Optimizing Population Healthcare Resource Allocation Under Uncertainty Using Global Optimization Methods
Linz, David Desmmon
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Due to the rise in American healthcare costs, clinic administrators are increasingly concerned with optimally delivering service to patients. Due to the complex and uncertain nature of patient demand and other factors, models for healthcare systems may have to rely on discrete event simulation that incorporates random effects in order to realistically describe systems. Subsequently, optimization for decision-making must be applicable to objective functions with noise, which are often the output of complex simulation models. Second, many stakeholders may have an aversion to the risk generated by the system's uncertainty. For this reason, a well suited optimization approach must provide solutions to problems with stochastic "black-box" objective functions that provide insight to decision makers. This dissertation research has two main objectives: first, to develop models that can generate robust optimal staffing recommendations for healthcare systems in order to minimize the risk to patients while considering system constraints, and second to develop new simulation optimization theory and algorithms that can effectively minimize noisy black-box objective functions. The first research objective is met by addressing two practical problems concerning the delivery of medical services to patients in a patient-centered medical system using a modeled decision making framework. The first problem concerns locating specialist care across geographically distributed clinics with uncertain demand. This problem highlights the trade-offs between risk and an average penalty function associated with centralized versus distributed care. The second problem addresses the question of optimal panel design in primary care that combines both operational and strategic decisions. Since the second model cannot be easily written with closed-form equations, a discrete event simulation model is created to measure the effectiveness of chosen paneling policies in delivering care to patients. The second research objective is met by developing two adaptive random search theoretical frameworks with provable finite time results and exploring partition-based algorithms for global optimization with noise. The two theoretical frameworks are called Quantile Adaptive Search (QAS) and Hesitant Adaptive Search with Estimation (HAS-E). Under certain assumptions the expected number of function evaluations of HAS-E and QAS increases only linearly in dimension. This dissertation explores the implementation of partition-based algorithms that focus on sampling within quantiles to address problems with a higher number of dimensions. First, an extension to Optimal Computational Budget Allocation (OCBA) partition-based random search is developed that uses a look-ahead algorithm to improve optimizer performance. Second, an extension of the Nested Partition algorithm is adapted to sample points from a decreasing quantile level set. Third, an algorithm that samples from successive quantile level sets through the application of the Probabilistic Branch and Bound (PBnB) algorithm for level set approximation is explored. Finally, the dissertation also develops an algorithm where the PBnB algorithm is incorporated into a Nested Partition framework and the target quantile is decreased iteratively. To provide a broad overview of potential black-box optimization for our applications, this dissertation contains research on benchmarking the numerical performance of derivative-free optimization techniques in a variety of contexts. The dissertation contains numerical results in benchmarking the effectiveness of a single observation with a "shrinking ball" approximation when estimating the objective function of a problem with noise. In addition to benchmarking existing algorithms, this effort also includes numerical performance analysis of the newly developed algorithms in this dissertation. Overall, this research contributes to the advancement of stochastic global optimization methodology in order to practically improve real-world decision making. With the developed algorithms, healthcare administrators are able to generate near-optimal strategies for staffing and resource allocation and gain a better understanding of trade-offs in resource allocation that enable risk-averse decision makers to better serve patients.