Locating emergency facilities with random demand for risk minimization

Locating emergency service facilities is a challenging problem. Planners do not know specifically where emergencies will occur and, therefore, struggle to find a location that effectively ensures that the risk of poor service to any specific emergency is minimized. In this paper, we study the problem where locations of each demand point (emergency occurence) are random. Our objective is to minimize the expected maximum rectilinear distance from the facility to the demand points. This problem has practical importance in public sector as it aims to minimize the expected maximum risk when locating an emergency response facility. We start with a one dimensional problem and extend the results to the more complex two dimensional case. We present some properties of the problem along with examples for special cases. We propose a simulation approach to solving complex two dimensional cases and present simulation results for general cases to illustrate the problem and provide insight into solutions. We show that the simulation approach provides solutions very close to optimal for the linear case and suggest that it may provide valuable insight into the location selection system.