Stochastic Models in Operations Research with Applications to Financial Markets and Health Care Systems
Year: 2015
Type: dissertation
Abstract: In the first chapter, we study a double-sided queue with batch arrivals and abandonment. We assume there are two types of customers, patient ones who queue but may abandon, and impatient ones who depart immediately if their order is not filled. The system matches units from opposite sides of the queue using a FCFS policy. The model is applicable to alternative trading systems called crossing networks. We characterize, in closed-form, the steady-state queue length distribution and the system-level average system time and fill rate. For a customer who arrives to the system in steady-state, we derive formulae for the expected fill rate and system time as functions of her order size and deadline. We compare the system- and customer-level results from our model to a simulation and find a close correspondence. In the second chapter, we study a multistage, outpatient health care program culminating in elective surgery. We investigate current operational performance by determining how demographic factors, medical information and operational modifications affect attrition and system times. We develop a discrete-event simulation to model patient flow in the current system using data from the Bariatric Surgery Program at Toronto Western Hospital to estimate uncertainties in the simulation. We propose routing and priority policies based on information obtained from an intake questionnaire. We demonstrate that several policies decrease the average time patients spend in the system while not reducing throughput. We show that the policy with the largest system time reduction is robust to moderate amounts of type-I/II errors in the information provided by the questionnaire. In the third chapter, we investigate the scheduling practices of a multistage, outpatient health care program with no-show patients. Patients must undergo several assessments before completion. We formulate the problem as a Markov Decision Process and use approximate dynamic programming to find policies to schedule patients to appointments. We propose several heuristic policies and examine the quality of our solutions via structural results and by comparing them to a discrete-event simulation of the clinic. We apply our results to the operation of a bariatric surgery program at a large tertiary hospital in Toronto, Canada to determine how these policies can improve their operations.
Source: TSpace (University of Toronto)
Author: Adam Diamant
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2770220442