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

Stability Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance … Read more

Quantitative Stability Analysis for Distributionally Robust Optimization With Moment Constraints

In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is de ned through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment … Read more

The impact of the existence of multiple adjustable robust solutions

In this note we show that multiple solutions exist for the production-inventory example in the seminal paper on adjustable robust optimization in [2]. All these optimal robust solutions have the same worst-case objective value, but the mean objective values differ up to 21.9% and for individual realizations this difference can be up to 59.4%. We … Read more

Robust Sensitivity Analysis of the Optimal Value of Linear Programming

We propose a framework for sensitivity analysis of linear programs (LPs) in minimiza- tion form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact, convex uncertainty set. This framework unifies and extends multiple approaches for LP sensitivity analysis in the literature and has close ties … Read more

Robust Dual Response Optimization

This article presents a robust optimization reformulation of the dual response problem developed in response surface methodology. The dual response approach fits separate models for the mean and the variance, and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may … Read more

Duality in Two-stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds

In this paper we derive and exploit duality in general two-stage adaptive linear optimization models. The equivalent dualized formulation we derive is again a two-stage adaptive linear optimization model. Therefore, all existing solution approaches for two-stage adaptive models can be used to solve or approximate the dual formulation. The new dualized model differs from the … Read more

A Data Driven Functionally Robust Approach for Coordinating Pricing and Order Quantity Decisions with Unknown Demand Function

We consider a retailer’s problem of optimal pricing and inventory stocking decisions for a product. We assume that the price-demand curve is unknown, but data is available that loosely specifies the price-demand relationship. We propose a conceptually new framework that simultaneously considers pricing and inventory decisions without a priori fitting a function to the price-demand … Read more

When are static and adjustable robust optimization with constraint-wise uncertainty equivalent?

Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraint-wise and the adjustable variables lie … Read more