Power system optimization and healthcare optimization

Date

2020-04-23

Authors

Guo, Jia, Ph. D.

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Abstract

Mixed-integer-linear-program (MILP) models and statistics are very often applied to different industries, such as production, health care, logistics and transportation. In this dissertation, MILP models are developed for power system optimization and healthcare optimization. Statistical tests are conducted to improve the system service. Computational experiments are designed for both small and large data sets to test how efficiently the models work.

In Stochastic Optimization for Discrete Overcurrent Relay Tripping Characteristics and Coordination, there is a relay in each node to protect the power system. When the relay detects a fault current, it operates for a certain amount of time before it opens up. We need to decide the operating time of each relay, taking backup relays and sense time into consideration. Meanwhile, we need to make sure the fault in each node can be cleared by at least one relay to keep the system safe. The objective function is to minimize the expected energy loss in the system. A three-bus system and a 34-node feeder examples are illustrated to test how efficiently the model works. Furthermore, comparisons with conventional settings and parameter optimization approaches are launched.

In Protective Device and Switch Allocation for Reliability Optimization with Distributed Generators, we have different types of devices. Some devices, such as reclosers, fuses and circuit breakers, can clear fault currents and prevent the system from burning out, but will also lead to energy loss. Other devices, such as sectionalizers and isolating switches, can restore part of the energy loss. We need to decide the location of each device to minimize the sum of expected energy loss and device cost. Computational experiments on a 10-node system and a 58-node system are launched. We also compare the objective function value of our MILP optimization model with that of other algorithms.

In the project on the transportation improvement for the Family Health Center (FHC) in San Antonio, Texas, our purpose is to determine the financial feasibility of offering improved transportation services to inner city patients. We begin by analyzing data for 636 patients at the FHC, and conduct logistic regressions to determine the impact of various transportation factors on cancellations/no-shows and late arrivals. Next, an optimization model in the form of a modified vehicle routing problem is developed for constructing shuttle routes. We then investigate the costs savings that could potentially be realized by reducing the no-show rate due to transportation difficulties from its current level of 24.3% by 20 to 60%. This is followed by an analysis of the costs associated with providing subsidized and free transportation to and from the FHC for those patients who are most in need. Results are presented as a function of maximum inter-arrival time and route length. The full analysis indicates that a cost reduction of more than $15,000 per month can be achieved when the no-show rate is reduced by 25% down to 18.2%.

In the nurse scheduling optimization project, we aim to design a schedule that minimizes the sum of weighted uncovered demand and nurses' preference violations. The planning horizon is one month. We take nurses' birthdays, vacations, maximum number of consecutive working days and days off, and minimum number of rest hours into consideration. In addition, the model considers each nurse's working status in the last few days of the previous month. The problem can be solved in two stages. In Stage 1, we develop a mixed integer linear model to assign shifts to nurses, based on the condition that nurses do not work overtime. Column Generation is applied to solve the model in Stage 1. In Stage 2, we develop a heuristic algorithm to assign overtime hours based on the schedule in Stage 1. Computational experiments are implemented on instances with 10 to 60 nurses. Finally, we conduct sensitivity analysis on the uncovered demand weight to investigate the impact of the weight on solutions.

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