BCAM Alumni & Former Members Seminar | From Stochastic Programming to Distributionally Robust Optimization

Title: From Stochastic Programming to Distributionally Robust Optimization, an application to Emergency Medical Services.

Abstract:
This master's thesis aims to analyze various frameworks within the field of Operational Research (OR). Initially developed in 1937, OR focused on constructing deterministic models to describe and analyze real-world problems to aid decision-making. It was not until the early 1950s that uncertainty was incorporated into these models. Traditionally, two primary methodologies have been employed: Stochastic Optimization (SO) and Robust Optimization (RO). In SO, stochastic parameters are modeled as random variables with known probability distributions. However, a significant criticism of this approach in recent
years is its computational expense. Alternatively, RO addresses uncertainty by considering worst-case scenarios, often resulting in over-conservative decisions
for more likely scenarios.

An emerging paradigm, Distributionally Robust Optimization (DRO), has recently garnered significant attention for its potential to address the limitations of both SO and RO. DRO serves as a unifying framework by introducing the concept of an ambiguity set, which encompasses a family of distributions deemed "close
enough" to a reference distribution. The closeness can be measured using the Wasserstein metric, among others. This thesis includes an experimental comparison of time-memory efficiency and solution robustness using a Facility Location Problem for Emergency Medical Services.