply our robust location models to the problem of ambulance positioning using cardiac arrest location data from the City of Toronto, and show that hedging against demand location uncertainty may help decrease EMS response times to cardiac arrest emergencies. |
