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Optimization Models for Resource Allocation Under Perturbation University of Louisville ThinkIR: The University of Louisville's Institutional Repository Electronic Theses and Dissertations 12-2013 Optimization models for resource allocation under perturbation. Dongxue Bridgeman 1986- University of Louisville Follow this and additional works at: https://ir.library.louisville.edu/etd Recommended Citation Bridgeman, Dongxue 1986-, "Optimization models for resource allocation under perturbation." (2013). Electronic Theses and Dissertations. Paper 151. https://doi.org/10.18297/etd/151 This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Institutional Repository. This title appears here courtesy of the author, who has retained all other copyrights. For more information, please contact [email protected]. OPTIMIZATION MODELS FOR RESOURCE ALLOCATION UNDER PERTURBATION By Dongxue Bridgeman B.E., Beijing University of Posts and Telecommunications, 2008 M.S., University of Louisville, 2009 A Dissertation Submitted to the Faculty of the J. B. Speed School of Engineering of the University of Louisville in Partial Fulfillment of the Requirements for the Doctor of Philosophy Department of Industrial Engineering University of Louisville Louisville, Kentucky December 2013 © Copyright 2013 by Dongxue Bridgeman All rights reserved OPTIMIZATION MODELS FOR RESOURCE ALLOCATION UNDER PERTURBATION By Dongxue Bridgeman B.E., Beijing University of Posts and Telecommunications, 2008 M.S., University of Louisville, 2009 A Dissertation Approved on July 26th, 2013 by the following Dissertation Committee: Dissertation Director: Dr. Lijian Chen Dr. Sunderesh Heragu Dr. Gerald Evans Dr. Lihui Bai Dr. Anup Kumar ii DEDICATION This dissertation is dedicated to my parents Mr. Jing Ma and Mrs. Lihuang Yang who have given me invaluable educational opportunities. iii ACKNOWLEDGMENTS It is a pleasure to thank those who made this dissertation possible, such as my advisor, Dr. Lijian Chen, whose encouragement, supervision, and support from the preliminary to the concluding level enabled me to develop an understanding of the subject. I am heartily thankful to Dr. Heragu, who gave me an opportunity to promote my research to a new level and provide my financial support. I would also like to thank the other committee members for their valuable comments and assistance. I need to express my gratitude and deep appreciation to Dr. Holman and Anala Pandit whose inputs to the RTDSS project are invaluable. I would also like to express my thanks to my supporting husband Jarrod Bridgeman and our baby Cordelia Bridgeman who motivate me to complete the work. Also, many thanks to my family members in China and extended family in Indiana. Finally, I must acknowledge as well the many friends who assisted, advised, and supported my research and writing efforts over the years. iv ABSTRACT OPTIMIZATION MODELS FOR RESOURCE ALLOCATION UNDER PERTURBATION Dongxue Bridgeman July 26th, 2013 Optimization Models for Resource allocation are investing in how to make the best use of available but limited resources in order to achieve the best results. In strategic planning, resource allocation is a plan for using available resources, especially in the near future, to achieve the goals of the future. It is a process of allocating resources during the entire planning horizon and among the various units. Resource allocation plans can be decided by using mathematical programming. In this dissertation, the research has been focused on how to allocate resources in the uncertain environment. The mathematical programming formulations for the resource allocation model under severe uncertainty will be studied. In particular, we will focus on solving the stability issues of the traditional probabilistic mod- el. We propose an approach consisting of solving a sequence of convex robust optimization models with unknown-but-bounded random variables along with the stochastic program- ming to pursue the allocation performance for the expected overall objective value. Our theoretical results show that the proposed approach can always obtain an equivalent or a better expected revenue with the corresponding allocation, while significantly reducing the risk under perturbations. Although this method requires solving two convex mathematical v programming models, both models are solved within a timely manner thanks to their con- vex model instances and with effective, and less, computationally demanding algorithms. With the increasing threats from public health emergencies, such as earthquakes, tornados, pandemic flus, or terrorist attacks, high attention has been paid to the public health response to a pandemic from federal to national level, together with local health departments, and the health-care community. Various organizations cooperate with each other to strengthen the preparedness for the pandemic and disastrous emergencies, thus to improve the public health. The Strategic National Stockpile (SNS) is maintained by the Centers for Disease Control and Prevention (CDC) and the U.S. Department of Health and Human Services (DHHS) for the United States in the event of a shortage of local medical resources or other unanticipated supply problems. The SNS is the United States’ national repository of antibiotics, vaccines, chemical antidotes, antitoxins, and other critical medical equipment and supplies. It has the capability to supplement or re-supply local health authorities with necessary materials for relief action within the response time in as little as 12 hours. The pilot study is done with the support of Kentucky SNS to determine the capacity allocation plan for each county in order to maximize the health benefit under various uncertainties, which can never be accurately estimated. We thereby employ a heuristic method named “resource reservation” to suggest the resource allocation plan for Kentucky SNS. vi TABLE OF CONTENTS ACKNOWLEDGEMENTS . iv ABSTRACT.................................................................. v LIST OF TABLES. ix LIST OF FIGURES . x CHAPTER 1. INTRODUCTION . 1 1.1. Real-Time Decision-Support System for Health Care and Public Health Protection Project . 1 1.2. The Problem . 2 1.3. Key Contribution . 5 1.4. Background on Resource Allocation . 7 1.5. Background on Strategic National Stockpile . 9 CHAPTER 2. LITERATURE REVIEW . 14 2.1. Applications of Operations Research in Health-care Delivery. 14 2.2. Vaccination Strategies under Parameter Uncertainty for Emergency Response 21 2.3. Introduction of Optimization Models under Uncertainty . 23 CHAPTER 3. RESOURCE RESERVATION MODELS . 47 3.1. Resource Reservation Heuristic . 49 3.2. Solution Technique and Computational Complexity . 60 CHAPTER 4. CASE STUDY: KENTUCKY SNS VACCINE ALLOCATION. 64 vii 4.1. Numerical Results for One Time Period Resource Allocation. 65 4.2. Numerical Results for Multiple Time Periods Resource Allocation . 70 4.3. Model Interface on the Web Application. 78 CHAPTER 5. CONCLUSION . 86 REFERENCES . 93 APPENDIX A. MATLAB CODE. 97 CURRICULUM VITAE. 103 viii LIST OF TABLES 2.1 Yields under different weather condition . 27 4.1 Population size of selected counties . 66 4.2 One Time Period Vaccines Allocation Plan Result #1 . 68 4.3 One Time Period Vaccines Allocation Plan Result #2 . 69 4.4 One Time Period Vaccines Allocation Plan Result #3 . 70 4.5 One Time Period Vaccines Allocation Plan Result #4 . 71 4.6 Inputs to RR models for two time period resource allocation . 72 4.7 Two Time Period Vaccines Allocation Plan Result #1 . 73 4.8 Two Time Period Vaccines Allocation Plan Result #2 . 74 4.9 Two Time Period Vaccines Allocation Plan Result #3 . 75 4.10 Three Time Periods Vaccines Allocation Plan Result #1 .. 76 4.11 Three Time Period Vaccines Allocation Plan Result #2 .. 76 4.12 Three Time Period Vaccines Allocation Plan Result #3 . 79 ix LIST OF FIGURES 3.1 Sensitivity analysis: available doses vs reserved resource/available doses vs q.. 58 4.1 Vaccines allocation plan when available doses = 50000. 77 4.2 Compare RO and SP results with the same available dose and q . 77 4.3 Home page of RTDSS web application . 79 4.4 Available Planning and Analysis Tools . 80 4.5 Vaccine Distribution Estimator - Page 1:User login . 80 4.6 Vaccine Distribution Estimator - Page 2 . 81 4.7 Vaccine Distribution Estimator - Page 3: User Inputs. 82 4.8 Vaccine Distribution Estimator - Page 3: Inputs Are Filled. 83 4.9 Vaccine Distribution Estimator - Page 4: User Inputs. 84 4.10 Vaccine Distribution Estimator - Page 4: User Inputs continued . 85 x CHAPTER 1 INTRODUCTION 1.1. Real-Time Decision-Support System for Health Care and Public Health Protection Project The research work presented in this dissertation is funded and part of the real-time, decision- support system (RTDSS) for health care and public health protection project. The goal of this project involves developing a RTDSS to help personnel in the health-care and pub- lic health (HPH), as well as emergency services sectors (ESS), make real-time decisions relative to allocation and re-allocation of scarce resources in the aftermath of a pandemic influenza or other viral attack. Dr. Heragu, as the Project Director, says “some studies indicate that up to 40% of the pop- ulation could be stricken and hospitals could be operating at 50% of their capacity during a pandemic attack. During a time of medical surge when we really need HPH as well as ESS personnel and equipment to be operating at full capacity, the challenge for planners is to allocate the few resources at their disposal in the most efficient manner in response to fast changing conditions on the ground so that a large number of people can be served in as short a time as possible.” 1 1.2. The Problem The idea of the study is the applying scientific approach to improve the decision making accuracy in order to better prepare for public health emergencies, such as pandemic, es- pecially using scientific approaches to determine how best to design and operate a system, usually under conditions requiring the allocation of scarce resources.
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