Optimized Dimensionality Reduction for Moment-based Distributionally Robust Optimization

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint distribution of random parameters runs in a distributional ambiguity set constructed by moment information and makes decisions against the worst-case distribution within the set. Although most moment-based DRO problems … Read more

Differential Privacy via Distributionally Robust Optimization

In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the statistics to be published, which in turn leads to a privacy-accuracy trade-off: larger perturbations provide stronger privacy guarantees, but they … Read more

Data-driven distributionally robust optimization: Intersecting ambiguity sets, performance analysis and tractability

We consider stochastic programs in which the probability distribution of uncertain parameters is unknown and partial information about it can only be captured from limited data. We use distributionally robust optimization (DRO) to model such problems. As opposed to the commonly used approach for DRO problems that suggests creating an ambiguity set by following a specific … Read more

Multi-Stage Robust Mixed-Integer Programming

Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more

Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

We study distributionally robust chance constrained programs (DRCCPs)  with individual chance constraints and random right-hand sides. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. We consider … Read more

Robust Workforce Management with Crowdsourced Delivery

We investigate how crowdsourced delivery platforms with both contracted and ad-hoc couriers can effectively manage their workforce to meet delivery demands amidst uncertainties. Our objective is to minimize the hiring costs of contracted couriers and the crowdsourcing costs of ad-hoc couriers while considering the uncertain availability and behavior of the latter. Due to the complication … Read more

Robust Two-Dose Vaccination Schemes and the Directed b-Matching Problem

In light of the recent pandemic and the shortage of vaccinations during their roll-out, questions arose regarding the best strategy to achieve immunity throughout the population by adjusting the time gap between the two necessary vaccination doses. This strategy has already been studied from different angles by various researches. However, the deliveries of vaccination doses … Read more

Robust two-stage combinatorial optimization problems under discrete demand uncertainties and consistent selection constraints

In this paper, we study a robust two-stage concept of combinatorial optimization problems under discrete demand uncertainty. Combinatorial optimization problems are based on a finite set of elements for which we decide whether they are part of a solution. We divide the elements into two types, the so-called fixed and free elements. In a first … Read more

Approximation Guarantees for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

In this work we investigate the min-max-min robust optimization problem for binary problems with uncertain cost-vectors. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It is known that the min-max-min robust problem … Read more

Two-stage and Lagrangian Dual Decision Rules for Multistage Adaptive Robust Optimization

In this work, we design primal and dual bounding methods for multistage adjustable robust optimization (MSARO) problems by adapting two decision rules rooted in the stochastic programming literature. This approach approximates the primal and dual formulations of an MSARO problem with two-stage models. From the primal perspective, this is achieved by applying two-stage decision rules … Read more