Optimal survivor search for a target with conditionally deterministic motion under reward criterion

In this paper, an optimal search-and-rescue operation maximizing the expected reward for a survivor with a conditionally deterministic motion and with a random lifetime is investigated. Necessary conditions for the optimal distribution of the searching effort and the optimal stopping time of the search are derived and the meaning of the conditions for the optimal plan are elucidated. To show the properties of the optimal search plan, several numerical examples are presented and special cases and generalization of the model are also discussed.