About the speaker: Jeff Linderoth is the Harvey D. Spangler Professor in the Department of Industrial and Systems Engineering at the University of Wisconsin-Madison, and he served as the department's chairperson from 2016 to 2021. Prof. Linderoth holds a courtesy appointment in the Computer Sciences department and as a Discovery Fellow at the Wisconsin Institutes of Discovery. Dr. Linderoth received his Ph.D. degree from the Georgia Institute of Technology in 1998. He was previously employed in the Mathematics and Computer Science Division at Argonne National Laboratory, with the optimization-based financial products firm of Axioma, and as an Assistant Professor at Lehigh University. His awards include multiple best paper awards, an Early Career Award from the Department of Energy, the SIAM Activity Group on Optimization Prize, and the INFORMS Computing Society (ICS) Prize. In 2016, he was elected to membership as an INFORMS Fellow. Dr. Linderoth was once stranded in Marseille with Jon Lee for five days.

Abstract: We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables X through a set of discrete actions that we refer to as probing. Specifically, probing allows the decision-maker to observe components of a random vector Y that is jointly distributed with X. We propose a three-stage optimization model for this problem, wherein the first-stage variables select components of Y to observe, and decisions in subsequent stages must be consistent with the obtained information. In the case that X and Y have finite support, Goel and Grossmann gave a mixed-integer programming formulation of this problem whose size is proportional to the square of cardinality of the sample space of the random variables. We propose to solve the model using bounds obtained from an information-based relaxation, combined with a branching scheme that enforces the consistency of decisions with observed information. The branch-and-bound approach can naturally be combined with sampling in order to estimate both lower and upper bounds on the optimal solution value. We demonstrate the scalability of our approach against the exact MIP formulation on instances of a stochastic facility location problem.