Goal Programming

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Goal Programming has been first discussed by Charles and Cooper in their research work A lot of research has taken place since the evolution of goal programming. It is used as a tool by operations researchers for finding optimal conditions for their problems . Goal Programming is divided to two types as shown in the document.

Transcript of Goal Programming

  • APPLICATIONS OF DECISION ANALYSIS TO HEALTHCARE

    A ThesisPresented to

    The Academic Faculty

    by

    Reidar Hagtvedt

    In Partial Fulfillmentof the Requirements for the Degree

    Doctor of Philosophy in theSchool of Industrial and Systems Engineering

    Georgia Institute of TechnologyApril 2008

  • APPLICATIONS OF DECISION ANALYSIS TO HEALTHCARE

    Approved by:

    Professor Paul Griffin,Committee ChairSchool of Industrial and SystemsEngineeringGeorgia Institute of Technology

    Professor David GoldsmanSchool of Industrial and SystemsEngineeringGeorgia Institute of Technology

    Professor Pinar KeskinocakSchool of Industrial and SystemsEngineeringGeorgia Institute of Technology

    Douglas Scott IIPrevention Effectiveness and HealthEconomics BranchCenters for Disease Control and Pre-vention

    Professor Mark FergusonCollege of ManagementGeorgia Institute of Technology

    Date Approved: 30 November, 2007

  • ACKNOWLEDGEMENTS

    There are a number of people to thank for their help. In chronological order, Steve

    Hackman was instrumental in helping me start and navigate ISyE. Gary Parker made

    it easy to cut through the red tape, and spelled out the information I needed very

    clearly. My advisor, Paul Griffin, has been a great help, and remarkably patient.

    The committee members have all contributed substantively and helpfully: Pinar Ke-

    skinocak, Mark Ferguson, David Goldsman and Doug Scott of the CDC.

    In addition, Rebecca Roberts, M.D., of Cook County Hospital, provided valuable

    advice and volunteered a great deal of her time. She also provided access to her

    CARP data.

    I wish to thank Amanda Hardy and Susan Te at the DeKalb Medical Center, Bill

    Deak, M.D. at the Volunteer Hospital Association, and Jeff Cole, M.D. for helpful

    comments. Amber Cocks, of Childrens Healthcare of Atlanta, has also been a helpful

    collaborator.

    Finally, I want to thank the people who supported me when I questioned my

    sanity: My parents, Finn and Berit Hagtvedt, my brother, Henrik, and selected

    friends: Greg and Sherry Jones, Kari Jones, Jan-Aage Larsen, and Sasha Mukerjee.

    The ambulance diversion study was partially funded through an NSF grant. The

    HAI study was partially funded through a Health Systems Initiative Grant at Georgia

    Institute of Technology.

    iii

  • TABLE OF CONTENTS

    ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

    LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

    LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

    SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

    I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.1 Repeated Negotiations in Health care: Hospitals and Payers . . . . 1

    1.2 A Simulation Model to Compare Strategies for the Reduction ofHealthcare-Associated Infections . . . . . . . . . . . . . . . . . . . 3

    1.3 The Effect of Flexible Hospital Contracts on Emergency DepartmentDiversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    II REPEATEDNEGOTIATIONS IN HEALTHCARE: HOSPITALS AND PAY-ERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.3 Assumptions and model formulation . . . . . . . . . . . . . . . . . 14

    2.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.3.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.3.4 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . 20

    2.3.5 Extensions to a Multi-Payer game . . . . . . . . . . . . . . 22

    2.4 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    2.4.1 Statistical support . . . . . . . . . . . . . . . . . . . . . . . 26

    2.4.2 Numerical example . . . . . . . . . . . . . . . . . . . . . . . 32

    2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    iv

  • III A SIMULATION MODEL TO COMPARE STRATEGIES FOR THE RE-DUCTION OF HEALTHCARE-ASSOCIATED INFECTIONS . . . . . 36

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.2.1 Public Health and Medical Literature . . . . . . . . . . . . 38

    3.2.2 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

    3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    3.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    3.4.1 Base Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    3.4.2 Model with Area Reserved for Isolation . . . . . . . . . . . 49

    3.4.3 Model with Additional Isolation Ward . . . . . . . . . . . . 49

    3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    3.6.1 Contribution to the Literature . . . . . . . . . . . . . . . . 55

    3.6.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . 56

    IV THE EFFECT OF FLEXIBLE HOSPITAL CONTRACTS ON EMER-GENCY DEPARTMENT DIVERSION . . . . . . . . . . . . . . . . . . 61

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    4.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    4.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

    4.2.1 Overcrowding . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    4.2.2 Proposed solutions to overcrowding . . . . . . . . . . . . . . 70

    4.2.3 Current recommendations . . . . . . . . . . . . . . . . . . . 71

    4.2.4 Incentives to change . . . . . . . . . . . . . . . . . . . . . . 71

    4.2.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . 72

    4.3 Assumptions and model formulation . . . . . . . . . . . . . . . . . 73

    4.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    4.3.2 State Space and Notation . . . . . . . . . . . . . . . . . . . 75

    v

  • 4.3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    4.3.4 Small-Scale model . . . . . . . . . . . . . . . . . . . . . . . 77

    4.3.5 Full-Scale Model . . . . . . . . . . . . . . . . . . . . . . . . 79

    4.4 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

    4.5 Empirical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

    4.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

    4.5.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

    4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    V CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

    APPENDIX A PROOFS OF THEOREMS FOR REPEATED NEGOTIA-TIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    APPENDIX B ADDITIONAL DATA AND NUMERICAL RESULTS FORHEALTH-CARE ASSOCIATED INFECTIONS SIMULATION . . . . . 100

    APPENDIX C DERIVATION OF LIMITING PROBABILITIES FOR THEFULL-SCALE MODEL IN THE AMBULANCE DIVERSION ANALYSIS 101

    REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

    vi

  • LIST OF TABLES

    1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2 Data Used in Numerical Analysis: Assets in millions per year . . . . . 27

    3 Data Used in Numerical Analysis: Revenue in millions per year . . . 28

    4 Data Used in Numerical Analysis: Price Index . . . . . . . . . . . . . 28

    5 Excel OLS output for Price index regressed on Total Assets . . . . . . 29

    6 Excel OLS output for Price index regressed on Total Assets with zeroconstant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    7 Excel OLS output for Price index regressed on Total Assets with quadraticterm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    8 Excel worksheet with intercepts and tests H0 : 0 = 0 . . . . . . . . . 31

    9 ICU Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 44

    10 Base Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 57

    11 Parameter and Variable Definitions . . . . . . . . . . . . . . . . . . . 58

    12 Output from Base Model . . . . . . . . . . . . . . . . . . . . . . . . . 58

    13 Output from the model with an additional isolation ward . . . . . . . 59

    14 Output from the model with an isolation ward carved out form the ICU 60

    15 The average effect across scenarios of changes in hand-hygiene efficacy 60

    16 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    17 Simulation Results for DeKalb Medical Center . . . . . . . . . . . . . 87

    18 Excel OLS output for Total Cost regressed on LOS and HAILOS . . . 100

    19 Limiting Probabilities for the Full-Scale Model . . . . . . . . . . . . . 108

    20 Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    vii

  • LIST OF FIGURES

    1 Numerical illustration of capital growth in this model . . .