Stochastic Selection Problems with Testing

Abstract

We study the problem of a decision-maker having to select one of many competing alternatives (e.g., choosing between projects, designs, or suppliers) whose future revenues are a priori unknown and modeled as random variables of known probability distributions. The decision-maker can pay to test each alternative to reveal its specific revenue realization (e.g., by conducting market research), and her goal is to maximize the expected revenue of the selected alternative minus the testing costs. This model captures an interesting trade-off between gaining revenue of a high-yield alternative and spending resources to reduce the uncertainty in selecting it. The combinatorial nature of the problem leads to a dynamic programming (DP) formulation with high-dimensional state space that is computationally intractable. By characterizing the structure of the optimal policy, we derive efficient optimal and near-optimal policies that are simple and easy-to-compute. In fact, these policies are also myopic -- they only consider a limited horizon of one test. Moreover, our policies can be described using intuitive `testing intervals' around the expected revenue of each alternative, and in many cases, the dynamics of an optimal policy can be explained by the interaction between the testing intervals of various alternatives.

Keywords: Selection, Testing, Dynamic programming, Approximation algorithms, Myopic policies