Optimal transport and healthcare operations

Mathematical problems in the intersection of operations research and healthcare operations have received increasing attention in recent years. This thesis is composed of four parts. In the first two parts, we study the surgical scheduling problem via discrete event patient flow simulation, optimization algorithm, and the optimal transport theory. In the last two parts, we briefly introduce atheoretical findings in optimal transport and a real-world application of data-driven decision-making in healthcare operations in response to the outbreak of COVID-19. In the first part, we report the development and deployment of BEDS (better elective day of surgery), a simple algorithm for smoothing across days the number of surgical patients requiring post-procedural beds. We introduce challenges faced by medical institutions for surgical schedule planning and a hospital-level patient flow simulation model, in which the impact of scheduling policies can be modeled without implementation. With the support of simulation results, BEDS was implemented in the Stanford Children's Hospital scheduling system in 2020.7. BEDS does not require significant reductions to surgeon autonomy or centralized scheduling, and is compatible with changes such as surgeon vacations, illness, or joining/leaving the hospital workforce; long-term changes in surgical volumes; and the opening or closing of new operating rooms and post-procedural beds. We present data from over the implementation of BEDS at an academic medical center and make the tool available as a dashboard in Tableau, a commercial software used by hundreds of hospitals in the United States. In the second part, we talk about supply-demand matching and scheduling via optimal transport. The optimal transport problem was formalized by the French mathematician Gaspard Monge in1781. We formulate the offline scheduling problem by a constrained optimization program with a demand density and a capacity bound in the format of optimal transport. We present the results for the optimal plan for the one-dimensionalL1cost function case. Next, we present the results of the optimal plan of the optimal scheduling problem via optimal transport in the presence of class-specific costs. In the third part, we present a result in empirical optimal transport projections with non-symmetric costs. Distributionally Robust Optimization (DRO) is a technique that generates estimators with enhanced generalization performance by introducing an adversary which quantifies the impact in out-of-sample variations in the training set. To provide an optimal approach for choosing the distributional uncertainty size in DRO, we contribute to the literature of DRO by considering more generally optimal transport costs, including the Bregman distance and the local Mahalanobis distance, and present an empirical experiment in portfolio optimization. Finally, we describe a personal protective equipment and hospital policy planning model we developed with Stanford Hospital in response to the outbreak of COVID-19. The model supports early decision-making and policy planning in the hospital to face the global shortage of personal protective equipment

Advisor: Blanchet Jose H.
Glynn Peter W.
Scheinker David