Optimal hostage rescue problem where action can only be taken once : case where effect vanishes thereafter

摘要

we propose the following model for optimal rescue problems concerning hostages. Suppose that a person is taken as a hostage and that a decision has to be made from among three alternatives: rescuing, no rescuing, or taking one action which will save the situation. It is assumed that the action can only be taken once and it will be effective only at that time, i.e., the effect vanishes thereafter. The objective here is to find the optimal decision rule so as to maximize the probability of the hostage not being killed. Several properties of the optimal rescuing rule are revealed.