On Solving Two-Stage Distributionally Robust Disjunctive Programs with a General Ambiguity Set

We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). … Read more

Decomposition Algorithms for Distributionally Robust Optimization using Wasserstein Metric

We study distributionally robust optimization (DRO) problems where the ambiguity set is de ned using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-in nite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, … Read more

Decomposition Algorithms for Two-Stage Distributionally Robust Mixed Binary Programs

In this paper, we introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or L-shaped method, to solve TSDR-MBPs with binary … Read more

Generation of Feasible Integer Solutions on a Massively Parallel Computer

We present an approach to parallelize generation of feasible solutions of mixed integer linear programs in distributed memory high performance computing environments. The approach combines a parallel framework with feasibility pump (FP) as the rounding heuristic. The proposed approach runs multiple FP instances with different starting so- lutions concurrently, while allowing them to share information. … Read more

On Solving General Two-Stage Stochastic Programs

We study general two-stage stochastic programs and present conditions under which the second stage programs can be convexified. This allows us to relax the restrictions, such as integrality, binary, semi-continuity, and many others, on the second stage variables in certain situations. Next, we introduce two-stage stochastic disjunctive programs (TSS-DPs) and extend Balas’s linear programming equivalent … Read more

Tight second-stage formulations in two-stage stochastic mixed integer programs

We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more

A Data Driven Functionally Robust Approach for Coordinating Pricing and Order Quantity Decisions with Unknown Demand Function

We consider a retailer’s problem of optimal pricing and inventory stocking decisions for a product. We assume that the price-demand curve is unknown, but data is available that loosely specifies the price-demand relationship. We propose a conceptually new framework that simultaneously considers pricing and inventory decisions without a priori fitting a function to the price-demand … Read more

A Distributionally-robust Approach for Finding Support Vector Machines

The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population … Read more

A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

We study the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules, well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the … Read more

A Robust Additive Multiattribute Preference Model using a Nonparametric Shape-Preserving Perturbation

This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust … Read more