David P. Morton

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of our modeling approach, illustrating ideas with a series of examples of increasing complexity. As a solution method, we develop new variants of stochastic dual dynamic programming, including approximations to handle non-convexities.

Inspired by its success for their continuous counterparts, the standard approach to deal with mixed-integer recourse (MIR) models under distributional uncertainty is to use distributionally robust optimization (DRO). We argue, however, that this modeling choice is not always justified since DRO techniques are generally computationally challenging when integer decision variables are involved. That is why we propose an alternative approach for dealing with distributional uncertainty for the special case of simple integer recourse (SIR) models, which is aimed at obtaining models with improved computational tractability. We show that such models can be obtained by pragmatically selecting the uncertainty set. Here, we consider uncertainty sets based on the Wasserstein distance and also on generalized moment conditions. We compare our approach with standard DRO both numerically and theoretically. An important side result of our analysis is the derivation of performance guarantees for convex approximations of SIR models. In contrast to the literature, these error bounds are not only valid for a continuous distribution but hold for any distribution.

Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging a...

Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency diesel fuel demand for power generation in a hurricane’s immediate aftermath can be mitigated. It can be challenging to estimate diesel fuel demand and make informed decisions in the distribution process, accounting for the hurricane’s path and severity. We develop predictive and prescriptive models to guide diesel fuel supply chain operations for hurricane disaster relief. We estimate diesel fuel demand from historical weather forecasts and power outage data. This predictive model feeds a prescriptive stochastic programming model implemented in a rolling-horizon fashion to dispatch tank trucks. This data-driven optimization tool provides a framework for decision support in preparation for approaching hurricanes, and our numerical results provide insights regarding key aspects of operations.