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Inspired by its success for their continuous counterparts, the standard approach to deal with mixed-integer recourse (MIR) models under distributional uncertainty is to use distribu- tionally robust optimization (DRO). We argue, however, that this modeling choice is not always justified since DRO techniques are generally computationally challenging when integer decision variables are involved. That is why we propose an alternative approach for dealing with distributional uncertainty for the special case of simple integer recourse (SIR) models, which is aimed at obtaining models with improved computational tractability. We show that such models can be obtained by pragmatically selecting the uncertainty set. Here, we consider uncertainty sets based on the Wasserstein distance and also on generalized moment conditions. We compare our approach with standard DRO both numerically and theoretically. An important side result of our analysis is the derivation of performance guarantees for convex approximations of SIR models. In contrast to the literature, these error bounds are not only valid for a continuous distribution but hold for any distribution. [ABSTRACT FROM AUTHOR]

Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging against a range of distributions, properly characterized in an ambiguity set, is of interest. We study two-stage stochastic programs with linear recourse in the context of distributional ambiguity, and formulate several distributionally robust models that vary in how the ambiguity set is built. We focus on the Wasserstein distance under a p-norm, and an extension, an optimal quadratic transport distance, as mechanisms to construct the set of probability distributions, allowing the support of the random variables to be a continuous space. We study both unbounded and bounded support sets, and provide guidance regarding which models are meaningful in the sense of yielding robust first-stage decisions. We develop cutting-plane algorithms to solve two classes of problems, and test them on a supply-allocation problem. Our numerical experiments provide further evidence as to what type of problems benefit the most from a distributionally robust solution. [ABSTRACT FROM AUTHOR]

Dupacová's early work in minimax solutions of stochastic programs [[6], [24]] predated by half a century a recent surge of work in distributionally robust optimization. Two others major lines of Dupacová's research contributions concern scenario generation and scenario reduction [[15]], with precursor work including [[5], [21]], and her work on asymptotics [[10], [23]]. Jitka Dupacová was the first woman vice dean at the Faculty of Mathematics and Physics at Charles University in 1979. Stochastic programming has seen recent advances with far-reaching impact involving risk measures, distributionally robust optimization, and applications in areas ranging from energy and natural resources to economics and finance to statistics and machine learning. [Extracted from the article]

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current (AC) optimal power flow (ACOPF) problem has been considered challenging since the 1960s due to its nonconvexity. Linear approximation of the AC power flow system sees pervasive use, but does not guarantee a physically feasible system configuration. In recent years, various convex relaxation schemes for the ACOPF problem have been investigated, and under some assumptions, a physically feasible solution can be recovered. Based on these convex relaxations, we construct a robust convex optimization problem with recourse to solve for optimal controllable injections (fossil fuel, nuclear, etc.) in electric power systems under uncertainty (renewable energy generation, demand fluctuation, etc.). We propose a cutting-plane method to solve this robust optimization problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound. [ABSTRACT FROM AUTHOR]

We consider a multistage stochastic linear program that lends itself to solution by stochastic dual dynamic programming (SDDP). In this context, we consider a distributionally robust variant of the model with a finite number of realizations at each stage. Distributional robustness is with respect to the probability mass function governing these realizations. We describe a computationally tractable variant of SDDP to handle this model using the Wasserstein distance to characterize distributional uncertainty. [ABSTRACT FROM AUTHOR]

Package carriers use sophisticated automated sorting facilities to efficiently process inbound packages and sort them to their down line destinations. During each of several daily processing windows, primary sorters perform high level sortation of the packages and direct them to one of several secondary sorters that are then used to segregate the packages by their outbound loading destinations. We examine the problem of assigning package destinations to the secondary sorters in a way that balances the workload in the facility, while incorporating the day-to-day fluctuation in package volumes and adhering to the outbound loading capacities of the various workcenters in the facility. We present a general stochastic modeling framework using chance constraints to balance the flows, and robust constraints to model the capacity limits. We propose and evaluate the performance of three alternative mixed integer nonlinear formulations for the problem and determine which is most effective. Significant improvement in package flow balance and loading capacity robustness is shown for the test sorting facilities by comparing the solutions from the proposed new model to those obtained when ignoring, partially or completely, the stochasticity in the package volumes. [ABSTRACT FROM AUTHOR]