Algorithmic advancements in discrete optimization : applications to machine learning and healthcare operations

Abstract

In the next ten years, hospitals will operate like air-traffic control centers whose role is to coordinate care across multiple facilities. Consequently, the future of hospital operations will have three salient characteristics. First, data. The ability to process, analyze and exploit data effectively will become a vital skill for practitioners. Second, a holistic approach, since orchestrating care requires the concurrent optimization of multiple resources, services, and time scales. Third, real-time personalized decisions, to respond to the increasingly closer monitoring of patients. To support this transition and transform our healthcare system towards better outcomes at lower costs, research in operations and analytics should address two concurrent goals: First, develop new methods and algorithms for decision-making in a data-rich environment, which answer key concerns from practitioners and regulators, such as reliability, interpretability, and fairness.

Second, put its models and algorithms to the test of practice, to ensure a path towards implementation and impact. Accordingly, this thesis is comprised of two parts. The first three chapters present methodological contributions to the discrete optimization literature, with particular emphasis on problems emerging from machine learning under sparsity. Indeed, the most important operational decision-making problems are by nature discrete and their sizes have increased with the widespread adoption of connected devices and sensors. In particular, in machine learning, the gigantic amount of data now available contrasts with our limited cognitive abilities. Hence, sparse models, i.e., which only involve a small number of variables, are needed to ensure human understanding. The last two chapters present applications and implementation of machine learning and discrete optimization methods to improve operations at a major academic hospital.

From raw electronic health records of patients, we build predictive models to predict patient flows and prescriptive models to optimize patient-bed assignment in real-time. More importantly, we implement our models in a 600-bed institution. Our impact is two-fold: methodological and operational. Integrating advanced analytics in their daily operations and building a data-first culture constitutes a major paradigm shift.