Robust Optimization Under Controllable Uncertainty

We call an optimization problem an optimization problem with controllable uncertainty if a) it contains uncertain input data and b) prior to deciding the optimization variables, the optimizer can for a certain cost reduce the scenario set of this uncertain data. In particular, we are interested in situations where each uncertain parameter is a priori … Read more

Improving the Security of United States Elections with Robust Optimization

For more than a century, election officials across the United States have inspected voting machines before elections using a procedure called Logic and Accuracy Testing (LAT). This procedure consists of election officials casting a test deck of ballots into each voting machine and confirming the machine produces the expected vote total for each candidate. We … Read more

A robust approach to food aid supply chains

One of the great challenges in reaching zero hunger is to secure the availability of sufficient nourishment in the worst of times such as humanitarian emergencies. Food aid operations during a humanitarian emergency are typically subject to a high level of uncertainty. In this paper, we develop a novel robust optimization model for food aid … 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

An Extension of the Bertsimas & Sim Result for Discrete, Linear, and Γ-Robust Min-Max Problems

Due to their nested structure, bilevel problems are intrinsically hard to solve – even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. We provide an extension of the … Read more

Recycling Valid Inequalities for Robust Combinatorial Optimization with Budget Uncertainty

Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more

Connections and Reformulations between Robust and Bilevel Optimization

Robust and bilevel optimization share the common feature that they involve a certain multilevel structure. Hence, although they model something rather different when used in practice, they seem to have a similar mathematical structure. In this paper, we analyze the connections between different types of robust problems (strictly robust problems with and without decision-dependence of … Read more

Distributionally Ambiguous Multistage Stochastic Integer and Disjunctive Programs: Applications to Sequential Two-player Interdiction Games

This paper studies the generalizations of multistage stochastic mixed-integer programs (MSIPs) with distributional ambiguity, namely distributionally risk-receptive and risk-averse multistage stochastic mixed-integer programs (denoted by DRR- and DRA-MSIPs). These modeling frameworks have applications in non-cooperative Stackelberg games involving two players, namely a leader and a follower, with uncertainty in the impact of the decisions made … Read more

Randomized Robust Price Optimization

The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be realized in practice. A tacit assumption in this approach is that the pricing decision … Read more

Mixed-Integer Programming for a Class of Robust Submodular Maximization Problems

\(\) We consider robust submodular maximization problems (RSMs), where given a set of \(m\) monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes two variants of robust submodular maximization problems in the literature, depending on the choice of the scaling vector. On one hand, by … Read more