In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP) called ISDDP was introduced which uses approximate (instead of exact with SDDP) primal dual solutions of the problems solved in the forward and backward passes of the method. That variant of SDDP was studied in [13] for linear and for differentiable nonlinear Multistage Stochastic … Read more
We develop a dual decomposition of two-stage distributionally robust mixed-integer programming (DRMIP) under the Wasserstein ambiguity set. The dual decomposition is based on the Lagrangian dual of DRMIP, which results from the Lagrangian relaxation of the nonanticipativity constraints and min-max inequality. We present two Lagrangian dual problem formulations, each of which is based on different principle. We show … Read more
We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse … Read more
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a novel formulation that introduces a modest number of additional variables and a class of inequalities that can be efficiently … Read more
Distributionally robust optimization (DRO) has arose as an important paradigm to address the issue of distributional ambiguity in decision optimization. In its standard form, DRO seeks an optimal solution against the worst-possible expected value evaluated based on a set of candidate distributions. In the case where a decision maker is not risk neutral, the most … Read more
We consider exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets. The existing MIP formulations are known to have weak continuous relaxation bounds, and, consequently, for hard instances with small radius, or with a large number of scenarios, the branch-and-bound based solution processes suffer … Read more
We propose a novel approach for optimization and decision problems under uncertainty. We first describe it for stochastic optimization under distributional ambiguity with and without data for the random parameter. Distributional ambiguity means that an entire family $P$ of distributions is considered instead of a single one. For our approach, which avoids non-verifiable assumptions and … Read more
Contingency research to find optimal operations and post-contingency recovery plans in distribution networks has gained a major attention in recent years. To this end, we consider a multi-period optimal power flow (OPF) problem in distribution networks, subject to the N-1 contingency where a line or distributed energy resource fails. The contingency can be modeled as … Read more
Planning for uncertainty is crucial for finding good, stable solutions. However, it is often impractical to incorporate stochastic elements into a large production system. Our paper tackles this issue in the context of the Technician Routing and Scheduling Problem (TRSP). We develop a set of techniques, based on phase-type distributions, to quickly and accurately evaluate … Read more
This paper studies a fusion of concepts from stochastic optimization and non-parametric statistical learning, in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of the predictors (leading indicators). Specialized algorithms can be … Read more