Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more
Bilevel optimization is a very active field of applied mathematics. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision making processes. This ability, however, also makes the resulting problems challenging to solve—both in theory and practice. Fortunately, there have been significant algorithmic advances in the field … Read more
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
We introduce a novel approach to prescriptive analytics that leverages robust satisficing techniques to determine optimal decisions in situations of risk ambiguity and prediction uncertainty. Our decision model relies on a reward function that incorporates uncertain parameters, which can be partially predicted using available side information. However, the accuracy of the linear prediction model depends … Read more
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
We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two new features: an uncertainty set linearly dependent on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to … Read more
In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view … Read more
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
We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability … Read more