Wasserstein distributionally robust optimization (DRO) estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify model parameters (or) decision choices that are … Read more
This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more
The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. … Read more
Discrete approximation which is the prevailing scheme in stochastic programming in the past decade has been extended to distributionally robust optimization (DRO) recently. In this paper we conduct rigorous quantitative stability analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined through … Read more
Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … Read more
We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable … Read more
Optimal routing solutions based on deterministic models usually fail to deliver promised on-time services in an uncertain real world, which can lead to the loss of customers and revenue. We study a vehicle routing problem with time windows (VRPTW) toward the end of mitigating the risk of late customer arrivals as much as possible when … Read more
Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have … Read more
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded … Read more