The Sequential Selection of Approaches to a Task

A task (e.g., development of a satisfactory item by a Research and Development team) is to be performed. A population of distinct approaches to the task is available. The decision maker's preferences over completed approaches are representable by a utility indicator. The utility of an approach is unknown until it is completed, but as the approach is pursued successive estimates of its utility become available at each of a finite sequence of decision points. The vector composed of an approach's estimates and its true utility is a random variable with known distribution. Pursuing an approach from one decision point to the next costs a fixed amount. Starting from an initial random drawing from the population of approaches, the set of approaches to be further pursued is narrowed down at each decision point. The paper seeks, under alternative conditions on the distribution, computationally and economically interesting properties of an optimal policy, prescribing both the sequential narrowing down and the size of the initial drawing.