Open Access Dissertation
Date of Award
Industrial and Manufacturing Engineering
Ratna B. Chinnam
Deterministic mathematical modeling is a branch of optimization that deals with decision making in real-world problems. While deterministic models assume that data and parameters are known, these numbers are often unknown in the real world applications.The presence of uncertainty in decision making can make the optimal solution of a deterministic model infeasible or sub-optimal.
On the other hand, stochastic programming approach assumes that parameters and coefficients are unknown and only their probability distribution can be estimated. Although stochastic programming could include uncertainties in objective function and/or constraints, we only study problems that the goal of stochastic programming is to maximize (minimize) the expectation of the objective function of random variables. Stochastic programming has a wide range of application in manufacturing production planning, machine scheduling, dairy farm expansion planning, asset liability management, traffic management, and automobile dealership inventory management that involve uncertainty in decision making. One limitation of stochastic programming is that considering uncertainty in mathematical modeling often leads to a large-scale programming problem.
The most widely used stochastic programming model is two-stage stochastic programming. In this model, first-stage decision variables are determined before observing the realization of uncertainties and second-stage decision variables are selected after exposing first-stage variables into the uncertainties. The goal is to determine the value of first-stage decisions in a way to
maximize (minimize) the expected value of second-stage objective function.
1.1 Motivation for Designing Community-Aware Charging Network for Electric Vehicles
Electric vehicles (EVs) are attracting more and more attentions these days due to increase concern about global warming and future shortage of fossil fuels. These vehicles have potential to reduce greenhouse gas emissions, improve public health condition by
reducing air pollution and improving sustainability, and addressing diversication of transportation energy feedstock. Governments and policy makers have proposed two types of policy incentives in order to encourage consumers to buy an EV: direct incentives and indirect incentives. Direct incentives are those that have direct monetary value to consumers and include purchase subsidies, license
tax/fee reductions, Electric Vehicle Supply Equipment (EVSE) financing, free electricity, free parking and emission test exemptions. On the other hand, indirect incentives are the ones that do not have direct monetary value and consist of high-occupancy vehicle access, emissions testing exemption time savings, and public charger availability. Lack of access to public charging network is considered to be a major barrier in adoption of EVs . Access to public charging infrastructure will provide confidence for EV owners to drive longer distances without going out of charge and encourage EV ownership in the community. The current challenge for policy makers and city planners in installing public charging infrastructure is determining the location of these charging service stations, number of required stations and level of charging since the technology is still in its infancy and the installation cost is high. Since recharging of EV battery takes more time than refueling conventional vehicles, parking lots and garages are considered as potential locations for installing charging stations. The aim of this research is to develop a mathematical programming model to find the optimal
locations with potentially high utilization rate for installing community-aware public EV charging infrastructure in order to improve accessibility to charging service and community livability metrics. In designing such charging network, uncertainties such as EV market share, state of battery charge at the time of arrival, driver’s willingness to charge EV away from home, arrival time to final destination, driver’s activity duration (parking duration), and driver’s walking distance preference play major role. Incorporating these uncertainties in the model, we propose a two-stage stochastic programming approach to determine the location and capacity of public EV charging network in a community.
1.2 Motivation for Managing Access to Care at Primary Care Clinics
Patient access to care along with healthcare efficiency and quality of service are dimensions of health system performance measurement . Improving access to primary care is a major step of having a high-performing health care system. However, many patients are struggling to get an in-time appointment with their own primary care provider (PCP). Even two years aer health insurance coverage was expanded, new patients have to wait 82% longer to get an internal-medicine appointment. A national survey shows that percentage of patients that need urgent care and could not get an appointment increased from 53% to 57% between 2006 and 2011 . This delay may negatively impact health status of patients and may even lead to death. Patients that cannot get
an appointment with their PCP may seek care with other providers or in emergency departments which will decrease continuity of care and increase total cost of health system. The main issue behind access problem is the imbalance between provider capacity and patient demand. While provider panel size is already large, the shortage in primary care providers and increasing number of patients mean that providers have to increase their panel size and serve more patients which will potentially lead to lower access to primary care. The ratio of adult primary care providers to population is expected to drop by 9% between 2005 and 2020 .
Moreover, patient flow analysis can increase efficiency of healthcare system and quality of health service by increasing patient and provider satisfaction through better resource allocation and utilization . Effective resource allocation will smooth patient ow and reduce waste which will in turn results in better access to care.
One way to control patient flow in clinic is managing appointment supply through appointment scheduling system. A well-designed appointment scheduling system can decrease appointment delay and waiting time in clinic for patients and idle time and/or overtime for physicians at the same time and increase their satisfaction. Appointment scheduling requires to make a balance
between patient needs and facility resources .
The purpose of this study is to gain a better understanding for managing access to care in primary care outpatient clinics through operations management research. As a result of this under standing, we develop appointment scheduling models using two-stage stochastic programming to improve access while maintaining high levels of provider capacity utilization and improving patient flow in clinic by leveraging uncertainties in patient demand, patient no-show and provider service time variability.
Faridimehr, Sina, "Essays On Stochastic Programming In Service Operations Management" (2017). Wayne State University Dissertations. 1801.