James R. Luedtke Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statistical estimates on the optimal value of the true problem can be obtained by solving … Read more
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 $\xi$ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector $\eta$ that is jointly-distributed with $\xi$ allows the … Read more
In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more
We consider a multi-stage stochastic lot-sizing problem with service level constraints and supplier-driven product substitution. A firm has multiple products and it has the option to meet demand from substitutable products at a cost. Considering the uncertainty in future demands, the firm wishes to make ordering decisions in every period such that the probability that … Read more
We propose a new method for separating valid inequalities for the epigraph of a function of binary variables. The proposed inequalities are disjunctive cuts defined by disjunctive terms obtained by enumerating a subset $I$ of the binary variables. We show that by restricting the support of the cut to the same set of variables $I$, … Read more
In the High-Rank Matrix Completion (HRMC) problem, we are given a collection of n data points, arranged into columns of a matrix X, and each of the data points is observed only on a subset of its coordinates. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of … Read more
We study the static chance-constrained lot sizing problem, in which production decisions over a planning horizon are made before knowing random future demands, and the backlog and inventory variables are then determined by the demand realizations. The chance constraint imposes a service level constraint requiring that the probability that any backlogging is required should be … Read more
We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs … Read more
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained … Read more
We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation, and are derived from solving single scenario integer programming subproblems identical to those used in the nonanticipative Lagrangian dual of a stochastic integer program. While Lagrangian cuts have the potential to significantly … Read more