Copyright by Jia Guo 2020
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Copyright by Jia Guo 2020 The Dissertation Committee for Jia Guo certifies that this is the approved version of the following dissertation: Power System Optimization and Healthcare Optimization Committee: Jonathan F. Bard, Supervisor Douglas J. Morrice Erhan Kutanoglu Benjamin D. Leibowicz Power System Optimization and Healthcare Optimization by Jia Guo Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin In Partial Fulfillment of the Requirements for the Degree of DOCTORAL OF PHILOSOPHY The University of Texas at Austin May 2020 Dedication I dedicate this dissertation to God. It is also my genuine gratefulness that I dedicate this work to my parents who consistently encourage me, believe me and love me. Acknowledgements I wish to thank the numerous people who have helped me throughout my career. First and foremost, I would like to express my gratitude to my supervisor Professor Jonathan Bard for his advice, mentorship and dedication to improving my critical thinking, mathematical and writing skills. I would also like to thank Professor Douglas Morrice for his valuable guidance, and my committee members, Professor Erhan Kutanoglu and Professor Benjamin Leibowicz, for serving on my committee and providing their important suggestions and input. I am also grateful to Professor Ned Dimitrov and Professor Surya Santoso for their guidance and input on my research. I am fortunate to have had the opportunity to collaborate with the great colleagues during my academic career including Professor Ramin Poursani, Professor Carlos Jaen, Professor Kristin Harvey, Dr. Min Lwin, Dr. Richard Leu, Dr. Alex Zolan, Dr. Shreya Gupta, Dr. Areesh Mittal, Dr. Murat Karatas, Huidong Zhang and Yanyue Ding. Last but not least, I am sincerely grateful to my family and friends for their support. In particular, I would like to show my greatest appreciation to my parents for their continuing dedication. I am especially grateful to my fianc´eShu, who has been a source of unyielding encouragement. v Power System Optimization and Healthcare Optimization Jia Guo, Ph.D. The University of Texas at Austin, 2020 Supervisor: Jonathan F. Bard 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 op- timization. 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 consid- eration. 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 vi 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 transporta- tion 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 transporta- tion 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 consecu- tive 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 pre- vious 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. vii Contents Abstract 1 1 Introduction 1 2 Stochastic Optimization for Discrete Overcurrent Relay Tripping Charac- teristics and Coordination 4 2.1 Introduction . .4 2.2 Literature Review . .5 2.3 Problem Statement . .6 2.4 Problem Formulation . .6 2.4.1 Formulation . .8 2.4.2 Model Explanation . 11 2.5 Case Study: Simple Radial Test System . 12 2.5.1 Illustrative Example . 12 2.5.2 Comparison with Conventional Settings . 14 2.5.3 Comparison with Parameter Optimization Approach . 18 2.6 Case Study: IEEE 34-Node Feeder . 19 2.6.1 Probabilistic Fault Scenarios with DG . 19 2.6.2 Optimal Tripping Characteristics . 21 2.7 Discussion and Conclusion . 23 3 Protective Device and Switch Allocation for Reliability Optimization with Distributed Generators 25 3.1 Introduction . 25 3.2 Literature Review . 26 3.3 Problem Statement . 27 3.4 Notation and Preprocessing . 28 3.4.1 Notation . 28 viii 3.4.2 Protection Capabilities of Each Device . 30 3.4.3 Graph Representation of Distribution Systems . 31 3.4.4 Feasible Sets for Restoration Operations . 32 3.4.5 Function and Operation of Each Device . 33 3.5 Formulation . 34 3.5.1 Objective Function . 34 3.5.2 Constraints . 37 3.6 Case Study: 10-Node Feeder . 41 3.6.1 Example Solution and Analysis . 41 3.6.2 Impact of Varying Budget . 43 3.6.3 Impact of DG Location and Capacity . 44 3.7 Case Study: 58-Node RBTS System . 46 3.7.1 Comparison of Solutions . 47 3.8 Conclusion . 49 4 Offering Transportation Services to Economically Disadvantaged Patients at a Family Health Center: A Case Study 50 4.1 Introduction . 50 4.2 Literature Review . 53 4.2.1 Transportation Barriers and No-shows . 53 4.2.2 Financial Impacts on Clinic Operations . 55 4.2.3 No-show Reduction Efforts . 56 4.2.4 Vehicle Routing-based Models . 57 4.3 Problem Statement . 59 4.4 Shuttle Design for Zip Code 78207 . 61 4.4.1 Problem Description . 61 4.4.2 Computational Results for VRP . 65 4.5 Data Analysis . 67 4.5.1 Data Highlights . 69 ix 4.5.2 A Logistic Regression Model for Cancellation Probability . 76 4.5.3 Logistic Regression on Probability of Arrivals Greater than 15 Minutes 79 4.5.4 Impact of cancellations on ED visit within 30 days . 81 4.6 Cost Analysis . 81 4.6.1 Cost Saving by Offering Transportation Services . 82 4.6.2 Transportation cost analysis . 84 4.6.3 Sensitivity Analysis on Percent Reduction in Number of Missed Ap- pointments (α) due to Transportation Issues . 88 4.7 Discussion and Conclusions . 89 5 Midterm Nurse Scheduling with Specialized Constraints and Preference Considerations 92 5.1 Introduction . 92 5.2 Literature Review . 93 5.3 Problem Statement . 96 5.4 Stage 1 Problem Formulation . 97 5.5 Stage 1 Column Generation Algorithm . 105 5.5.1 Formulation . 105 5.5.2 Stabilization . 110 5.5.3 Column Generation Algorithm Procedure . 111 5.6 Stage 2 Problem Description . 112 5.7 Stage 2 Heuristic . 113 5.7.1 Stage 2 Step 1 Algorithm . 115 5.7.2 Stage 2 Step 2 Algorithm . 116 5.8 Computational Results . 117 5.8.1 Stage 1 Results . 119 5.8.2 Stage 2 Results . 125 5.8.3 Sensitivity Analysis on Uncovered Demand Weight α ......... 130 5.9 Conclusions and Discussions . 133 x Appendices 135 A FHC Transportation: Sensitivity Analysis for VRP Model 135 B Nurse Scheduling Optimization: Pseudocode of Stage 2 Heuristics 137 Bibliography 140 xi List of Tables 1 System Data .