On the Sparsity of Optimal Linear Decision Rules in Robust Inventory Management

We consider the widely-studied class of production-inventory problems from the seminal work of Ben-Tal et al. (2004) on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule for this class of problems in which the number of nonzero parameters in the linear decision rule is equal to … Read more

The Value of Robust Assortment Optimization Under Ranking-based Choice Models

The ranking-based choice model is a popular model in revenue management for predicting demand for a firm’s products based on the assortment of products that the firm offers to their customers. Because this model has a huge number of parameters, many different ranking-based choice models can be consistent with the historical sales data generated by … Read more

A nonparametric algorithm for optimal stopping based on robust optimization

Optimal stopping is a class of stochastic dynamic optimization problems with applications in finance and operations management. In this paper, we introduce a new method for solving stochastic optimal stopping problems with known probability distributions. First, we use simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary … Read more

A Data-Driven Approach to Multi-Stage Stochastic Linear Optimization

We propose a new data-driven approach for addressing multi-stage stochastic linear optimization problems with unknown distributions. The approach consists of solving a robust optimization problem that is constructed from sample paths of the underlying stochastic process. We provide asymptotic bounds on the gap between the optimal costs of the robust optimization problem and the underlying … Read more

Computation of exact bootstrap confidence intervals: complexity and deterministic algorithms

The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we establish several … Read more