Improving health care delivery through multi-objective resource allocation
Griffin, Jacqueline A.
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This dissertation addresses resource allocation problems that occur in both public and private health care settings with the objective of characterizing the tradeoffs that occur when simultaneously incorporating multiple objectives and developing methods to address these tradeoffs. We examine three resource allocation problems (i) strategic allocation of financial resources and limited staffing capacity for the mobile delivery of health care within African countries, (ii) real-time allocation of hospital beds to internal patient requests, and (iii) development of patient redirection policies in response to limited bed availability in units within a system of hospitals. For each problem we define models, each with a different methodology, and utilize the models to develop allocation strategies that account for multiple competing objectives and examine the performance of the strategies with computational studies. In Chapter 2, we model African health care delivery systems utilizing a mixed-integer program (MIP) which accounts for financial and personnel constraints as well as infrastructure quality. We characterize tradeoffs in effectiveness, efficiency, and equity resulting from four allocation strategies with computational experiments representing the variety of spatial patterns that occur throughout the continent. The main contributions include (i) the development of a model that incorporates spatial and infrastructure characteristics and allows for a study of equity in the delivery of care, rather than access to care, and (ii) the characterization of tradeoffs in the three objectives under a variety of settings. In Chapter 3, we model the real-time assignment of bed requests to available beds as a queueing system and a Markov decision process (MDP). Through the development of bed assignment algorithms and simulation experiments, we illustrate the value of implementing strategic bed assignment practices which balance the bed management objectives of timeliness and appropriateness of assignments. The main contributions of this section include (i) the development of new bed assignment algorithms which use stochastic optimization techniques and outperform algorithms which mimic processes currently used in practice and (ii) the definition of a model and methods for the control of a large complex system that includes flexible units, multiple patient types, and type-dependent routing. In Chapter 4, we model the impact of a patient redirection policy in a hospital unit as a Markov chain. Assuming preferences for patient redirection are aligned with costs, we examine the impact of incremental changes to redirection policies on the probability of the unit being completely occupied, the long-run average utilization, and the long-run average cost of redirection. The main contributions of this chapter include (i) the introduction of a model of patient redirection with multiple patient thresholds and patient preference constraints and (ii) the definition of necessary conditions for an optimal patient redirection policy that minimizes the average cost of redirection.