Distributionally robust inventory control when demand is a martingale

Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification in this context, various forms of distributionally robust optimization have been applied. Although many of these methodologies suffer from the problem of time-inconsistency, the work of Klabjan, Simchi-Levi and Song [85] established a general time-consistent framework … Read more

Piecewise static policies for two-stage adjustable robust linear optimization problems under uncertainty

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

Data-Driven Patient Scheduling in Emergency Departments: A Hybrid Robust-Stochastic Approach

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

Decomposition for adjustable robust linear optimization subject to uncertainty polytope

We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to poly- tope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row gen- eration or column-and-row generation algorithms. The novelty … Read more

Robust Optimal Control with Adjustable Uncertainty Sets

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

Ambiguous Joint Chance Constraints under Mean and Dispersion Information

We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic) ambiguous chance constraints, which require the corresponding classical chance constraints … Read more

A robust optimization model for the risk averse reservoir management problem

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

Robust Markov Decision Processes for Medical Treatment Decisions

Medical treatment decisions involve complex tradeoffs between the risks and benefits of various treatment options. The diversity of treatment options that patients can choose over time and uncertainties in future health outcomes, result in a difficult sequential decision making problem. Markov decision processes (MDPs) are commonly used to study medical treatment decisions; however, optimal policies … Read more

Distributionally Robust Logistic Regression

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

Adaptive Elective Surgery Planning Under Duration and Length-Of-Stay Uncertainty: A Robust Optimization Approach

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