The rational management of emergency services centers focuses on two important goals, the optimal positioning of these centers to be able to provide services in the fastest possible way, and the second is to ensure that these centers can provide, with no delay, service to every one upon his/her request, especially in emergency cases when demand on these services are at the peak  which means that in urban design it is very important to locate the emergency service centers in   a position that satisfy both the two above goals. In fact, several research works concerned with determining the optimum location of the service centers but with a little concern of the limited capacity of each center. This research discusses how to achieve these two goals by treating the problem mathematically. Limitation of the capacity of each center is also a matter of concern. Finally, an effective computer algorithm is provided to illustrate the practical implication of the performed mathematical solution.