The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) … Read more
We develop a modular and tractable framework for solving an adaptive distributionally robust linear opti- mization problem, where we minimize the worst-case expected cost over an ambiguity set of probability dis- tributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in … Read more
Common approaches to solve a robust optimization problem decompose the problem into a master problem (MP) and adversarial separation problems (APs). MP contains the original robust constraints, however written only for finite numbers of scenarios. Additional scenarios are generated on the fly by solving the APs. We consider in this work the budgeted uncertainty polytope … Read more
We consider combinatorial optimization problems with uncertain objective functions. In the min-max-min robust optimization approach, a fixed number k of feasible solutions is computed such that the respective best of them is optimal in the worst case. The idea is to calculate a set of candidate solutions in a potentially expensive preprocessing and then select … Read more
In radiation therapy planning, uncertainties in target volume definition yield a risk of underdosing the tumor. The classical way to prevent this in the context of external beam radiotherapy (EBRT) has been to expand the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept … Read more
In this paper, we consider two-stage adjustable robust linear optimization problems under uncertain constraints and study the performance of piecewise static policies. These are a generalization of static policies where we divide the uncertainty set into several pieces and specify a static solution for each piece. We show that in general there is no piecewise … Read more
Emergency care necessitates adequate and timely treatment, which has unfortunately been compromised by crowding in many emergency departments (EDs). To address this issue, we study patient scheduling in EDs so that mandatory targets imposed on each patient’s door-to-provider time and length of stay can be collectively met with the largest probability. Exploiting patient flow data … Read more
Robust control design for constrained uncertain systems is a well-studied topic. Given a known uncertainty set, the objective is to find a control policy that minimizes a given cost and satisfies the system’s constraints for all possible uncertainty realizations. In this paper, we extend the classical robust control setup by treating the uncertainty sets as … Read more
This paper presents a new formulation for the risk averse stochastic reservoir management problem. Using recent advances in robust optimization and stochastic programming, we propose a dynamic, multi-objective model based on minimization of a multidimensional risk measure associated with floods and droughts for a hydro-electrical complex. We present our model and then identify approximate solutions … Read more
Scheduling elective surgeries is a complicated task due to the coupled effect of multiple sources of uncertainty and the impact of the proposed schedule on the downstream units. In this paper, we propose an adaptive robust optimization model to address the existing uncertainty in surgery duration and length-of-stay in the surgical intensive care unit. The … Read more