Quantitative Methods in Health Care Management:

Techniques and Applications, 2nd Edition

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QUANTITATIVE
METHODS IN
HEALTH CARE
MANAGEMENT
QUANTITATIVE
METHODS IN
HEALTH CARE
MANAGEMENT
Techniques
and Applications
Second Edition

YA S A R A . O Z C A N
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.

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Library of Congress Cataloging-in-Publication Data

Ozcan, Yasar A.
Quantitative methods in health care management : techniques and applications / Yasar A.
Ozcan.—2nd ed.
p. ; cm.
Includes bibliographical references and index.
ISBN-13: 978-0-470-43462-8
ISBN-10: 0-470-43462-7
1. Health services administration—Statistical methods. 2. Health services
administration—Decision making. 3 Health services administration—Methodology. I. Title.
[DNLM: 1. Health Services Administration. 2. Statistics as Topic. 3. Decision
Making, Organizational. 4. Decision Support Techniques. 5. Models, Theoretical.
WA 950 O99q 2009]
RA394.O98 2009
362.1072⬘7—dc22
2009001457

Printed in the United States of America

FIRST EDITION

PB Printing 10 9 8 7 6 5 4 3 2 1
 CONTENTS
Tables, Figures, & Exhibits ix

Foreword xix

Acknowledgments xxi

The Author xxiii

Introduction xxv

1 INTRODUCTION TO QUANTITATIVE
DECISION-MAKING METHODS IN HEALTH CARE MANAGEMENT 1
Historical Background and the Development of Decision Techniques 2
The Health Care Manager and Decision Making 3
Information Technology (IT) and Health Care Management 3
The Scope of Health Care Services, and Recent Trends 4
Health Care Services Management 6
Distinctive Characteristics of Health Care Services 6
Summary 9
Key Terms 9

2 FORECASTING 11
Steps in the Forecasting Process 12
Forecasting Approaches 13
Summary 44
Key Terms 44
Exercises 45

3 DECISION MAKING IN HEALTH CARE FACILITIES 51

The Decision Process 52
The Decision Tree Approach 66

v
vi Contents

Decision Analysis with Nonmonetary Values and Multiple Attributes 68

Summary 73
Key Terms 73
Exercises 73

4 FACILITY LOCATION 81
Location Methods 83
Summary 99
Key Terms 99
Exercises 99

5 FACILITY LAYOUT 103

Product Layout 104
Process Layout 105
Summary 116
Key Terms 116
Exercises 116

6 REENGINEERING 121
Work Design in Health Care Organizations 123
Summary 155
Key Terms 155
Exercises 155

7 STAFFING 161
Workload Management Overview 162
Summary 182
Key Terms 182
Exercises 182

8 SCHEDULING 187
Staff Scheduling 187
Summary 202
Key Terms 202
Exercises 203
 Contents vii

9 PRODUCTIVITY 205
Trends in Health Care Productivity: Consequences of PPS 206
Summary 231
Key Terms 231
Exercises 232

10 RESOURCE ALLOCATION 237

Linear Programming 237
Summary 258
Key Terms 258
Exercises 258

11 SUPPLY CHAIN AND INVENTORY MANAGEMENT 263

Health Care Supply Chain 263
Summary 285
Key Terms 285
Exercises 285

12 QUALITY CONTROL 289

Quality in Health Care 289
Quality Measurement and Control Techniques 296
Summary 318
Key Terms 320
Exercises 320

13 PROJECT MANAGEMENT 327

The Characteristics of Projects 328
Summary 353
Key Terms 354
Exercises 354

14 QUEUING MODELS AND CAPACITY PLANNING 365

Capacity Analysis and Costs 382
Summary 384
Key Terms 386
Exercises 386
viii Contents

15 SIMULATION 395
Simulation Process 395
Performance Measures and Managerial Decisions 406
Summary 408
Key Terms 408
Exercises 408

APPENDIXES
Appendix A Standard Normal Distribution P(0 < z < x) 411

Appendix B Standard Normal Distribution P(ⴚ3.5 < z < 3.5) 413

Appendix C Cumulative Poisson Probabilities 416

Appendix D t Distribution 423

References 425

Index 429
TABLES, FIGURES, & EXHIBITS
TABLES
1.1. Total Expenditures on Health as % GDP for 30 OECD Countries 4
1.2. Distribution of Health Providers and Health Workers in Health
Services in 2006, and Expected Growth 5
1.3. Health Services by Occupation in 2006, and Projected Growth 7
2.1. Heal-Me Hospital Average Daily Patient Days 35
2.2. Quarterly Indexes for Heal-Me Hospital 37
2.3. Monthly Indexes for Heal-Me Hospital 37
2.4. Daily Indexes for Heal-Me Hospital 38
2.5. Monthly and Daily Adjusted Forecasts for Heal-Me Hospital 40
2.6. Error Calculations 41
3.1. Payoff Table 55
3.2. Demand for Additional MRIs 56
3.3. Maximin Solution 57
3.4. Maximax Solution 57
3.5. Sensitivity Analysis Using Hurwitz Optimism Parameters 59
3.6. Opportunity Losses (Regrets) 59
3.7. Laplace Strategy 60
3.8. Payoff Table for EMV 63
3.9. Expected Opportunity Loss 63
3.10. Best Outcomes Under Certainty 65
3.11. Total Cost of Alternatives Under Various Demand Conditions 65
3.12. Regret Table Using Costs 66
3.13. Summary of Supplier Proposals 71
4.1. Factors to be Considered in Establishing a Satellite Clinic 87
4.2. Relative Scores on Factors for a Satellite Clinic 89
4.3. Relative Factor Scores and Weights 89
4.4. Composite Scores 90

ix
x Contents

4.5. Satellite Clinic Factor Rankings and Minimum Acceptable Levels 91

4.6. Satellite Clinic Factor Minimum Acceptable Levels 93
4.7. Satellite Clinic Factor Importance Rankings 93
4.8. Selected Richmond Metropolitan Area Hospitals 95
4.9. Selected Richmond Metropolitan Area Hospitals and Their
Interaction with the Blood Bank 96
5.1. Distance and Flows Among Three Hospital Departments 112
5.2. Possible Assignment Configurations of Departments to
Three Locations 113
5.3. Ranking Departments According to Highest Flow 113
5.4. Total Cost of a Layout 114
6.1. Typical Allowance Percentages for Varying Health Care Delivery
Working Conditions 131
6.2. Observed Times and Performance Ratings for
Nursing Unit Activities 133
6.3. Observed and Normal Time Calculations for Nursing Unit
Activities 134
6.4. Abridged Patient Care Tasks in a Nursing Unit 136
6.5. Work Sampling Data Collection Form for Nursing Unit 137
6.6. Random Numbers 141
6.7. Development of the Schedule for a Work Sampling Study 143
6.8. Final Work Sampling Schedule 144
6.9. Partial Work Distribution Chart for Nursing Unit 144
7.1. Examples of Work Standards 164
7.2. Daily Census, Required Labor Hours, and Acuity Level Statistics
for a Medical or Surgical Floor 168
7.3. Average Census, Required Labor Hours, and Acuity
Level Statistics for a Medical or Surgical Floor 169
7.4. Weighted Average Utilization for a Laboratory Based on
Workload Fluctuations by Shift 172
7.5. Workload Standards for Microscopic Procedures in Laboratory 173
7.6. Calculation of Staffing Requirements for Microscopic Procedures 174
7.7. The Effect of Shift Alternatives on Staffing—The Coverage Factor 177
10.1. Nurse Scheduling with Integer Programming 257
11.1. A-B-C Classification Analysis 275
12.1. Factors for Determining Control Limits for Mean and Range
Charts (for Three-Sigma or 99.7 Percent–Confidence Level) 307
 Contents xi

13.1. Activity Precedence Relationships 332

13.2. Path Lengths for the Radiation Oncology Project 335
13.3. Probabilistic Time Estimates for Radiation Oncology Clinic 341
13.4. Calculation of Expected Time and Standard Deviations on
Each Path for the Radiation Oncology Clinic 342
13.5. Path Completion Probabilities 344
13.6. Project Completion Probabilities 346
14.1. Summary Analysis for M/M/s Queue for Diabetes
Information Booth 385
15.1. Simple Simulation Experiment for Public Clinic 396
15.2. Summary Statistics for Public Clinic Experiment 397
15.3. Patient Arrival Frequencies 399
15.4. Probability Distribution for Patient Arrivals 400
15.5. Cumulative Poisson Probabilities for ␭ ⫽ 1.7 401
15.6. Cumulative Poisson Probabilities for Arrivals: ␭ ⫽ 1.7 402
15.7. Monte Carlo Simulation Experiment for Public Health Clinic 403
15.8. Summary Statistics for Public Clinic Monte Carlo
Simulation Experiment 405

FIGURES
2.1. Seasonal Variation Characteristics 15
2.2. Cycle Variation 15
2.3. Random Variation and Trend 15
2.4. Excel Template Solution: Moving Average (MA3) for OB/GYN Clinic 17
2.5. Excel Template Solution: Weighted Moving Average (WMA3) for
OB/GYN Clinic 20
2.6. Excel Template Solutions to the OB/GYN Example, Using Single
Exponential Smoothing (SES) with ␣ = 0.3 and ␣ = 0.5 22
2.7. Excel Template Solutions to the OB/GYN Example, Using Single
Exponential Smoothing (SES) with ␣ = 0 and ␣ = 1.0 24
2.8. Linear Regression 25
2.9. Excel Setup – Linear Regression for the Multihospital
System Example 27
2.10. Excel Solution to the Multihospital System Example 28
2.11. Linear Regression as a Trend 29
2.12. Excel Linear Trend Graphic Solution to the OB/GYN Example 30
xii Contents

2.13. Excel Template Solution to the OB/GYN Example 30

2.14. Excel Template – SEST Solution to Example 2.9 33
2.15. Seasonality-Removed Trend Data for Heal-Me Hospital
Patient Demand 39
2.16. Alternative Forecasting Methods and Accuracy, Measured by
MAD and MAPE 42
2.17. Linear Trend with Tracking Signal for Patient Visit Forecast,
Heal-Me Hospital 43
2.18. Tracking Signal for Patient Visit Forecast, Heal-Me Hospital 44
3.1. Decision Tree 67
3.2. Rollback Method 68
3.3. Payoff Table Analysis Using Excel Template for Decision
Analysis 69
3.4. Decision Tree and Rollback Procedure Using Excel Template
for Decision Analysis 70
4.1. Total Cost of Alternative Imaging Sites 85
4.2. Profit Evaluation of Alternative Sites 86
4.3. Richmond Metropolitan Area Hospitals 94
4.4. Richmond Metropolitan Area Blood Bank Locations 97
4.5. Geographic Information Systems 98
5.1. Available Space for Layout of Long-Term Care Facility 106
5.2. Closeness Rating Chart for Long-Term Care Facility 107
5.3. A and X Closeness Representation 108
5.4. Layout Solution 108
5.5. Excel Template Solution 115
5.6. Excel Template Solution and Final Layout for a Small Hospital 115
6.1. Work Design—A Systems Perspective 124
6.2. Socio-Technical School Approach 127
6.3. Random Observation Schedule 147
6.4. Stabilized Dates and Times 148
6.5. Valid Dates and Times 149
6.6. Final Observation Schedule 150
6.7. Flow Process Chart for Emergency Room Specimen Processing 152
6.8. Commonly Used Flow Chart Symbols 153
6.9. Flow Chart for Emergency Room Specimen Processing 154
7.1. Workload Management 163
 Contents xiii

7.2. Distribution of Daily Workload on a Nursing Unit 178

7.3. Workload Standard Tolerance Ranges 180
8.1. Comparison of Eight- and Ten-Hour Shifts 189
8.2. Pattern of Alternating Eight- and Twelve-Hour Shifts 190
9.1. Productivity and Quality Trade-Off 223
9.2. Substitution of Physicians and Nurse Practitioners:
A Look at Technical Efficiency 226
9.3. Example of DEA Efficiency Frontier Formulation 229
10.1. Graphic Solution for Insurance Company Problem 242
10.2. Excel Setup for the Insurance Company Problem 243
10.3. Excel Solver 244
10.4. Identifying Constraints and Solution Cells 244
10.5. Selection of Solution Reports 245
10.6. Answer Report 246
10.7. Sensitivity Report 247
10.8. Limits Report 248
10.9. Graphic Explanation of Sensitivity Analysis: Shadow
Price and its Impact on Alternative Optimal Solutions 249
10.10. Graphic Solution for Minimization Example 250
10.11. Excel Setup for the Minimization Problem 251
10.12 Solution to the Minimization Problem 251
10.13. Minimization Problem Answer Report 252
10.14. Minimization Problem Sensitivity Report 252
10.15. Minimization Problem Limits Report 253
10.16. Integer Programming: Excel Setup for the Staff
Scheduling Problem 255
10.17. Identifying Constraints and Integer Values 255
10.18. Solution to the Staff Scheduling Problem 256
10.19. Answer Report for the Staff Scheduling Problem 256
11.1. Health Care Supply Chain 264
11.2. The Inventory Order Cycle for Basic EOQ Model 276
11.3. The Economic Ordering Quantity Model 277
11.4. Excel Solution to the Syringe Problem 282
11.5. Multi-Item Inventory EOQ and ABC Analysis 283
12.1. Quality Measurement 290
12.2. The Deming Wheel/Shewhart Cycle 294
xiv Contents

12.3. Process Capability 297

12.4. Control Limits, Random and Nonrandom Sample Observations 299
12.5. ABC Medical Center Infection Control Monitoring 301
12.6. Holistic Care Corporation’s Quality Monitoring 304
12.7. Use of Mean and Range Charts 305
12.8. Identification of Runs 310
12.9. Zone Test 313
12.10. A Check Sheet and Corresponding Histogram for Emergency
Room Wait Times 316
12.11. Scatter Diagram 317
12.12. A Flow Chart for the X-Ray Order Process in an
Emergency Department 318
12.13. Cause-and-Effect Diagram 319
12.14. Pareto Diagram 319
13.1. Network Representations 333
13.2. AON Network Diagram for Radiation Oncology 334
13.3. Activity Start and Finish Times 336
13.4. Excel Setup and Solution to the Radiation Oncology Project,
CPM Version 338
13.5. Project Completion Probabilities by the Specified Time 343
13.6. Completion Probabilities for Sixty-Five Weeks 344
13.7. Excel Setup and Solution to the Probabilistic Radiation
Oncology Project 345
13.8. Project Duration and Compression (Crashing) Costs 348
13.9. Project Compression 349
13.10. Total Cost of Compression 353
14.1. Queue Phenomenon 366
14.2. Health Care Service Capacity and Costs 367
14.3. Queuing Conceptualization of Flu Inoculations 368
14.4. Conceptualization of a Single-Line, Multiphase System 369
14.5. Multiple-Line Queuing System 370
14.6. Emergency Room Arrival Patterns 371
14.7. Measures of Arrival Patterns 372
14.8. Poisson Distribution 373
14.9. Service Time for ER Patients 373
 Contents xv

14.10. Excel Setup and Solution to the Diabetes Information Booth Problem 379
14.11. System Probability Summary for Diabetes Information Booth 380
14.12. System Performance for Expanded Diabetes Information Booth 382
14.13. System Performance Summary for Expanded Diabetes Information
Booth with M/M/3 383
14.14. Capacity Analysis 385
15.1. Random Numbers 401
15.2. Excel-Based Simulated Arrivals 406
15.3. Excel Program for Simulated Arrivals 407
15.4. Performance-Measure-Based Managerial Decision Making 407

EXHIBITS
5.1. From-To Chart for a Small Hospital 111
8.1. Cyclical Staffing Schedules for Four and Five Weeks 192
8.2. An Example of OR Block Schedule: Surgical Suite
Scheduling Method 199
13.1 Gantt Chart for Launching a New Radiation Oncology Service 331
14.1 Queuing Model Classification 374
14.2 Queuing Model Notation 376
To my wife, Gulperi, and my daughters, Gunes and Nilufer
 FOREWORD
I would like to congratulate Professor Yasar Ozcan on producing this excellent, com-
prehensive textbook, Quantitative Methods in Health Care Management. The field has
needed such a textbook for a very long time, and Professor Ozcan is eminently quali-
fied in bringing it to us.
The last textbook in this area was written over twenty years ago. To all of us in
health services research and management, we know that health care delivery today
bears little resemblance to that era. So too, the use, types, and depth of quantitative
methods and techniques have progressed greatly in this time period. Professor Ozcan
brings us not only the latest and best methods and techniques, but also illustrates their
uses through current cases and examples.
And what I like best about this textbook is that it has been written by one of the
leading and most knowledgeable health care management professors in the world.
Professor Ozcan has been at the forefront in developing and applying many of the
methods in the book, and as founding editor of the journal Health Care Management
Science, he draws on the latest knowledge available from other areas.
For those of us who teach quantitative methods in health care management courses,
this book will make our task far easier. More importantly, it will provide our students
with a comprehensive text that they can draw on in their health care management
careers. In addition, this text is a welcome, comprehensive, and up-to-date addition
to the work of current managers and to all those who say, “There must be a better way to
deliver health care.”
Indeed there is, and the application of the methods and ideas in this book will pro-
vide many, many answers.
William P. Pierskalla, Ph.D.
Distinguished Professor and Dean Emeritus,
The Anderson School, UCLA,
and Ronald Rosenfeld Professor Emeritus,
The Wharton School, University of Pennsylvania

xix
 ACKNOWLEDGMENTS
Writing this book could not have been achieved without the help and encouragement
of many individuals. I take this opportunity to thank them; if I miss anyone, it is
through authorial oversight only, as all the help received was deeply appreciated. First
of all, I thank my colleague Ramesh K. Shukla, who provided valuable insights and
material for the productivity chapter. Many thanks go to my graduate students from
the MSHA Class of 2007 and MSHA Class of 2006 who received the first draft of the
manuscript and pointed out many corrections. Similarly, graduate students from
the MSHA Class of 2005 lent their real-life experiences with quantitative techniques
and associated materials and data, which are used in the examples and exercises
throughout the text. In that vein, more specifically, I thank Adrian Amedia, Joani
Brough, Mark Cotter, Sandy Chung, Suzanne Coyner, Alan Dow, and Paulomi Sanyal
for their resourcefulness.
I would like to acknowledge Dorothy Silvers for her diligent editing of the manu-
script from cover to cover. I extend my sincere thanks as well to Jossey-Bass/Wiley
staff members Andrew Pasternack and Seth Schwartz, for their cooperativeness and
help in the production of this manuscript.
No book can be written on time without the support and encouragement of loved
ones. I am indebted to my wife, Gulperi Ozcan, who became my sounding board for
every example in this book. Moreover, she extended her support throughout the devel-
opment of the manuscript even as I deprived her of my time in favor of my desktop.
I thank her for the sustained support she has given me throughout my academic career
and our personal life.
Yasar A. Ozcan, Ph.D.
May 15, 2008
Richmond, Virginia

xxi