A stochastic model for a researcher's problem

Abstract

We consider the problem of a researcher who successively uses some random mechanism to select topics to work on for certain time periods, where a random non-increasing output rate is associated to each topic. The objective is to find a strategy, i.e., a sequence of stopping times (sojourn times for the topics) so as to maximize the long-run average expected yield per unit time. If the chosen topics form an IID sequence, a stationary strategy, consisting of independent replications of a certain threshold stopping time, is optimal. This strategy however requires a complete knowledge of the underlying probability distributions. As an alternative, we suggest a non-stationary strategy which is defined in terms of the observable development of the research process. It is shown that this strategy is also optimal in the sense that it achieves the maximum long-run average expected yield almost surely. © 1992, Taylor & Francis Group, LLC. All rights reserved.