A Best-Choice Problem with Linear Travel Cost

Abstract

The concepts of sampling cost and recall of previously seen applicants are here combined in a natural way: The best, second best, and so forth, of infinitely many applicants are located at points independently and uniformly distributed on the unit interval. A traveler, observing relative ranks, hopes to select the best applicant, and incurs a cost proportional to the total distance traveled, plus a unit loss if the applicant selected is not overall best. The optimal policy and its risk are derived. A finite version of the problem is also solved.