Date of Award
Doctor of Philosophy (PhD)
One of the essential challenges in healthcare operations management is to efficiently utilize the expensive resources needed in the healthcare system, while maintaining or increasing the quality of care. Optimization methods can be used to increase the supply of healthcare services, to minimize the cost of the system, and maximize the quality of care by minimizing patients' waiting times, minimizing travel needs, maximizing health outcomes and maximizing access to services. In this dissertation, we study some of the important tactical and operational problems in healthcare, and propose plans to efficiently improve the current healthcare systems by applying optimization methods.
In chapter 1 of this dissertation, we develop a novel scheduling model called ``postponement model'' to reduce the indirect waiting time of higher priority outpatients in a diagnostic clinic. In diagnostic clinics, the arrivals mostly arise from three sources: inpatients, emergency patients, and outpatients. Emergency patients are seen as soon as they arrive and inpatients receive appointments within 24 hours. However, outpatient appointments are scheduled within a longer time horizon based on appointment availability. Currently, most diagnostic clinics save a proportion of their capacity for inpatients and emergency patients, and offer the earliest remaining appointments to the outpatients on a first-come-first-serve basis. This capacity allocation and scheduling mechanism may lead to unused inpatient capacity. Furthermore, there is no prioritization in scheduling of outpatients whose medical needs may be at different urgency levels. We model the appointment scheduling problem as a two-stage stochastic integer program. In the first stage we compute the proportion of capacity that is allocated to emergency patients and inpatients. In the second stage the decisions regarding scheduling of outpatients are taken. Outpatient appointments are not necessarily scheduled immediately upon patients' arrivals and may be postponed to observe more requests. This postponement strategy enables the scheduler to observe more of the demand and schedule outpatient appointments considering the patient priorities. We solve the problem using Sample Average Approximation (SAA) and a decomposition based branch and bound algorithm. The results show that using the postponement acceptance patients with higher priority receive sooner appointments compared to the no-postponement scheduling policy used in current practice. Meanwhile, the utilization of the system is increased.
In chapter 2, we study a dynamic model for Tuberculosis (TB) screening of healthcare personnel. Healthcare employees take TB diagnostic tests regularly as part of efforts to prevent TB outbreaks in hospitals. A simple strategy that is mostly used in countries with low rate of TB infections is annual screening of all employees. There are currently two TB diagnostic tests on the market: skin test and blood test. The blood test is more expensive than the skin test, however it is more accurate. In this study, we propose an alternative testing scheme where testing frequency and test type for different groups of employees is dependent on their infection risk and the cost of time lost due to testing. We develop a discrete time infinite horizon Markov Decision Process (MDP) model which determines the optimal time between the tests for different groups of employees. Another outcome of our model is the type of the TB diagnostic test administered for each employee group. Classification of employees into groups is done based on the characteristics that affect the probability of getting infected with TB (e.g., job type and work location) and employee salary levels. The objective of our model is to minimize the total cost of the healthcare facility which depends on the type of the tests administered, employees' lost time, and the number of false-positive or false-negative results in each group tested. Due to the curse of dimensionality, we use Approximate Dynamic Programming (ADP) to estimate the value function. Then, we use column generation to solve the ADP-based linear program associated with the proposed MDP model. The results provide screening policies that determine which test should be allocated to each group of employee in different states of the system. By investigating the results, we also estimate the frequency of the test for each group. Comparison of the screening policies obtained using our model with the current annual screening policy show that the screening costs can be reduced by half while achieving the same the overall infection rate among the healthcare personnel.
In chapter 3, we propose a dynamic model for scheduling of healthcare workers during an infectious disease outbreak, with a specific focus on the ongoing Coronavirus Disease 2019 (COVID-19) pandemic. Healthcare workers play an important role during a pandemic to control the infection spread in the general population. On the other hand, they are at high risk of getting infected because of being in direct contact with patients. Thus, taking operational measures to limit the exposure of healthcare workers to infectious patients is critical for the safety of the healthcare workers and their patients. Emerging literature indicates that creating teams of healthcare workers and scheduling or isolating these teams in coordination might be beneficial during the COVID-19 pandemic. In this study, we build a MDP model to determine the optimal policy for scheduling such worker teams. The objective of the model is to maximize the expected total discounted number of working employees while taking the possibility of infection, and thus quarantine, for workers who are scheduled to work into account. The optimal policy specifies which teams of workers should work and which teams should isolate dependent on the system state. This problem is difficult to solve due to the large size of the state space of the MDP. Thus, we use state space reduction techniques to decrease the number of states. Using the data on number of infections in the state of South Carolina, we obtain optimal scheduling policies under different infection probabilities for the general population. We also consider additional scenarios to understand the effect of changing model parameters on the state space reduction results and the approximate optimal policy. The results show that strategic benching of healthcare worker teams can significantly improve the total discounted workable physician days compared to only segregating workers into teams.
Kiani, Mahsa, "Essays on Tactical and Operational Problems in Healthcare" (2020). All Dissertations. 2688.