An extension to models for the Maximal Covering Location Problem (MCLP) is applied to the Saudi Arabian Red Crescent Society (SARCS), Riyadh City, Saudi Arabia. The purpose is to identify the optimal locations of emergency medical service (EMS) stations. This is achieved by firstly locating these stations so the maximum expected demand may be reached within a pre-specified target time. Then, secondly, ensuring that any demand located within the target time will find at least one ambulance available. The demand rates are identified when it is necessary to add an ambulance in order to maintain the performance level for the availability of ambulances.