We developed algorithms to determine the optimal location of emergency service centers in a given city. We give consideration both to the peculiarities of a particular town, Rio Rancho, and to the procedure by which problems of this nature can be solved in general. The streets of Rio Ranch0 are laid out in a uniform grid, except for two obstacles through which there are no streets. We are given data for the demand for emergency service at each block in the grid. We developed algorithms to find the transit times between any two points on the grid for Rio Rancho. To do this. we calculated a distance on a grid with no obstacles, then adjusted for the particular obstructions. We first assumed that demand was concentrated at the center of each block and that stations were located at street intersections. Under these assumptions, the problem is amenable to an exhaustive trial of all possibilities. We then made the more sophisticated assumption that the distribution of demand is continuous, and that the emergency facilities could be located anywhere on the streets. We prove two results which greatly reduce this problem: (I) it is necessary that the location of such emergency statton be at an intersection; and (2) it is an equivalent problem to consider the demand to be located discretely at the center of each block, rather than being continuously distributed over the block. Due to these results, it is possible to run an exhaustive case study in this case as well. Statistical distributions were calculated to provide a means of comparison of the optimal result with the average result. We studied the stability of the solution with respect to the demand distribution and obstacle configuration and found it to be very stable in the first case, and reasonably stable in the latter. Finally, we discuss how similar problems would be approached, and in particular, how an approximation scheme could be implemented if the large number of possibilities prohibits an exhaustive analysis. RESTATEMENT OF THE PROBLEM The township of Rio Ranch0 has hitherto not had its own emergency facilities. It has secured funds to erect two emergency facilities in 1986, each of which will combine ambulance, fire. and police facilities. Figure I indicates the demand, or number of emergencies per square block for 1985. The “L” region in the north is an obstacle, while the rectangle to the south is a park with a shallow pond. It takes an emergency vehicle an average of 15 set to go one block in the N-S direction and 20 set in the E-W direction. Our task is to locate the two facilities so as to minimize the total response time. GENERAL ASSUMPTIONS We modelled an urban traffic grid with two obstructions. We made the following assumptions: 61 I