The generalized linear search problem. Existence of optimal search paths. (English) Zbl 0642.90061

Balkhi, Zaid T.

J. Oper. Res. Soc. Japan 30, 399-421 (1987).

The linear search problem deals with searching for a hidden target x on the real line the position of which is given by the value of a random variable X. A searcher looks for x from a starting point, with an upper bound on his speed and using a continuous path. The author generalizes previous work by A. Beck [Isr. J. Math. 2, 221-228 (1964; Zbl 0168.395)] in the sense that an arbitrary point on the real line (and not only the origin) can be used as the starting point. The conditions on the distribution of X under which the expected cost can be minimized (i.e. the optimal search paths exist) are given. Some possible applications of the linear search problem are mentioned.

Reviewer: T.Cipra

MSC:

90B40

Search theory

Keywords:

sequential search path; linear search problem; continuous path; expected cost; optimal search paths

Citations:

Zbl 0168.395