In this paper, we solve a class of two-stage distributionally robust optimization problems which have the property of supermodularity. We exploit the explicit upper bounds on the expectation of supermodular functions and derive the worst-case distribution for the robust counterpart. This enables us to develop an efficient method to derive an exact optimal solution of … Read more
For many classical combinatorial optimization problems such as, e.g., the shortest path problem or the spanning tree problem, the robust counterpart under general discrete, polytopal, or ellipsoidal uncertainty is known to be intractable. This implies that any algorithm solving the robust counterpart that can access the underlying certain problem only by an optimization oracle has … Read more
Adaptive robust optimization is a modelling paradigm for multistage optimization under uncertainty where one seeks decisions that minimize the worst-case cost with respect to all possible scenarios in a prescribed uncertainty set. However, optimal policies for adaptive robust optimization problems are difficult to compute. Therefore, one often restricts to the class of affine policies which … Read more
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of n dependent Bernoulli random variables exceeds an integer k. Under knowledge of all pairs of bivariate distributions denoted by a complete graph, the bounds are NP-hard to compute. When the bivariate distributions are specified on a … Read more
We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-robustified LCPs for … Read more
We study the nurse staffing problem under random nurse demand and absenteeism. While the demand uncertainty is exogenous (stemming from the random patient census), the absenteeism uncertainty is endogenous, i.e., the number of nurses who show up for work partially depends on the nurse staffing level. For the quality of care, many hospitals have developed … Read more
We develop a general methodology to derive probabilistic guarantees for solutions of robust optimization problems. Our analysis applies broadly to any convex compact uncertainty set and to any constraint affected by uncertainty in a concave manner, under minimal assumptions on the underlying stochastic process. Namely, we assume that the coordinates of the noise vector are … Read more
Robust optimization (RO) is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, such as R&D project selection, production planning, or preference elicitation for product or policy recommendations, the time of information discovery is decision-dependent and the uncertain parameters only become observable after an often costly … Read more
A concentrated solar tower power plant consists of a receiver mounted atop of a central tower and a field of movable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle. Aiming strategies are used to assign each heliostat to an … Read more
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test … Read more