Stochastic Selection Problems with Testing

29 Pages Posted: 11 Dec 2017

See all articles by Chen Attias

Chen Attias

Weizmann Institute of Science

Robert Krauthgamer

Weizmann Institute of Science

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Yaron Shaposhnik

University of Rochester - Simon Business School

Date Written: December 6, 2017

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

Suggested Citation

Attias, Chen and Krauthgamer, Robert and Levi, Retsef and Shaposhnik, Yaron, Stochastic Selection Problems with Testing (December 6, 2017). Available at SSRN: https://ssrn.com/abstract=3076956 or http://dx.doi.org/10.2139/ssrn.3076956

Chen Attias

Weizmann Institute of Science

Rehovot, 76100
Israel

Robert Krauthgamer

Weizmann Institute of Science ( email )

234 Herzl Street
Rehovot, 76100
Israel

HOME PAGE: http://www.wisdom.weizmann.ac.il/~robi/

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Yaron Shaposhnik (Contact Author)

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
92
Abstract Views
682
rank
310,570
PlumX Metrics