The secretary problem of minimizing the expected rank: a simple suboptimal approach with generalizations
Abba Μ. Krieger, Ester Samuel‐Cahn · Advances in Applied Probability · 2009
The secretary problem for selecting one item so as to minimize its expected rank, based on observing the relative ranks only, is revisited. A simple suboptimal rule, which performs almost as well as the optimal rule, is given. The rule stops with the smallest i such that R i ≤ ic /( n+1-i ) for a given constant c , where R i is the relative rank of the i th observation and n is the total number of items. This rule has added flexibility. A curtailed version thereof can be used to select an item with a given probability P, P<1. The rule can be used to select two or more items. The problem of selecting a fixed percentage, α, 0<α<1, of n , is also treated. Numerical results are included to illustrate the findings.