Distributionally Robust Linear and Discrete Optimization with Marginals

In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to … Read more

Constraint Generation for Two-Stage Robust Network Flow Problem

In this paper, we propose new constraint generation algorithms for solving the two-stage robust minimum cost flow problem, a problem that arises from various applications such as transportation and logistics. In order to develop efficient algorithms under general polyhedral uncertainty set, we repeatedly exploit the network-flow structure to reformulate the two-stage robust minimum cost flow … Read more

Designing Response Supply Chain Against Bioattacks

Bioattacks, i.e., the intentional release of pathogens or biotoxins against humans to cause serious illness and death, pose a significant threat to public health and safety due to the availability of pathogens worldwide, scale of impact, and short treatment time window. In this paper, we focus on the problem of prepositioning inventory of medical countermeasures … Read more

Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs

We present a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely the Calculus of K-approximation Functions and the Calculus of K-approximation Sets. Using our framework, we provide … Read more