Surgical scheduling via optimization and machine learning with long-tailed data : Health care management science, in press.

Using data from cardiovascular surgery patients with long and highly variable post-surgical lengths of stay (LOS), we develop a modeling framework to reduce recovery unit congestion. We estimate the LOS and its probability distribution using machine learning models, schedule procedures on a rolling basis using a variety of optimization models, and estimate performance with simulation. The machine learning models achieved only modest LOS prediction accuracy, despite access to a very rich set of patient characteristics. Compared to the current paper-based system used in the hospital, most optimization models failed to reduce congestion without increasing wait times for surgery. A conservative stochastic optimization with sufficient sampling to capture the long tail of the LOS distribution outperformed the current manual process and other stochastic and robust optimization approaches. These results highlight the perils of using oversimplified distributional models of LOS for scheduling procedures and the importance of using optimization methods well-suited to dealing with long-tailed behavior.

Temperature Extrapolation of Molecular Dynamics Simulations of Complex Chemistry to Microsecond Timescales Using Kinetic Models: Applications to Hydrocarbon Pyrolysis.

We develop a method to construct temperature-dependent kinetic models of hydrocarbon pyrolysis, based on information from molecular dynamics (MD) simulations of pyrolyzing systems in the high-temperature regime. MD simulations are currently a key tool to understand the mechanism of complex chemical processes such as pyrolysis and to observe their outcomes in different conditions, but these simulations are computationally expensive and typically limited to nanoseconds of simulation time. This limitation is inconsequential at high temperatures, where equilibrium is reached quickly, but at low temperatures, the system may not equilibrate within a tractable simulation timescale. In this work, we develop a method to construct kinetic models of hydrocarbon pyrolysis using the information from the high-temperature high-reactivity regime. We then extrapolate this model to low temperatures, which enables microsecond-long simulations to be performed. We show that this approach accurately predicts the time evolution of small molecules, as well as the size and composition of long carbon chains across a wide range of temperatures and compositions. Further, we show that the range of suitable temperatures for extrapolation can easily be improved by adding more simulations to the training data. Compared to experimental results, our kinetic model leads to similar compositional trends while allowing for more detailed kinetic and mechanistic insights.