Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 1, pp. 76--84



A. A. K. MAJUMDAR, Jahangirnagar University

SUMMARY.  This paper extends the classical secretary problem with three stops to the case when offers arrive in [0, T], where T itself is a random variable, uniformly distributed on [0,1]. A traveler, observing relative ranks, wishes to select the absolute best in three stops before the random time T; if he succeeds, it would be termed his "win". The objective is to devise a stopping rule which stops at and accepts three applicants before T such that the probability of win is maximized. The dynamic programming has been employed to show that the optimal policy is characterized by three critical constants $\alpha_3$, $\alpha_2$ and $\alpha_1$ such that the traveler makes his first, second and third stops at the earliest candidates after $\alpha_3$, $\alpha_2$ and $\alpha_1$ respectively.

AMS (1991) subject classification.  90C39.

Key words and phrases. Classical secretary problem, best-choice problem, random termination, dynamic programming.

Full paper (PDF)

This article in mathematical reviews.