The Navy passive ranging problem

One of the important interfaces between the operations researcher and the real world is data, particularly data involving human decisions. Such data often contain information that is hard to understand because we are not expecting to hear what it is saying. The easy route is to discard it as ‘contaminated’ or ‘full of errors’ when persistence and open mindedness would be rewarded. This is a brief account of such a case. The task was to develop an improved decision processes to be used by a submarine commander in determining when to fire a torpedo at a target submarine he is approaching. The critical element in the decision is knowledge of the distance between him and his target. The decision inputs are a series of measurements of bearing to the target coupled with heading changes during his approach which are called ‘passive ranging maneuvers’. Each such maneuver, consisting of two straight legs with a large heading change in between, yields a measurement of target range through a process related to triangulation. The accuracy of the measurement increases with the time spent on each leg of the maneuver and also improves as the actual range becomes shorter. On the other hand, if the legs are too long, the rate at which the attacking submarine gets range information may be too slow and he may inadvertently get too close before firing. Hence the need for optimizing his ‘approach tactics’. The Navy had developed a substantial quantity of realistic exercise data on which the decision processes were to be based, and it was examined quantitatively with surprising conclusions.