Keeping Them Honest: How Medical Services can Maximize Profit while Maintaining Quality of Service with an Optimal Control Policy

Abstract

Recent U.S. legislation and management policies attempt to address the growing costs and quality of health care delivery. In this thesis, we use principles of queueing theory and Lagrangian mechanics to evaluate the performance of a medical service. With a particular focus on setting staffing schedules, we consider a medical care delivery system as a multi-server queueing model where waiting patients may choose to abandon. Using a tractable set of fluid and diffusion approximations, we use time-varying arrival rates to estimate the mean and variance of the patient queue length. We assume positive revenue for service completions, costs for leased resources, and a service level agreement that constrains the number of patient abandonments. With these system parameters, we design an optimal control framework to evaluate the performance of health care delivery by maximizing revenue and managing costs while still providing a certain quality of service. We reformulate this optimal control problem by applying Lagrangian mechanics, and characterize the solution results in terms of the state, dual and control variables within the system. We conclude with a focus on the opportunity cost’s behavior and influence on the optimal control policy solution.