Dynamic and Stochastic Decision-Making: Applications in Healthcare Operations

Abstract

Healthcare delivery, disaster response, and other large-scale operational problems in healthcare share a common challenge: they require the efficient allocation of scarce resources under uncertainty, time pressure, and complex interdependencies. This dissertation develops novel optimization and decision-support frameworks that address this challenge by combining rigorous mathematical modeling with advanced approximation techniques. While the application domains differ, from scheduling patients in specialized clinics to evacuating vulnerable populations during wildfires, the underlying motivation is the same: to design resource allocation strategies that are both effective in practice and computationally tractable for real-world problems. The second chapter of this thesis addresses the scheduling of patients in healthcare settings where multiple appointment types, priorities, and dependencies must be managed simultaneously. Most traditional scheduling practices ignore the fact that diagnostic tests and specialist consultations are interdependent, or that lead times and patient priority levels critically affect care quality. To bridge this gap, a dynamic scheduling model is developed that integrates these factors, ensuring that tests and consultations are coordinated in a timely and efficient manner. Using the linear programming approach to Approximate Dynamic Programming (ADP), an efficient approximation of the value function is derived, resulting in an efficient scheduling policy. Simulation experiments based on real-world clinical data show that the proposed policy outperforms existing benchmarks, significantly reducing waiting times and improving compliance with care protocols. In addition, a practical heuristic, designed for direct adoption by hospitals, achieves comparable performance while remaining interpretable and easy to implement. These contributions underscore the importance of bridging theoretical advances with practical applicability. The third chapter of this thesis shifts to the context of disaster response, focusing on supported evacuations during wildfires. Unlike self-evacuations, supported evacuations involve individuals who require direct assistance, such as hospital patients or residents of long-term care facilities, for whom evacuation is significantly more complex. Here, the problem is not only one of vehicle routing and fleet sizing, but also of ensuring that evacuations occur within narrow time windows while considering the possibility of infrastructure disruptions. A two-stage stochastic optimization framework is proposed to capture diverse sources of uncertainty and complexity associated with vehicle routing, facility location, and fleet sizing decisions. Given the computational challenges of such decisions, a novel solution methodology based on Logic-Based Benders Decomposition is developed, further enhanced by combinatorial inequalities and neighborhood search strategies. Numerical experiments, including one based on data from a community wildfire drill in Colorado, demonstrate that the proposed solution approach provides substantial improvements in evacuation time and resource utilization compared to existing approaches. This work highlights how stochastic modeling and advanced decomposition methods can produce actionable strategies in time-critical disaster management settings. The fourth chapter of this thesis is methodological and addresses the broader challenge of solving high-dimensional infinite-horizon dynamic programming problems. Many resource allocation problems in healthcare, disaster response, and beyond can be framed as sequential decision-making problems, but exact solutions are typically intractable due to the curse of dimensionality. To mitigate this, a novel piecewise affine approximation framework is introduced for regional value function approximation. Instead of assuming a single global approximation, the method adaptively partitions the state space and fits localized affine functions in regions where the value function is highly nonlinear or irregular. The proposed approach, which is simulation-driven, iteratively refines partitions, balancing accuracy with interpretability. Experiments across diverse domains, including queueing systems, energy storage management, and patient scheduling, show that this method achieves superior performance compared to traditional single-function approximations. More importantly, it provides better approximations while maintaining computational efficiency, making it a versatile tool for approximate dynamic programming applications. Taken together, the contributions of this dissertation demonstrate both breadth and depth. From an application perspective, the research presented in this thesis addresses two globally critical challenges: improving access and timeliness in healthcare delivery, and enhancing preparedness in disaster response. From a methodological perspective, this thesis advances the frontier of approximate optimization techniques, particularly in dynamic programming and large-scale stochastic systems. A unifying theme across all three studies is the emphasis on balancing rigor with practicality. Each chapter not only provides a novel theoretical approach, but also yields solutions that can be implemented and trusted in real-world settings where decisions are urgent and stakes are high. This dissertation thus contributes to the fields of operations research, healthcare analytics, and disaster management by developing scalable, interpretable, and implementable optimization frameworks. By integrating domain-specific modeling with generalizable approximation methods, it provides a foundation for tackling a broad class of resource allocation problems under uncertainty, that are increasingly central in today’s complex and interconnected world.