Health Care Management Science https://doi.org/10.1007/s10729-018-9454-6 A Multi-Fidelity Rollout Algorithm for Dynamic Resource Allocation in Population Disease Management Ting-Yu Ho 1 · Shan Liu 1 · Zelda B. Zabinsky 1 Received: 17 April 2018 / Accepted: 20 August 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Dynamic resource allocation for prevention, screening, and treatment interventions in population disease management has received much attention in recent years due to excessive healthcare costs. In this paper, our goal is to design a model and an efficient algorithm to optimize sequential intervention policies under resource constraints to improve population health outcomes. We consider a discrete-time finite-horizon budget allocation problem with disease progression within a closed birth-cohort population. To address the computational challenges associated with large-state and multiple-period dynamic decision-making problems, we propose a low-fidelity approximation that preserves the population dynamics under a stationary policy. To improve the healthcare interventions in terms of population health outcomes, we then embed the low-fidelity approximation into a high-fidelity optimization model to efficiently identify a good non-stationary sequential intervention policy. Our approach is illustrated by a numerical example of screening and treatment policy implementation for chronic hepatitis C virus (HCV) infection over a budget planning period. We numerically compare our Multi-Fidelity Rollout Algorithm (MF-RA) to a grid search approach and demonstrate the similarity of sequential policy trends and closeness of overall health outcomes measured by quality-adjusted life-years (QALYs) and the total number of individuals that undergo screening and treatment for different annual budgets and birth-cohorts. We also show how our approach scales well to problems with high dimensionality due to many decision periods by studying time to elimination of HCV. Keywords Screening and treatment interventions · Dynamic programming · Markov processes · Simulation · Rollout algorithm · Hepatitis C 1 Introduction Complex population disease management problems have been under investigation from a dynamic resource allocation perspective in recent years. Operations research (OR) tools such as mathematical programming, simulation optimiza- tion, Markov decision process (MDP) and system dynamics models are becoming more common in healthcare policy modeling research [72]. A desired goal of healthcare policy makers is to improve population health outcomes through reductions in disease prevalence, incidence, morbidity, and mortality. However, a dynamic resource allocation problem is challenging because it involves making a sequence of  Shan Liu liushan@uw.edu 1 Department of Industrial and Systems Engineering, University of Washington, Box 352650, Seattle, WA, 98195, USA intervention decisions ahead of budgetary planning cycle over multiple time-periods. Factors that hinder optimal resource allocation include complex population-level dis- ease dynamics, resource constraints, intervention priority, and uncertain intervention effects. Therefore, it is neces- sary to develop an efficient solution algorithm to solve sequential decision problems for a large population. We focus our research question on the control and/or eradi- cation of a particular disease in a birth-cohort population. Birth-cohort-based healthcare interventions are effective to control diseases with highly varying prevalence by the pop- ulation’s birth-year. For example, birth-cohort screening for hepatitis C is cost-effective in the primary care setting [21, 46, 49, 57, 63]. The objective of our research is to identify optimal intervention strategies using a computationally tractable algorithm to improve population health outcomes over time while accounting for resource constraints, disease progression, and other population dynamics. We propose a dynamic programming (DP) model to analyze the