Title:

Probing-enhanced stochastic programming

Abstract:

We consider a two-stage stochastic program 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.  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, where the first-stage variables select components of Y to observe.  In the case that X and Y have finite support, a model of Goel and Grossmann can be applied to obtain a 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 even for problems with continuous distribution.  We demonstrate the approach on instances of a stochastic facility location problem.

This is joint work with Zhichao Ma, Jeff Linderoth, Youngdae Kim, and Logan Matthews.

Bio:

James (Jim) Luedtke is a Professor in the department of Industrial and Systems Engineering at the University of Wisconsin-Madison and a Discovery Fellow at the Wisconsin Institute for Discovery. Luedtke earned his Ph.D. at Georgia Tech and did postdoctoral work at the IBM T.J. Watson Research Center. Luedtke’s research is focused on methods for solving stochastic and mixed-integer optimization problems, as well as applications of such models. His current research interests include investigation of computational methods for solving two and multi-stage stochastic integer programming problems, and integration of optimization and machine learning models. Luedtke serves on the editorial boards of the journals SIAM Journal on Optimization and Mathematical Programming Computation and is chair of the Mathematical Optimization Society Publications Committee.
Georgia Tech ISyE Departmental Seminar Speaker Invitation