Optimal sequential selection and resource allocation under uncertainty

Abstract

Consider a decision-maker who is in charge of a number of activities. At each of a sequence of decision points in time, he selects—on the basis of their performance—the set of activities to be continued further and allocates his limited resources among them. Activities receiving larger allocations tend to improve their performance, while others receiving smaller allocations tend to deteriorate. We present a controlled random walk model for the progress of these activities. The problem of maximizing the net infinite horizon discounted return is formulated in the framework of Markov decision theory, and existence of optimal strategies established. It is shown that both the optimal selection and allocation strategies exhibit a ‘favoring the leaders' behavior. Finally, explicit solutions to certain special cases are obtained illustrating these results.