Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely … Read more

Adjustable Robust Optimization via Fourier-Motzkin Elimination

We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broader class of ARO problems. A scheme based on a blending of classical FME and a … Read more

Adaptive Distributionally Robust Optimization

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

Satisficing Models under Uncertainty

Satisficing, as an approach to decision-making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision-making include the P-model of Charnes and Cooper (1963). In this paper, we propose a general framework of satisficing decision criteria, and show a … 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

A practicable framework for distributionally robust linear optimization

We developed a modular framework to obtain exact and approximate solutions to a class of linear optimization problems with recourse with the goal to minimize the worst-case expected objective over an ambiguity set of distributions. The ambiguity set is specified by linear and conic quadratic representable expectation constraints and the support set is also linear … Read more

Distributionally Robust Convex Optimization

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose … Read more

Managing Operational and Financing Decisions to Meet Consumption Targets

We study dynamic operational decision problems where risky cash flows are being resolved over a finite planning horizon. Financing decisions via lending and borrowing are available to smooth out consumptions over time with the goal of achieving some prescribed consumption targets. Our target-oriented decision criterion is based on the aggregation of Aumann and Serrano (2008) … Read more

Preferences for Travel Time under Risk and Ambiguity: Implications in Path Selection and Network Equilibrium

In this paper, we study the preferences for uncertain travel time in which the probability distribution may not be fully characterized. In evaluating an uncertain travel time, we explicitly distinguish between risk, where probability distribution is precisely known, and ambiguity, where it is not. In particular, we propose a new criterion called ambiguity-aware CARA travel … Read more

Robust Optimization Made Easy with ROME

We introduce an algebraic modeling language, named ROME, for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically meaningful way. In this paper, we highlight key features of ROME which expediates the modeling and subsequent … Read more