Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more
Designing policies for a network of agents is typically done by formulating an optimization problem where each agent has access to state measurements of all the other agents in the network. Such policy designs with centralized information exchange results in optimization problems that are typically hard to solve, require to establish substantial communication links, and … 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 study a mobile facility (MF) routing and scheduling problem in which probability distributions of the time-dependent demand for MF services is unknown. To address distributional ambiguity, we propose and analyze two distributionally robust MF routing and scheduling (DMFRS) models that seek to minimize the fixed cost of establishing the MF fleet and maximum expected … 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
Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and ambiguity averse, we introduce a distributionally robust network interdiction game where the interdictor randomizes over the … Read more
We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical … Read more
We study the problem of strategically eliciting the preferences of a decision-maker through a moderate number of pairwise comparison queries with the goal of making them a high quality recommendation for a specific decision-making problem. We are particularly motivated by applications in high stakes domains, such as when choosing a policy for allocating scarce resources … Read more
Naturally imbalanced freight flows force consolidation carriers to reposition resources empty. When constructing empty repositioning plans, the cost of repositioning resources empty needs to be weighed against the cost of corrective actions in case of unavailable resources. This is especially challenging given the uncertainty of future demand. We design and implement a robust rolling horizon … Read more
We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust … Read more