Team orienteering with uncertain rewards and service times with an application to phlebotomist intrahospital routing

This study focuses on the intrahospital routing of phlebotomists at the University of Iowa Hospitals and Clinics (UIHC). Phlebotomists are responsible for drawing specimens from patients based on doctors' orders. The results of the analysis of these specimens play an important role in determining patient treatment. However, the demand for phlebotomists is likely to outpace supply over the next few years. Therefore, it is important to improve the efficiency of phlebotomists. In this paper, we formulate the phlebotomist intrahospital routing problem as a team orienteering problem with stochastic rewards and service times. The rewards and service times are particularly interesting as they are the result of a queueing process. We present an a priori solution approach and derive a method for efficiently sampling the value of a solution, a value that cannot be determined analytically. Finally, we demonstrate that our proposed approach outperforms the current practice at UIHC.