A multiple secretary problem with switch costs

Abstract

In this thesis, we utilize probabilistic reasoning and simulation methods to determine the optimal selection rule for the secretary problem with switch costs, in which a known number of applicants appear sequentially in a random order, and the objective is to maximize the sum of the qualities of all hired secretaries over all time. It is assumed that the quality of each applicant is uniformly distributed and any hired secretary can be replaced by a better qualified one at a constant switch cost. A dynamic program is formulated and the optimal selection rule for the single secretary case is solved. An approximate solution is given for the multiple secretary case, in which we are allowed to have more than one secretary at a time. An experiment was designed to simulate the interview process, in which respondents were sequentially faced with random numbers that represent the qualities of different applicants. Finally, the experimental results are compared against the optimal selection strategy.