Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications

We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. Only the information of the mean, covariance, and support is known. We formulate the problem as … Read more

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study two popular approximation schemes for distributionally robust … Read more

Adjusted Distributionally Robust Bounds on Expected Loss Functions

Optimization problems in operations and finance often include a cost that is proportional to the expected amount by which a random variable exceeds some fixed quantity, known as the expected loss function. Representation of this function often leads to computational challenges, depending on the distribution of the random variable of interest. Moreover, in practice, a … Read more

Wasserstein Logistic Regression with Mixed Features

Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments, it is inherently limited to numerical features. In this paper, we show that distributionally robust logistic regression with mixed (i.e., numerical and categorical) features, despite amounting … Read more

Distributionally Robust Inventory Management with Advance Purchase Contracts

We propose a distributionally robust inventory model for finding an optimal ordering policy that attains the minimum worst-case expected total cost. In a classical stochastic setting, this problem is typically addressed by dynamic programming and is solved by the famous base-stock policy. This approach however crucially relies on two controversial assumptions: the demands are serially … Read more

Distributionally Robust Disaster Relief Planning under the Wasserstein Set

We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. … Read more

Distributional robustness and inequity mitigation in disaster preparedness of humanitarian operations

We study a predisaster relief network design problem with uncertain demands. The aim is to determine the prepositioning and reallocation of relief supplies. Motivated by the call of the International Federation of Red Cross and Red Crescent Societies (IFRC) to leave no one behind, we consider three important practical aspects of humanitarian operations: shortages, equity, … Read more

Distributionally risk-receptive and risk-averse network interdiction problems with general ambiguity set

We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk-averse (or robust) network interdiction problem (DRA-NIP) and a distributionally risk-receptive network interdiction problem (DRR-NIP) where a leader maximizes a follower’s minimal expected objective value for either the worst-case or the best-case, respectively, probability distribution belonging to ambiguity set … Read more

A Column Generation Scheme for Distributionally Robust Multi-Item Newsvendor Problems

In this paper, we study a distributionally robust multi-item newsvendor problem, where the demand distribution is unknown but specified with a general event-wise ambiguity set. Using the event-wise affine decision rules, we can obtain a conservative approximation formulation of the problem, which can typically be further reformulated as a linear program. In order to efficiently … Read more

Convex Chance-Constrained Programs with Wasserstein Ambiguity

Chance constraints yield non-convex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, [Xie19] and [CKW18] showed that the distributionally robust (pessimistic) chance constraint admits a mixed-integer conic representation. This paper identifies sufficient conditions that lead to convex feasible regions of chance constraints with Wasserstein ambiguity. First, when … Read more