Minimax Detection Station Placement

A model for the placement of n detection stations for optimum coverage of an arbitrary plane area is described. The stations are assumed to be identical and to have a probability of detection that is a function only of the distance between the station and the event to be detected. Furthermore, the stations are assumed to operate independently of each other. It is also assumed that the enemy has complete knowledge of the station locations and effectiveness and is interested only in eluding detection by the detection stations. Thus, the situation is reduced to the minimax problem of placing the stations so that the maximum probability of not detecting an enemy event is minimized. A hill climbing iterative technique for finding the optimum locations is described in some detail. This technique is illustrated for the problem of locating detection stations within the United States and Soviet Union. The results of these applications are presented and discussed. The paper concludes with some remarks on how this model can be made more descriptive of the real world situations being modeled.