A secretary problem with missing observations
Treść / Zawartość
Two versions of a best choice problem in which an employer views a sequence of $N$ applicants are considered. The employer can hire at most one applicant. Each applicant is available for interview (and, equivalently, for employment) with some probability $p$.The available applicants are interviewed in the order that they are observed and the availability of the $i$-th applicant is ascertained before the employer can observe the $(i+1)$-th applicant. The employer can rank an available applicant with respect to previously interviewed applicants. The employer has no information on the value of applicants who are unavailable for interview. Applicants appear in a random order. An employer can only offer a position to an applicant directly after the interview. If an available applicant is offered the position, then he will be hired. In the first version of the problem, the goal of the employer is to obtain the best of all the applicants. The form of the optimal strategy is derived. In the second version of the problem, the goal of the employer to obtain the best of the available applicants. It is proposed that the optimal strategy for this second version is of the same form as the form of the optimal strategy for the first version. Examples and the results of numerical calculations are given.