AbstractProblematic situations often arise in which it is required to provide a solution which will tend to avoid events, which, if they occur, would be very costly, or, if not directly costable, they would be highly undesirable. Although direct approaches to this sort of problem exist, they can be unmanageable. If, however, we take as a posit, that the frequency with which the undesirable events arise, in the optimum solution, is small, considerable simplifications can be made. Naturally we need to check the posit once the solution has been found. This paper considers three applications of this principle, viz. determination of how many chargers are needed for steel furnaces, where the undesirable event is“a furnace waits for service”; determination of the number of emergency beds to set aside in a hospital unit, where the undesirable event is“an emergency case arrives and no bed is immediately available”; determination of an inventory reorder rule where the undesirable event is“stock run-out”. The general principle is formalized.