UCLA

In this dissertation I look at two problems of resource planning at two major healthcare organizations. The Greater Los Angeles Station of the Veterans Health Administration and the UCLA Ronald Reagan Medical Center.

The first chapter of this thesis is a brief introduction to the research presented in subsequent chapters. The second chapter of this thesis considers the problem of minimizing daily expected resource usage and overtime costs across multiple parallel resources such as anesthesiologists and operating rooms, which are used to conduct a variety of surgical procedures at large multi-specialty hospitals. To address this problem, a two-stage mixed-integer stochastic dynamic programming model with recourse is developed. The first stage allocates these resources across multiple surgeries with uncertain durations and prescribes the sequence of surgeries to these resources. The second stage determines actual start times to surgeries based on realized durations of preceding surgeries and assigns overtime to resources to ensure all surgeries are completed using the allocation and sequence determined in the first stage. A data driven robust optimization method that solves large-scale real-sized versions of this model close to optimality is developed. This model is validated and implemented as a decision support system at the UCLA Ronald Reagan Medical Center. This has led to an average daily cost savings of around 7\% or estimated to be \$2.2 million on an annual basis. In addition, the insights based on this model have significantly influenced decision making at the operating services department at this hospital.

In the third chapter of this thesis the planning problem for HIV screening, testing, and care is analyzed. This problem consists of determining the optimal fraction of patients to be screened in every period as well as the optimum staffing level at each part of the healthcare system to maximize the total health benefits to the patients measured by quality-adjusted life-years (QALYs) gained. This problem is modeled as a nonlinear mixed integer programming program comprising disease progression (the transition of the patients across health states), system dynamics (the flow of patients in different health states across various parts of the healthcare delivery system), and budgetary and capacity constraints. On applying the model to the Greater Los Angeles (GLA) station in the Veterans Health Administration system, it was found that a Centers for Disease Control and Prevention recommended routine screening policy in which all patients visiting the system are screened for HIV irrespective of risk factors may not be feasible because of budgetary constraints. Consequently, the model was used to develop and evaluate managerially relevant policies within existent capacity and budgetary constraints to improve upon the current risk based screening policy of screening only high risk patients. Our computational analysis showed that the GLA station can achieve substantial increase (20% to 300%) in the QALYs gained by using these policies over risk based screening. The fourth chapter of this thesis concludes with some remarks on future research.