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
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
Motivated by the worldwide Covid-19 vaccine procurement, we study an inventory problem with an advance purchase contract which requires all ordering decisions to be committed at once. In reality, not only the demand is uncertain, but its distribution can also be ambiguous. Hence, we assume that only the mean and the variance are known and … Read more
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
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
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
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
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
A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more
We propose a generic model for the capacitated vehicle routing problem (CVRP) under demand uncertainty. By combining risk measures or disutility functions with complete or partial characterizations of the probability distribution governing the demands, our formulation bridges the popular but often independently studied paradigms of stochastic programming and distributionally robust optimization. We characterize when an … Read more