This dissertation is divided into two parts. In the first portion, we study inflection points in biobjective variants of the traveling salesman problem (TSP) related to health care applications. In the second portion, we use a variety of techniques from operations research to improve hospital efficiency.

We used a TSP variant that prioritizes the ability to return to the depot, in addition to the standard distance, to study the collection of blood from remote collection sites. In an application related to emergency response, we looked into behavior of tours generated using the target visitation problem, a TSP variant that also includes node priority in the objective function.

Working with the University of Maryland Medical Center, we did three projects related to hospital efficiency. We used stochastic modeling and simulation to optimize the throughput of a cardiac surgery post-operative unit. We found that altering the mix of post-operative beds could significant increase the effective capacity. After unsuccessfully attempting to use data mining and survival analysis to predict hospital census, we performed a statistical analysis of patient length of stay patterns and discovered surgeons were improving their chances of having available beds for incoming cases by adjusting their discharge practices by day of week. In the final project, we used integer programming and heuristics to develop schedules that match incoming surgical patients with the discharge of earlier patients. The results indicate that altering the surgical schedule can substantially improve the flow of patients through the hospital.