Essays on Health Care Operations Management

Abstract

This dissertation consists of three separate essays on health care operations management. Abstracts of the three essays are as follows: Essay 1: We model emergency medical services (EMS) as Erlang loss systems and study ambulance shortage periods, intervals with few or no ambulances available to handle new emergency calls. We propose a simple recursion to calculate the expected duration of ambulance shortage periods and validate our recursion with data from Calgary, Canada, EMS. We develop analytical results for the second and higher moments, distribution, and Laplace transform of the shortage periods for some specific service time distributions. We provide analytical tools to investigate the impact of two possible actions that ambulance dispatchers can take: (1) requesting additional ambulances from neighbouring cities or other ambulance fleets, and (2) asking that busy ambulances be freed, for example the ones currently waiting to offload patients in EDs. Our models evaluate two performance measures: (1) the expected remaining duration of shortage periods, and (2) the expected number of lost calls. Essay 2: Except for some special cases, closed form solutions for multi-server queues with multiple classes of impatient customers do not exist due to their high complexity. We model these systems as level-dependent quasi-birth-and-death (LDQBD) processes and propose two novel methods to numerically solve them: (1) we use Lyapunov analysis to truncate the state space such that the probability mass in the truncated upper tail is guaranteed to be smaller than a pre-specified value. This method can potentially substitute the currently-used heuristics that are exploited within algorithms that truncate the system first and then calculate its performance measures. (2) we extend an existing algorithm such that we can calculate the stationary probabilities with a desired error tolerance---current methods do not provide bounds on the stationary probabilities. Essay 3: We propose a tool to accurately predict the number of heart attack patients in sufficiently small geographical areas of Alberta. Focusing on small spatial units enables researchers to calculate precise estimates of travel times from the heart attack scene to a treatment center, which is useful in finding appropriate locations for new treatment facilities. We use standard multiple linear, Poisson, and negative binomial regression methods to predict the number of heart attacks as a function of the population in cohorts of age, sex, education, and income. We build, validate, and compare the performance of these methods using an empirical data set of heart attack counts in postal codes of Alberta from 2003 to 2010, and 2006 census data for Alberta dissemination areas.