Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance

We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an “effect” on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis … Read more

Contextual Chance-Constrained Programming

Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more

A Model of Supply-Chain Decisions for Resource Sharing with an Application to Ventilator Allocation to Combat COVID-19

We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse … Read more

A Finitely Convergent Disjunctive Cutting Plane Algorithm for Bilinear Programming

In this paper we present and analyze a finitely-convergent disjunctive cutting plane algorithm to obtain an $\epsilon$-optimal solution or detect infeasibility of a general nonconvex continuous bilinear program. While the cutting planes are obtained in a manner similar to Saxena, Bonami, and Lee [Math. Prog. 130(2): 359-413, 2011] and Fampa and Lee [2018], a feature … Read more

Sequential Convexification of a Bilinear Set

We present a sequential convexification procedure to derive, in the limit, a set arbitrary close to the convex hull of $\epsilon$-feasible solutions to a general nonconvex continuous bilinear set. Recognizing that bilinear terms can be represented with a finite number nonlinear nonconvex constraints in the lifted matrix space, our procedure performs a sequential convexification with … Read more

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. … Read more

Distributionally Robust Newsvendor Problems with Variation Distance

We use distributionally robust stochastic programs (DRSPs) to model a general class of newsvendor problems where the underlying demand distribution is unknown, and so the goal is to fi nd an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in … Read more

Identifying Effective Scenarios in Distributionally Robust Stochastic Programs with Total Variation Distance

Traditional stochastic programs assume that the probability distribution of uncertainty is known. However, in practice, the probability distribution oftentimes is not known or cannot be accurately approximated. One way to address such distributional ambiguity is to work with distributionally robust convex stochastic programs (DRSPs), which minimize the worst-case expected cost with respect to a set … Read more