Quantitative Analysis For Management ELEVENTH EDITION
BARRY RENDER Charles Harwood Professor of Management Science Graduate School of Business, Rollins College
RALPH M. STAIR, JR. Professor of Information and Management Sciences, Florida State University
MICHAEL E. HANNA Professor of Decision Sciences, University of Houston—Clear Lake
Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
To my wife and sons – BR To Lila and Leslie – RMS To Susan, Mickey, and Katie – MEH
Editorial Director: Sally Yagan Editor in Chief: Eric Svendsen Senior Acquisitions Editor: Chuck Synovec Product Development Manager: Ashley Santora Director of Marketing: Patrice Lumumba Jones Senior Marketing Manager: Anne Fahlgren Marketing Assistant: Melinda Jones Senior Managing Editor: Judy Leale Project Manager: Mary Kate Murray Senior Operations Specialist: Arnold Vila Operations Specialist: Cathleen Petersen Senior Art Director: Janet Slowik Art Director: Steve Frim Text and Cover Designer: Wee Design Group
Manager, Rights and Permissions: Hessa Albader Cover Art: Shutterstock Media Project Manager, Editorial: Allison Longley Media Project Manager, Production: John Cassar Full-Service Project Management: PreMediaGlobal Composition: PreMediaGlobal Printer/Binder: Edwards Brothers Cover Printer: Lehigh-Phoenix Color/Hagerstown Text Font: 10/12 Times
Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U.S.A. and other countries. Screen shots and icons reprinted with permission from the Microsoft Corporation. This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation. Copyright © 2012, 2009, 2006, 2003, 2000 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, New Jersey 07458. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. CIP data for this title is available on file at the Library of Congress
10 9 8 7 6 5 4 3 2 1
ISBN-13: 978-0-13-214911-2 ISBN-10: 0-13-214911-7
ABOUT THE AUTHORS
Barry Render Professor Emeritus, the Charles Harwood Distinguished Professor of management science at the Roy E. Crummer Graduate School of Business at Rollins College in Winter Park, Florida. He received his MS in Operations Research and his PhD in Quantitative Analysis at the University of Cincinnati. He previously taught at George Washington University, the University of New Orleans, Boston University, and George Mason University, where he held the Mason Foundation Professorship in Decision Sciences and was Chair of the Decision Science Department. Dr. Render has also worked in the aerospace industry for General Electric, McDonnell Douglas, and NASA. Dr. Render has coauthored 10 textbooks published by Prentice Hall, including Managerial Decision Modeling with Spreadsheets, Operations Management, Principles of Operations Management, Service Management, Introduction to Management Science, and Cases and Readings in Management Science. Dr. Render’s more than 100 articles on a variety of management topics have appeared in Decision Sciences, Production and Operations Management, Interfaces, Information and Management, Journal of Management Information Systems, Socio-Economic Planning Sciences, IIE Solutions and Operations Management Review, among others. Dr. Render has been honored as an AACSB Fellow, and he was named a Senior Fulbright Scholar in 1982 and again in 1993. He was twice vice president of the Decision Science Institute Southeast Region and served as software review editor for Decision Line from 1989 to 1995. He has also served as editor of the New York Times Operations Management special issues from 1996 to 2001. From 1984 to 1993, Dr. Render was president of Management Service Associates of Virginia, Inc., whose technology clients included the FBI; the U.S. Navy; Fairfax County, Virginia and C&P Telephone. Dr. Render has taught operations management courses in Rollins College’s MBA and Executive MBA programs. He has received that school’s Welsh Award as leading professor and was selected by Roosevelt University as the 1996 recipient of the St. Claire Drake Award for Outstanding Scholarship. In 2005, Dr. Render received the Rollins College MBA Student Award for Best Overall Course, and in 2009 was named Professor of the Year by full-time MBA students. Ralph Stair is Professor Emeritus at Florida State University. He earned a BS in chemical engineering from Purdue University and an MBA from Tulane University. Under the guidance of Ken Ramsing and Alan Eliason, he received a PhD in operations management from the University of Oregon. He has taught at the University of Oregon, the University of Washington, the University of New Orleans, and Florida State University. He has twice taught in Florida State University’s Study Abroad Program in London. Over the years, his teaching has been concentrated in the areas of information systems, operations research, and operations management. Dr. Stair is a member of several academic organizations, including the Decision Sciences Institute and INFORMS, and he regularly participates at national meetings. He has published numerous articles and books, including Managerial Decision Modeling with Spreadsheets, Introduction to Management Science, Cases and Readings in Management Science, Production and Operations Management: A Self-Correction Approach, Fundamentals of Information Systems, Principles of Information Systems, Introduction to Information Systems, Computers in Today’s World, Principles of Data Processing, Learning to Live with Computers, Programming in BASIC, Essentials of BASIC Programming, Essentials of FORTRAN Programming, and Essentials of COBOL Programming. Dr. Stair divides his time between Florida and Colorado. He enjoys skiing, biking, kayaking, and other outdoor activities. iii
ABOUT THE AUTHORS
Michael E. Hanna is Professor of Decision Sciences at the University of Houston–Clear Lake (UHCL). He holds a BA in Economics, an MS in Mathematics, and a PhD in Operations Research from Texas Tech University. For more than 25 years, he has been teaching courses in statistics, management science, forecasting, and other quantitative methods. His dedication to teaching has been recognized with the Beta Alpha Psi teaching award in 1995 and the Outstanding Educator Award in 2006 from the Southwest Decision Sciences Institute (SWDSI). Dr. Hanna has authored textbooks in management science and quantitative methods, has published numerous articles and professional papers, and has served on the Editorial Advisory Board of Computers and Operations Research. In 1996, the UHCL Chapter of Beta Gamma Sigma presented him with the Outstanding Scholar Award. Dr. Hanna is very active in the Decision Sciences Institute, having served on the Innovative Education Committee, the Regional Advisory Committee, and the Nominating Committee. He has served two terms on the board of directors of the Decision Sciences Institute (DSI) and as regionally elected vice president of DSI. For SWDSI, he has held several positions, including president, and he received the SWDSI Distinguished Service Award in 1997. For overall service to the profession and to the university, he received the UHCL President’s Distinguished Service Award in 2001.
Introduction to Quantitative Analysis 1
Probability Concepts and Applications 21
Decision Analysis 69
Regression Models 115
Inventory Control Models 195
Linear Programming Models: Graphical and Computer Methods 249
Waiting Lines and Queuing Theory Models 499
Simulation Modeling 533
Markov Analysis 573
Statistical Quality Control 601
Linear Programming Applications 307
Transportation and Assignment Models 341
Integer Programming, Goal Programming, and Nonlinear Programming 395
1 Analytic Hierarchy Process M1-1 2 Dynamic Programming M2-1 3 Decision Theory and the Normal Distribution M3-1 4 Game Theory M4-1
Network Models 429
Project Management 459
5 Mathematical Tools: Determinants and Matrices M5-1 6 Calculus-Based Optimization M6-1 7 Linear Programming: The Simplex Method M7-1
This page intentionally left blank
Adding Mutually Exclusive Events 26 Law of Addition for Events That Are Not Mutually Exclusive 26
PREFACE xv CHAPTER 1 1.1 1.2 1.3
Introduction to Quantitative Analysis 1 Introduction 2 What Is Quantitative Analysis? 2 The Quantitative Analysis Approach 3 Defining the Problem 3 Developing a Model 3 Acquiring Input Data 4 Developing a Solution 5 Testing the Solution 5 Analyzing the Results and Sensitivity Analysis 5 Implementing the Results 5 The Quantitative Analysis Approach and Modeling in the Real World 7
How to Develop a Quantitative Analysis Model 7 The Advantages of Mathematical Modeling 8 Mathematical Models Categorized by Risk 8
The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach 9 Possible Problems in the Quantitative Analysis Approach 12 Defining the Problem 12 Developing a Model 13 Acquiring Input Data 13 Developing a Solution 14 Testing the Solution 14 Analyzing the Results 14
Probability Concepts and Applications 21 Introduction 22 Fundamental Concepts 22 Types of Probability 23
Mutually Exclusive and Collectively Exhaustive Events 24
Statistically Independent Events 27 Statistically Dependent Events 28 Revising Probabilities with Bayes’ Theorem 29 General Form of Bayes’ Theorem 31
2.7 2.8 2.9
Further Probability Revisions 32 Random Variables 33 Probability Distributions 34 Probability Distribution of a Discrete Random Variable 34 Expected Value of a Discrete Probability Distribution 35 Variance of a Discrete Probability Distribution 36 Probability Distribution of a Continuous Random Variable 36
The Binomial Distribution 38 Solving Problems with the Binomial Formula 39 Solving Problems with Binomial Tables 40
The Normal Distribution 41 Area Under the Normal Curve 42 Using the Standard Normal Table 42 Haynes Construction Company Example 44 The Empirical Rule 48
The F Distribution 48 The Exponential Distribution 50 Arnold’s Muffler Example 51
The Poisson Distribution 52 Summary 54 Glossary 54 Key Equations 55 Solved Problems 56 Self-Test 59 Discussion Questions and Problems 60 Case Study: WTVX 65 Bibliography 66
Implementation—Not Just the Final Step 15 Lack of Commitment and Resistance to Change 15 Lack of Commitment by Quantitative Analysts 15 Summary 16 Glossary 16 Key Equations 16 Self-Test 17 Discussion Questions and Problems 17 Case Study: Food and Beverages at Southwestern University Football Games 19 Bibliography 19
CHAPTER 2 2.1 2.2
2.4 2.5 2.6
Appendix 2.1 Appendix 2.2
Derivation of Bayes’ Theorem 66 Basic Statistics Using Excel 66
CHAPTER 3 3.1 3.2 3.3 3.4
Decision Analysis 69 Introduction 70 The Six Steps in Decision Making 70 Types of Decision-Making Environments 71 Decision Making Under Uncertainty 72 Optimistic 72 Pessimistic 73 Criterion of Realism (Hurwicz Criterion) 73 vii
Equally Likely (Laplace) 74 Minimax Regret 74
Decision Making Under Risk 76
Expected Monetary Value 76 Expected Value of Perfect Information 77 Expected Opportunity Loss 78 Sensitivity Analysis 79 Using Excel QM to Solve Decision Theory Problems 80
How Probability Values are Estimated by Bayesian Analysis 87 Calculating Revised Probabilities 87 Potential Problem in Using Survey Results 89
5.3 5.4 5.5
Utility Theory 90
Decision Models with QM for Windows 113 Decision Trees with QM for Windows 114 5.6
CHAPTER 4 4.1 4.2 4.3 4.4
Using Computer Software for Regression 122 Assumptions of the Regression Model 123
Testing the Model for Significance 125
Estimating the Variance 125 Triple A Construction Example 127 The Analysis of Variance (ANOVA) Table 127 Triple A Construction ANOVA Example 128
Forecasting with QM for Windows 191
CHAPTER 6 6.1 6.2
Inventory Control Models 195 Introduction 196 Importance of Inventory Control 196 Decoupling Function 197 Storing Resources 197 Irregular Supply and Demand 197 Quantity Discounts 197 Avoiding Stockouts and Shortages 197
Multiple Regression Analysis 128 Evaluating the Multiple Regression Model 129 Jenny Wilson Realty Example 130
4.9 4.10 4.11 4.12
Binary or Dummy Variables 131 Model Building 132 Nonlinear Regression 133 Cautions and Pitfalls in Regression Analysis 136
Formulas for Regression Calculations 146
Inventory Decisions 197 Economic Order Quantity: Determining How Much to Order 199 Inventory Costs in the EOQ Situation 200 Finding the EOQ 202 Sumco Pump Company Example 202 Purchase Cost of Inventory Items 203 Sensitivity Analysis with the EOQ Model 204
Summary 136 Glossary 137 Key Equations 137 Solved Problems 138 Self-Test 140 Discussion Questions and Problems 140 Case Study: North–South Airline 145 Bibliography 146
Monitoring and Controlling Forecasts 179 Adaptive Smoothing 181 Summary 181 Glossary 182 Key Equations 182 Solved Problems 183 Self-Test 184 Discussion Questions and Problems 185 Case Study: Forecasting Attendance at SWU Football Games 189 Case Study: Forecasting Monthly Sales 190 Bibliography 191
Regression Models 115 Introduction 116 Scatter Diagrams 116 Simple Linear Regression 117 Measuring the Fit of the Regression Model 119 Coefficient of Determination 120 Correlation Coefficient 121
Scatter Diagrams and Time Series 156 Measures of Forecast Accuracy 158 Time-Series Forecasting Models 160 Components of a Time Series 160 Moving Averages 161 Exponential Smoothing 164 Using Excel QM for Trend-Adjusted Exponential Smoothing 169 Trend Projections 169 Seasonal Variations 171 Seasonal Variations with Trend 173 The Decomposition Method of Forecasting with Trend and Seasonal Components 175 Using Regression with Trend and Seasonal Components 177
Measuring Utility and Constructing a Utility Curve 91 Utility as a Decision-Making Criterion 93 Summary 95 Glossary 95 Key Equations 96 Solved Problems 97 Self-Test 102 Discussion Questions and Problems 103 Case Study: Starting Right Corporation 110 Case Study: Blake Electronics 111 Bibliography 113
Appendix 3.1 Appendix 3.2
Forecasting 153 Introduction 154 Types of Forecasts 154 Time-Series Models 154 Causal Models 154 Qualitative Models 155
Decision Trees 81 Efficiency of Sample Information 86 Sensitivity Analysis 86
CHAPTER 5 5.1 5.2
Regression Models Using QM for Windows 148 Regression Analysis in Excel QM or Excel 2007 150
Reorder Point: Determining When to Order 205
EOQ Without the Instantaneous Receipt Assumption 206
Quantity Discount Models 210 Brass Department Store Example 212
Use of Safety Stock 213 Single-Period Inventory Models 220 Marginal Analysis with Discrete Distributions 221 Café du Donut Example 222 Marginal Analysis with the Normal Distribution 222 Newspaper Example 223
ABC Analysis 225 Dependent Demand: The Case for Material Requirements Planning 226 Material Structure Tree 226 Gross and Net Material Requirements Plan 227 Two or More End Products 229
Just-in-Time Inventory Control 230 Enterprise Resource Planning 232 Summary 232 Glossary 232 Key Equations 233 Solved Problems 234 Self-Test 237 Discussion Questions and Problems 238 Case Study: Martin-Pullin Bicycle Corporation 245 Bibliography 246
Inventory Control with QM for Windows 246
Sensitivity Analysis 276 High Note Sound Company 278 Changes in the Objective Function Coefficient 278 QM for Windows and Changes in Objective Function Coefficients 279 Excel Solver and Changes in Objective Function Coefficients 280 Changes in the Technological Coefficients 280 Changes in the Resources or Right-Hand-Side Values 282 QM for Windows and Changes in Right-HandSide Values 283 Excel Solver and Changes in Right-Hand-Side Values 285 Summary 285 Glossary 285 Solved Problems 286 Self-Test 291 Discussion Questions and Problems 292 Case Study: Mexicana Wire Works 300 Bibliography 302
Annual Carrying Cost for Production Run Model 207 Annual Setup Cost or Annual Ordering Cost 208 Determining the Optimal Production Quantity 208 Brown Manufacturing Example 208
Excel QM 302
CHAPTER 8 8.1 8.2
Linear Programming Applications 307 Introduction 308 Marketing Applications 308 Media Selection 308 Marketing Research 309
Manufacturing Applications 312 Production Mix 312 Production Scheduling 313
Employee Scheduling Applications 317
Financial Applications 319
Labor Planning 317
CHAPTER 7 7.1 7.2 7.3
Linear Programming Models: Graphical and Computer Methods 249 Introduction 250 Requirements of a Linear Programming Problem 250 Formulating LP Problems 251 Flair Furniture Company 252
Portfolio Selection 319 Truck Loading Problem 322
Diet Problems 324 Ingredient Mix and Blending Problems 325
Solving Flair Furniture’s LP Problem Using QM For Windows and Excel 263 Using QM for Windows 263 Using Excel’s Solver Command to Solve LP Problems 264
Solving Minimization Problems 270
Four Special Cases in LP 274
CHAPTER 9 9.1 9.2
Transportation and Assignment Models 341 Introduction 342 The Transportation Problem 342 Linear Program for the Transportation Example 342 A General LP Model for Transportation Problems 343
Holiday Meal Turkey Ranch 270 No Feasible Solution 274 Unboundedness 275 Redundancy 275 Alternate Optimal Solutions 276
Transportation Applications 327 Shipping Problem 327 Summary 330 Self-Test 330 Problems 331 Case Study: Chase Manhattan Bank 339 Bibliography 339
Graphical Solution to an LP Problem 253 Graphical Representation of Constraints 253 Isoprofit Line Solution Method 257 Corner Point Solution Method 260 Slack and Surplus 262
Ingredient Blending Applications 324
The Assignment Problem 344 Linear Program for Assignment Example 345
The Transshipment Problem 346 Linear Program for Transshipment Example 347
Linear Objective Function with Nonlinear Constraints 414 Summary 415 Glossary 415 Solved Problems 416 Self-Test 419 Discussion Questions and Problems 419 Case Study: Schank Marketing Research 425 Case Study: Oakton River Bridge 425 Bibliography 426
The Transportation Algorithm 348 Developing an Initial Solution: Northwest Corner Rule 350 Stepping-Stone Method: Finding a Least-Cost Solution 352
Special Situations with the Transportation Algorithm 358 Unbalanced Transportation Problems 358 Degeneracy in Transportation Problems 359 More Than One Optimal Solution 362 Maximization Transportation Problems 362 Unacceptable or Prohibited Routes 362 Other Transportation Methods 362
Special Situations with the Assignment Algorithm 371 Unbalanced Assignment Problems 371 Maximization Assignment Problems 371 Summary 373 Glossary 373 Solved Problems 374 Self-Test 380 Discussion Questions and Problems 381 Case Study: Andrew–Carter, Inc. 391 Case Study: Old Oregon Wood Store 392 Bibliography 393
Using QM for Windows 393
Integer Programming, Goal Programming, and Nonlinear Programming 395 Introduction 396 Integer Programming 396
Harrison Electric Company Example of Integer Programming 396 Using Software to Solve the Harrison Integer Programming Problem 398 Mixed-Integer Programming Problem Example 400
CHAPTER 12 12.1 12.2
Project Crashing 479 General Foundary Example 480 Project Crashing with Linear Programming 480
Other Topics in Project Management 484 Subprojects 484 Milestones 484 Resource Leveling 484 Software 484 Summary 484 Glossary 485 Key Equations 485 Solved Problems 486 Self-Test 487 Discussion Questions and Problems 488 Case Study: Southwestern University Stadium Construction 494 Case Study: Family Planning Research Center of Nigeria 494 Bibliography 496
Goal Programming 406
Nonlinear Programming 411 Nonlinear Objective Function and Linear Constraints 412 Both Nonlinear Objective Function and Nonlinear Constraints 413
PERT/Cost 473 Planning and Scheduling Project Costs: Budgeting Process 473 Monitoring and Controlling Project Costs 477
Example of Goal Programming: Harrison Electric Company Revisited 408 Extension to Equally Important Multiple Goals 409 Ranking Goals with Priority Levels 409 Goal Programming with Weighted Goals 410
Project Management 459 Introduction 460 PERT/CPM 460 General Foundry Example of PERT/CPM 461 Drawing the PERT/CPM Network 462 Activity Times 463 How to Find the Critical Path 464 Probability of Project Completion 469 What PERT Was Able to Provide 471 Using Excel QM for the General Foundry Example 471 Sensitivity Analysis and Project Management 471
Modeling with 0–1 (Binary) Variables 402 Capital Budgeting Example 402 Limiting the Number of Alternatives Selected 404 Dependent Selections 404 Fixed-Charge Problem Example 404 Financial Investment Example 405
Shortest-Route Problem 439 Shortest-Route Technique 439 Linear Program for Shortest-Route Problem 441 Summary 444 Glossary 444 Solved Problems 445 Self-Test 447 Discussion Questions and Problems 448 Case Study: Binder’s Beverage 455 Case Study: Southwestern University Traffic Problems 456 Bibliography 457
The Assignment Algorithm 365 The Hungarian Method (Flood’s Technique) 366 Making the Final Assignment 369
Network Models 429 Introduction 430 Minimal-Spanning Tree Problem 430 Maximal-Flow Problem 433 Maximal-Flow Technique 433 Linear Program for Maximal Flow 438
Facility Location Analysis 363 Locating a New Factory for Hardgrave Machine Company 363
CHAPTER 11 11.1 11.2 11.3
Project Management with QM for Windows 497
CHAPTER 13 13.1 13.2
Waiting Lines and Queuing Theory Models 499 Introduction 500 Waiting Line Costs 500
Using Excel to Simulate the Port of New Orleans Queuing Problem 551
Characteristics of a Queuing System 501 Arrival Characteristics 501 Waiting Line Characteristics 502 Service Facility Characteristics 503 Identifying Models Using Kendall Notation 503
Multichannel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/M) 511 Equations for the Multichannel Queuing Model 512 Arnold’s Muffler Shop Revisited 512
Finite Population Model (M/M/1 with Finite Source) 516
CHAPTER 15 15.1 15.2
Some General Operating Characteristic Relationships 519 More Complex Queuing Models and the Use of Simulation 519 Summary 520 Glossary 520 Key Equations 521 Solved Problems 522 Self-Test 524 Discussion Questions and Problems 525 Case Study: New England Foundry 530 Case Study: Winter Park Hotel 531 Bibliography 532
Using QM for Windows 532
CHAPTER 14 14.1 14.2
Simulation Modeling 533 Introduction 534 Advantages and Disadvantages of Simulation 535 Monte Carlo Simulation 536
Harry’s Auto Tire Example 536 Using QM for Windows for Simulation 541 Simulation with Excel Spreadsheets 541
15.4 15.5 15.6 15.7
Port of New Orleans 550
Predicting Future Market Shares 577 Markov Analysis of Machine Operations 578 Equilibrium Conditions 579 Absorbing States and the Fundamental Matrix: Accounts Receivable Application 582 Summary 586 Glossary 587 Key Equations 587 Solved Problems 587 Self-Test 591 Discussion Questions and Problems 591 Case Study: Rentall Trucks 595 Bibliography 597
Appendix 15.1 Appendix 15.2
Markov Analysis with QM for Windows 597 Markov Analysis With Excel 599
CHAPTER 16 16.1 16.2 16.3
Statistical Quality Control 601 Introduction 602 Defining Quality and TQM 602 Statiscal Process Control 603 Variability in the Process 603
Control Charts for Variables 605 The Central Limit Theorem 605 Setting x-Chart Limits 606 Setting Range Chart Limits 609
Control Charts for Attributes 610 p-Charts 610 c-Charts 613 Summary 614 Glossary 614 Key Equations 614 Solved Problems 615 Self-Test 616 Discussion Questions and Problems 617 Bibliography 619
Simulation and Inventory Analysis 545
Simulation of a Queuing Problem 550
Matrix of Transition Probabilities 576 Transition Probabilities for the Three Grocery Stores 577
Simkin’s Hardware Store 545 Analyzing Simkin’s Inventory Costs 548
Markov Analysis 573 Introduction 574 States and State Probabilities 574 The Vector of State Probabilities for Three Grocery Stores Example 575
Equations for the Finite Population Model 517 Department of Commerce Example 517
Other Simulation Issues 557 Two Other Types of Simulation Models 557 Verification and Validation 559 Role of Computers in Simulation 560 Summary 560 Glossary 560 Solved Problems 561 Self-Test 564 Discussion Questions and Problems 565 Case Study: Alabama Airlines 570 Case Study: Statewide Development Corporation 571 Bibliography 572
Constant Service Time Model (M/D/1) 514 Equations for the Constant Service Time Model 515 Garcia-Golding Recycling, Inc. 515
Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/1) 506 Assumptions of the Model 506 Queuing Equations 506 Arnold’s Muffler Shop Case 507 Enhancing the Queuing Environment 511
Simulation Model for a Maintenance Policy 553 Three Hills Power Company 553 Cost Analysis of the Simulation 557
Three Rivers Shipping Company Example 501
Using QM for Windows for SPC 619
APPENDICES 621 APPENDIX A
Areas Under the Standard Normal Curve 622
APPENDIX B APPENDIX C
Binomial Probabilities 624 Values of eⴚL for use in the Poisson Distribution 629
F Distribution Values 630 Using POM-QM for Windows 632 Using Excel QM and Excel Add-Ins 635 Solutions to Selected Problems 636 Solutions to Self-Tests 639
APPENDIX E APPENDIX F APPENDIX G APPENDIX H
MODULE 3 M3.1 M3.2
Barclay Brothers Company’s New Product Decision M3-2 Probability Distribution of Demand M3-3 Using Expected Monetary Value to Make a Decision M3-5
ONLINE MODULES Analytic Hierarchy Process M1-1 Introduction M1-2 Multifactor Evaluation Process M1-2 Analytic Hierarchy Process M1-4 Judy Grim’s Computer Decision M1-4 Using Pairwise Comparisons M1-5 Evaluations for Hardware M1-7 Determining the Consistency Ratio M1-7 Evaluations for the Other Factors M1-9 Determining Factor Weights M1-10 Overall Ranking M1-10 Using the Computer to Solve Analytic Hierarchy Process Problems M1-10
Expected Value of Perfect Information and the Normal Distribution M3-6 Opportunity Loss Function M3-6 Expected Opportunity Loss M3-6 Summary M3-8 Glossary M3-8 Key Equations M3-8 Solved Problems M3-9 Self-Test M3-10 Discussion Questions and Problems M3-10 Bibliography M3-12
MODULE 1 M1.1 M1.2 M1.3
Decision Theory and the Normal Distribution M3-1 Introduction M3-2 Break-Even Analysis and the Normal Distribution M3-2
Appendix M3.1 Appendix M3.2
Derivation of the Break-Even Point M3-12 Unit Normal Loss Integral M3-13
MODULE 4 M4.1 M4.2 M4.3 M4.4 M4.5 M4.6
Game Theory M4-1 Introduction M4-2 Language of Games M4-2 The Minimax Criterion M4-3 Pure Strategy Games M4-4 Mixed Strategy Games M4-5 Dominance M4-7 Summary M4-7 Glossary M4-8 Solved Problems M4-8 Self-Test M4-10 Discussion Questions and Problems M4-10 Bibliography M4-12
Comparison of Multifactor Evaluation and Analytic Hierarchy Processes M1-11 Summary M1-12 Glossary M1-12 Key Equations M1-12 Solved Problems M1-12 SelfTest M1-14 Discussion Questions and Problems M1-14 Bibliography M1-16
Game Theory with QM for Windows M4-12
Using Excel for the Analytic Hierarchy Process M1-16
MODULE 2 M2.1 M2.2
Dynamic Programming M2-1 Introduction M2-2 Shortest-Route Problem Solved using Dynamic Programming M2-2 Dynamic Programming Terminology M2-6 Dynamic Programming Notation M2-8 Knapsack Problem M2-9
Mathematical Tools: Determinants and Matrices M5-1 Introduction M5-2 Matrices and Matrix Operations M5-2
M2.3 M2.4 M2.5
Types of Knapsack Problems M2-9 Roller’s Air Transport Service Problem M2-9 Summary M2-16 Glossary M2-16 Key Equations M2-16 Solved Problems M2-17 Self-Test M2-19 Discussion Questions and Problems M2-20 Case Study: United Trucking M2-22 Internet Case Study M2-22 Bibliography M2-23
Matrix Addition and Subtraction M5-2 Matrix Multiplication M5-3 Matrix Notation for Systems of Equations M5-6 Matrix Transpose M5-6
Determinants, Cofactors, and Adjoints M5-7 Determinants M5-7 Matrix of Cofactors and Adjoint M5-9
Finding the Inverse of a Matrix M5-10
Summary M5-12 Glossary M5-12 Key Equations M5-12 Self-Test M5-13 Discussion Questions and Problems M5-13 Bibliography M5-14
Using Excel for Matrix Calculations M5-15
MODULE 6 M6.1 M6.2 M6.3 M6.4
Calculus-Based Optimization M6-1 Introduction M6-2 Slope of a Straight Line M6-2 Slope of a Nonlinear Function M6-3 Some Common Derivatives M6-5
Maximum and Minimum M6-6 Applications M6-8 Economic Order Quantity M6-8 Total Revenue M6-9 Summary M6-10 Glossary M6-10 Key Equations M6-10 Solved Problem M6-11 Self-Test M6-11 Discussion Questions and Problems M6-12 Bibliography M6-12
MODULE 7 M7.1 M7.2
Linear Programming: The Simplex Method M7-1 Introduction M7-2 How to Set Up the Initial Simplex Solution M7-2 Converting the Constraints to Equations M7-3 Finding an Initial Solution Algebraically M7-3 The First Simplex Tableau M7-4
Simplex Solution Procedures M7-8 The Second Simplex Tableau M7-9 Interpreting the Second Tableau M7-12
M7.5 M7.6 M7.7
Developing the Third Tableau M7-13 Review of Procedures for Solving LP Maximization Problems M7-16 Surplus and Artificial Variables M7-16 Surplus Variables M7-17 Artificial Variables M7-17 Surplus and Artificial Variables in the Objective Function M7-18
Solving Minimization Problems M7-18 The Muddy River Chemical Company Example M7-18 Graphical Analysis M7-19 Converting the Constraints and Objective Function M7-20 Rules of the Simplex Method for Minimization Problems M7-21 First Simplex Tableau for the Muddy River Chemical Corporation Problem M7-21 Developing a Second Tableau M7-23 Developing a Third Tableau M7-24 Fourth Tableau for the Muddy River Chemical Corporation Problem M7-26
Second Derivatives M6-6
Review of Procedures for Solving LP Minimization Problems M7-27 Special Cases M7-28 Infeasibility M7-28 Unbounded Solutions M7-28 Degeneracy M7-29 More Than One Optimal Solution M7-30
Sensitivity Analysis with the Simplex Tableau M7-30 High Note Sound Company Revisited M7-30 Changes in the Objective Function Coefficients M7-31 Changes in Resources or RHS Values M7-33
The Dual M7-35 Dual Formulation Procedures M7-37 Solving the Dual of the High Note Sound Company Problem M7-37
Karmarkar’s Algorithm M7-39 Summary M7-39 Equation M7-40 Self-Test M7-44 Problems M7-45
Glossary M7-39 Key Solved Problems M7-40 Discussion Questions and Bibliography M7-53
This page intentionally left blank
OVERVIEW The eleventh edition of Quantitative Analysis for Management continues to provide both graduate and undergraduate students with a solid foundation in quantitative methods and management science. Thanks to the comments and suggestions from numerous users and reviewers of this textbook over the last thirty years, we are able to make this best-selling textbook even better. We continue to place emphasis on model building and computer applications to help students understand how the techniques presented in this book are actually used in business today. In each chapter, managerial problems are presented to provide motivation for learning the techniques that can be used to address these problems. Next, the mathematical models, with all necessary assumptions, are presented in a clear and concise fashion. The techniques are applied to the sample problems with complete details provided. We have found that this method of presentation is very effective, and students are very appreciative of this approach. If the mathematical computations for a technique are very detailed, the mathematical details are presented in such a way that the instructor can easily omit these sections without interrupting the flow of the material. The use of computer software allows the instructor to focus on the managerial problem and spend less time on the mathematical details of the algorithms. Computer output is provided for many examples. The only mathematical prerequisite for this textbook is algebra. One chapter on probability and another chapter on regression analysis provide introductory coverage of these topics. We use standard notation, terminology, and equations throughout the book. Careful verbal explanation is provided for the mathematical notation and equations used.
NEW TO THIS EDITION 䊉 䊉
Excel 2010 is incorporated throughout the chapters. The Poisson and exponential distribution discussions were moved to Chapter 2 with the other statistical background material used in the textbook.
The simplex algorithm content has been moved from the textbook to Module 7 on the Companion Website.
There are 11 new QA in Action boxes, 4 new Model in the Real World boxes, and more than 40 new problems.
Less emphasis was placed on the algorithmic approach to solving transportation and assignment model problems.
More emphasis was placed on modeling and less emphasis was placed on manual solution methods.
SPECIAL FEATURES Many features have been popular in previous editions of this textbook, and they have been updated and expanded in this edition. They include the following: 䊉
Modeling in the Real World boxes demonstrate the application of the quantitative analysis approach to every technique discussed in the book. New ones have been added.
Procedure boxes summarize the more complex quantitative techniques, presenting them as a series of easily understandable steps.
Margin notes highlight the important topics in the text.
History boxes provide interesting asides related to the development of techniques and the people who originated them. QA in Action boxes illustrate how real organizations have used quantitative analysis to solve problems. Eleven new QA in Action boxes have been added.
Solved Problems, included at the end of each chapter, serve as models for students in solving their own homework problems.
Discussion Questions are presented at the end of each chapter to test the student’s understanding of the concepts covered and definitions provided in the chapter.
Problems included in every chapter are applications oriented and test the student’s ability to solve exam-type problems. They are graded by level of difficulty: introductory (one bullet), moderate (two bullets), and challenging (three bullets). More than 40 new problems have been added.
Internet Homework Problems provide additional problems for students to work. They are available on the Companion Website.
Self-Tests allow students to test their knowledge of important terms and concepts in preparation for quizzes and examinations.
Case Studies, at the end of each chapter, provide additional challenging managerial applications. Glossaries, at the end of each chapter, define important terms. Key Equations, provided at the end of each chapter, list the equations presented in that chapter.
䊉 䊉 䊉 䊉
End-of-chapter bibliographies provide a current selection of more advanced books and articles. The software POM-QM for Windows uses the full capabilities of Windows to solve quantitative analysis problems. Excel QM and Excel 2010 are used to solve problems throughout the book. Data files with Excel spreadsheets and POM-QM for Windows files containing all the examples in the textbook are available for students to download from the Companion Website. Instructors can download these plus additional files containing computer solutions to the relevant end-of-chapter problems from the Instructor Resource Center website.
Online modules provide additional coverage of topics in quantitative analysis.
The Companion Website, at www.pearsonhighered.com/render, provides the online modules, additional problems, cases, and other material for almost every chapter.
SIGNIFICANT CHANGES TO THE ELEVENTH EDITION In the eleventh edition, we have incorporated the use of Excel 2010 throughout the chapters. Whereas information about Excel 2007 is also included in appropriate appendices, screen captures and formulas from Excel 2010 are used extensively. Most of the examples have spreadsheet solutions provided. The Excel QM add-in is used with Excel 2010 to provide students with the most up-to-date methods available. An even greater emphasis on modeling is provided as the simplex algorithm has been moved from the textbook to a module on the Companion Website. Linear programming models are presented with the transportation, transshipment, and assignment problems. These are presented from a network approach, providing a consistent and coherent discussion of these important types of problems. Linear programming models are provided for some other network models as well. While a few of the special purpose algorithms are still available in the textbook, they may be easily omitted without loss of continuity should the instructor choose that option.
In addition to the use of Excel 2010, the use of new screen captures, and the discussion of software changes throughout the book, other modifications have been made to almost every chapter. We briefly summarize the major changes here. Chapter 1 Introduction to Quantitative Analysis. New QA in Action boxes and Managing in the Real World applications have been added. One new problem has been added. Chapter 2 Probability Concepts and Applications. The presentation of discrete random variables has been modified. The empirical rule has been added, and the discussion of the normal distribution has been modified. The presentations of the Poisson and exponential distributions, which are important in the waiting line chapter, have been expanded. Three new problems have been added. Chapter 3 Decision Analysis. The presentation of the expected value criterion has been modified. A discussion is provided of using the decision criteria for both maximization and minimization problems. An Excel 2010 spreadsheet for the calculations with Bayes theorem is provided. A new QA in Action box and six new problems have been added. Chapter 4 Regression Models. Stepwise regression is mentioned when discussing model building. Two new problems have been added. Other end-of-chapter problems have been modified. Chapter 5 Forecasting. The presentation of exponential smoothing with trend has been modified. Three new end-of-chapter problems and one new case have been added. Chapter 6 Inventory Control Models. The use of safety stock has been significantly modified, with the presentation of three distinct situations that would require the use of safety stock. Discussion of inventory position has been added. One new QA in Action, five new problems, and two new solved problems have been added. Chapter 7 Linear Programming Models: Graphical and Computer Methods. Discussion has been expanded on interpretation of computer output, the use of slack and surplus variables, and the presentation of binding constraints. The use of Solver in Excel 2010 is significantly changed from Excel 2007, and the use of the new Solver is clearly presented. Two new problems have been added, and others have been modified. Chapter 8 Linear Programming Modeling Applications with Computer Analysis. The production mix example was modified. To enhance the emphasis on model building, discussion of developing the model was expanded for many examples. One new QA in Action box and two new end-of-chapter problems were added. Chapter 9 Transportation and Assignment Models. Major changes were made in this chapter, as less emphasis was placed on the algorithmic approach to solving these problems. A network representation, as well as the linear programming model for each type of problem, were presented. The transshipment model is presented as an extension of the transportation problem. The basic transportation and assignment algorithms are included, but they are at the end of the chapter and may be omitted without loss of flow. Two QA in Action boxes, one Managing in the Real World situation, and 11 new end-of-chapter problems were added. Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming. More emphasis was placed on modeling and less emphasis was placed on manual solution methods. One new Managing in the Real World application, one new solved problem, and three new problems were added. Chapter 11 Network Models. Linear programming formulations for the max-flow and shortest route problems were added. The algorithms for solving these network problems were retained, but these can easily be omitted without loss of continuity. Six new end-of-chapter problems were added. Chapter 12 Project Management. Screen captures for the Excel QM software application were added. One new problem was added. Chapter 13 Waiting Lines and Queuing Models. The discussion of the Poisson and exponential distribution were moved to Chapter 2 with the other statistical background material used in the textbook. Two new QA in Action boxes and two new end-of-chapter problems were added. Chapter 14 Simulation Modeling. The use of Excel 2010 is the major change to this chapter. Chapter 15 Markov Analysis. One Managing in the Real World application was added. Chapter 16 Statistical Quality Control. One new QA in Action box was added. The chapter on the simplex algorithm was converted to a module that is now available on the Companion Website with the other modules. Instructors who choose to cover this can tell students to download the complete discussion.
ONLINE MODULES To streamline the book, seven topics are contained in modules available on the Companion Website for the book. 1. 2. 3. 4.
Analytic Hierarchy Process Dynamic Programming Decision Theory and the Normal Distribution Game Theory
5. Mathematical Tools: Matrices and Determinants 6. Calculus-Based Optimization 7. Linear Programming: The Simplex Method
SOFTWARE Excel 2010 Instructions and screen captures are provided for, using Excel 2010, throughout the book. Discussion of differences between Excel 2010 and Excel 2007 is provided where relevant. Instructions for activating the Solver and Analysis ToolPak add-ins for both Excel 2010 and Excel 2007 are provided in an appendix. The use of Excel is more prevalent in this edition of the book than in previous editions. Excel QM Using the Excel QM add-in that is available on the Companion Website makes the use of Excel even easier. Students with limited Excel experience can use this and learn from the formulas that are automatically provided by Excel QM. This is used in many of the chapters. POM-QM for Windows This software, developed by Professor Howard Weiss, is available to students at the Companion Website. This is very user friendly and has proven to be a very popular software tool for users of this textbook. Modules are available for every major problem type presented in the textbook.
COMPANION WEBSITE The Companion Website, located at www.pearsonhighered.com/render, contains a variety of materials to help students master the material in this course. These include: Modules There are seven modules containing additional material that the instructor may choose to include in the course. Students can download these from the Companion Website. Self-Study Quizzes Some multiple choice, true-false, fill-in-the-blank, and discussion questions are available for each chapter to help students test themselves over the material covered in that chapter. Files for Examples in Excel, Excel QM, and POM-QM for Windows Students can download the files that were used for examples throughout the book. This helps them become familiar with the software, and it helps them understand the input and formulas necessary for working the examples. Internet Homework Problems In addition to the end-of-chapter problems in the textbook, there are additional problems that instructors may assign. These are available for download at the Companion Website. Internet Case Studies Additional case studies are available for most chapters. POM-QM for Windows Developed by Howard Weiss, this very user-friendly software can be used to solve most of the homework problems in the text.
Excel QM This Excel add-in will automatically create worksheets for solving problems. This is very helpful for instructors who choose to use Excel in their classes but who may have students with limited Excel experience. Students can learn by examining the formulas that have been created, and by seeing the inputs that are automatically generated for using the Solver add-in for linear programming.
INSTRUCTOR RESOURCES 䊉
Instructor Resource Center: The Instructor Resource Center contains the electronic files for the test bank, PowerPoint slides, the Solutions Manual, and data files for both Excel and POM-QM for Windows for all relevant examples and end-of-chapter problems. (www.pearsonhighered.com/render).
Register, Redeem, Login: At www.pearsonhighered.com/irc, instructors can access a variety of print, media, and presentation resources that are available with this text in downloadable, digital format. For most texts, resources are also available for course management platforms such as Blackboard, WebCT, and Course Compass.
Need help? Our dedicated technical support team is ready to assist instructors with questions about the media supplements that accompany this text. Visit http://247.prenhall.com/ for answers to frequently asked questions and toll-free user support phone numbers. The supplements are available to adopting instructors. Detailed descriptions are provided on the Instructor Resource Center.
Instructor’s Solutions Manual The Instructor’s Solutions Manual, updated by the authors, is available to adopters in print form and as a download from the Instructor Resource Center. Solutions to all Internet Homework Problems and Internet Case Studies are also included in the manual. Test Item File The updated test item file is available to adopters as a downloaded from the Instructor Resource Center. TestGen The computerized TestGen package allows instructors to customize, save, and generate classroom tests. The test program permits instructors to edit, add, or delete questions from the test bank; edit existing graphics and create new graphics; analyze test results; and organize a database of test and student results. This software allows for extensive flexibility and ease of use. It provides many options for organizing and displaying tests, along with search and sort features. The software and the test banks can be downloaded at www.pearsonhighered.com/render.
ACKNOWLEDGMENTS We gratefully thank the users of previous editions and the reviewers who provided valuable suggestions and ideas for this edition. Your feedback is valuable in our efforts for continuous improvement. The continued success of Quantitative Analysis for Management is a direct result of instructor and student feedback, which is truly appreciated. The authors are indebted to many people who have made important contributions to this project. Special thanks go to Professors F. Bruce Simmons III, Khala Chand Seal, Victor E. Sower, Michael Ballot, Curtis P. McLaughlin, and Zbigniew H. Przanyski for their contributions to the excellent cases included in this edition. Special thanks also goes out to Trevor Hale for his extensive help with the Modeling in the Real World vignettes and the QA in Action applications, and for his serving as a sounding board for many of the ideas that resulted in significant improvements for this edition.
We thank Howard Weiss for providing Excel QM and POM-QM for Windows, two of the most outstanding packages in the field of quantitative methods. We would also like to thank the reviewers who have helped to make this one of the most widely used textbooks in the field of quantitative analysis: Stephen Achtenhagen, San Jose University M. Jill Austin, Middle Tennessee State University Raju Balakrishnan, Clemson University Hooshang Beheshti, Radford University Bruce K. Blaylock, Radford University Rodney L. Carlson, Tennessee Technological University Edward Chu, California State University, Dominguez Hills John Cozzolino, Pace University–Pleasantville Shad Dowlatshahi, University of Wisconsin, Platteville Ike Ehie, Southeast Missouri State University Sean Eom, Southeast Missouri State University Ephrem Eyob, Virginia State University Mira Ezvan, Lindenwood University Wade Ferguson, Western Kentucky University Robert Fiore, Springfield College Frank G. Forst, Loyola University of Chicago Ed Gillenwater, University of Mississippi Stephen H. Goodman, University of Central Florida Irwin Greenberg, George Mason University Trevor S. Hale, University of Houston–Downtown Nicholas G. Hall, Ohio State University Robert R. Hill, University of Houston–Clear Lake Gordon Jacox, Weber State University Bharat Jain, Towson State University Vassilios Karavas, University of Massachusetts–Amherst Darlene R. Lanier, Louisiana State University Kenneth D. Lawrence, New Jersey Institute of Technology Jooh Lee, Rowan College Richard D. Legault, University of Massachusetts–Dartmouth Douglas Lonnstrom, Siena College Daniel McNamara, University of St. Thomas Robert C. Meyers, University of Louisiana Peter Miller, University of Windsor Ralph Miller, California State Polytechnic University
Shahriar Mostashari, Campbell University David Murphy, Boston College Robert Myers, University of Louisville Barin Nag, Towson State University Nizam S. Najd, Oklahoma State University Harvey Nye, Central State University Alan D. Olinsky, Bryant College Savas Ozatalay, Widener University Young Park, California University of Pennsylvania Cy Peebles, Eastern Kentucky University Yusheng Peng, Brooklyn College Dane K. Peterson, Southwest Missouri State University Sanjeev Phukan, Bemidji State University Ranga Ramasesh, Texas Christian University William Rife, West Virginia University Bonnie Robeson, Johns Hopkins University Grover Rodich, Portland State University L. Wayne Shell, Nicholls State University Richard Slovacek, North Central College John Swearingen, Bryant College F. S. Tanaka, Slippery Rock State University Jack Taylor, Portland State University Madeline Thimmes, Utah State University M. Keith Thomas, Olivet College Andrew Tiger, Southeastern Oklahoma State University Chris Vertullo, Marist College James Vigen, California State University, Bakersfield William Webster, The University of Texas at San Antonio Larry Weinstein, Eastern Kentucky University Fred E. Williams, University of Michigan-Flint Mela Wyeth, Charleston Southern University
We are very grateful to all the people at Prentice Hall who worked so hard to make this book a success. These include Chuck Synovec, our editor; Judy Leale, senior managing editor; Mary Kate Murray, project manager; and Jason Calcano, editorial assistant. We are also grateful to Jen Carley, our project manager at PreMediaGlobal Book Services. We are very appreciative of the work of Annie Puciloski in error checking the textbook and Solutions Manual. Thank you all! Barry Render [email protected] Ralph Stair Michael Hanna 281-283-3201 (phone) 281-226-7304 (fax) [email protected]
Introduction to Quantitative Analysis
LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. Describe the quantitative analysis approach. 2. Understand the application of quantitative analysis in a real situation. 3. Describe the use of modeling in quantitative analysis.
4. Use computers and spreadsheet models to perform quantitative analysis. 5. Discuss possible problems in using quantitative analysis. 6. Perform a break-even analysis.
CHAPTER OUTLINE 1.1 1.2 1.3
Introduction What Is Quantitative Analysis? The Quantitative Analysis Approach
How to Develop a Quantitative Analysis Model
The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach
Possible Problems in the Quantitative Analysis Approach Implementation—Not Just the Final Step
Summary • Glossary • Key Equations • Self-Test • Discussion Questions and Problems • Case Study: Food and Beverages at Southwestern University Football Games • Bibliography
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
Introduction People have been using mathematical tools to help solve problems for thousands of years; however, the formal study and application of quantitative techniques to practical decision making is largely a product of the twentieth century. The techniques we study in this book have been applied successfully to an increasingly wide variety of complex problems in business, government, health care, education, and many other areas. Many such successful uses are discussed throughout this book. It isn’t enough, though, just to know the mathematics of how a particular quantitative technique works; you must also be familiar with the limitations, assumptions, and specific applicability of the technique. The successful use of quantitative techniques usually results in a solution that is timely, accurate, flexible, economical, reliable, and easy to understand and use. In this and other chapters, there are QA (Quantitative Analysis) in Action boxes that provide success stories on the applications of management science. They show how organizations have used quantitative techniques to make better decisions, operate more efficiently, and generate more profits. Taco Bell has reported saving over $150 million with better forecasting of demand and better scheduling of employees. NBC television increased advertising revenue by over $200 million between 1996 and 2000 by using a model to help develop sales plans for advertisers. Continental Airlines saves over $40 million per year by using mathematical models to quickly recover from disruptions caused by weather delays and other factors. These are but a few of the many companies discussed in QA in Action boxes throughout this book. To see other examples of how companies use quantitative analysis or operations research methods to operate better and more efficiently, go to the website www.scienceofbetter.org. The success stories presented there are categorized by industry, functional area, and benefit. These success stories illustrate how operations research is truly the “science of better.”
What Is Quantitative Analysis?
Quantitative analysis uses a scientific approach to decision making.
Both qualitative and quantitative factors must be considered.
Quantitative analysis is the scientific approach to managerial decision making. Whim, emotions, and guesswork are not part of the quantitative analysis approach. The approach starts with data. Like raw material for a factory, these data are manipulated or processed into information that is valuable to people making decisions. This processing and manipulating of raw data into meaningful information is the heart of quantitative analysis. Computers have been instrumental in the increasing use of quantitative analysis. In solving a problem, managers must consider both qualitative and quantitative factors. For example, we might consider several different investment alternatives, including certificates of deposit at a bank, investments in the stock market, and an investment in real estate. We can use quantitative analysis to determine how much our investment will be worth in the future when deposited at a bank at a given interest rate for a certain number of years. Quantitative analysis can also be used in computing financial ratios from the balance sheets for several companies whose stock we are considering. Some real estate companies have developed computer programs that use quantitative analysis to analyze cash flows and rates of return for investment property. In addition to quantitative analysis, qualitative factors should also be considered. The weather, state and federal legislation, new technological breakthroughs, the outcome of an election, and so on may all be factors that are difficult to quantify. Because of the importance of qualitative factors, the role of quantitative analysis in the decision-making process can vary. When there is a lack of qualitative factors and when the problem, model, and input data remain the same, the results of quantitative analysis can automate the decision-making process. For example, some companies use quantitative inventory models to determine automatically when to order additional new materials. In most cases, however, quantitative analysis will be an aid to the decision-making process. The results of quantitative analysis will be combined with other (qualitative) information in making decisions.
The Origin of Quantitative Analysis
uantitative analysis has been in existence since the beginning of recorded history, but it was Frederick W. Taylor who in the early 1900s pioneered the principles of the scientific approach to management. During World War II, many new scientific and quantitative techniques were developed to assist the military. These new developments were so successful that after World War II many companies started using similar techniques in managerial decision making and planning. Today, many organizations employ a staff
THE QUANTITATIVE ANALYSIS APPROACH
of operations research or management science personnel or consultants to apply the principles of scientific management to problems and opportunities. In this book, we use the terms management science, operations research, and quantitative analysis interchangeably. The origin of many of the techniques discussed in this book can be traced to individuals and organizations that have applied the principles of scientific management first developed by Taylor; they are discussed in History boxes scattered throughout the book.
The Quantitative Analysis Approach
Defining the problem can be the most important step. Concentrate on only a few problems.
FIGURE 1.1 The Quantitative Analysis Approach Defining the Problem
Developing a Model
Acquiring Input Data
Developing a Solution
Testing the Solution
Analyzing the Results
Implementing the Results
The types of models include physical, scale, schematic, and mathematical models.
The quantitative analysis approach consists of defining a problem, developing a model, acquiring input data, developing a solution, testing the solution, analyzing the results, and implementing the results (see Figure 1.1). One step does not have to be finished completely before the next is started; in most cases one or more of these steps will be modified to some extent before the final results are implemented. This would cause all of the subsequent steps to be changed. In some cases, testing the solution might reveal that the model or the input data are not correct. This would mean that all steps that follow defining the problem would need to be modified.
Defining the Problem The first step in the quantitative approach is to develop a clear, concise statement of the problem. This statement will give direction and meaning to the following steps. In many cases, defining the problem is the most important and the most difficult step. It is essential to go beyond the symptoms of the problem and identify the true causes. One problem may be related to other problems; solving one problem without regard to other related problems can make the entire situation worse. Thus, it is important to analyze how the solution to one problem affects other problems or the situation in general. It is likely that an organization will have several problems. However, a quantitative analysis group usually cannot deal with all of an organization’s problems at one time. Thus, it is usually necessary to concentrate on only a few problems. For most companies, this means selecting those problems whose solutions will result in the greatest increase in profits or reduction in costs to the company. The importance of selecting the right problems to solve cannot be overemphasized. Experience has shown that bad problem definition is a major reason for failure of management science or operations research groups to serve their organizations well. When the problem is difficult to quantify, it may be necessary to develop specific, measurable objectives. A problem might be inadequate health care delivery in a hospital. The objectives might be to increase the number of beds, reduce the average number of days a patient spends in the hospital, increase the physician-to-patient ratio, and so on. When objectives are used, however, the real problem should be kept in mind. It is important to avoid obtaining specific and measurable objectives that may not solve the real problem.
Developing a Model Once we select the problem to be analyzed, the next step is to develop a model. Simply stated, a model is a representation (usually mathematical) of a situation. Even though you might not have been aware of it, you have been using models most of your life. You may have developed models about people’s behavior. Your model might be that friendship is based on reciprocity, an exchange of favors. If you need a favor such as a small loan, your model would suggest that you ask a good friend. Of course, there are many other types of models. Architects sometimes make a physical model of a building that they will construct. Engineers develop scale models of chemical plants,
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
Operations Research and Oil Spills
perations researchers and decision scientists have been investigating oil spill response and alleviation strategies since long before the BP oil spill disaster of 2010 in the Gulf of Mexico. A four-phase classification system has emerged for disaster response research: mitigation, preparedness, response, and recovery. Mitigation means reducing the probability that a disaster will occur and implementing robust, forward-thinking strategies to reduce the effects of a disaster that does occur. Preparedness is any and all organization efforts that happen a priori to a disaster. Response is the location, allocation, and overall coordination of resources and procedures during the disaster that are aimed at preserving life and property. Recovery is the set of actions taken to minimize the long-term impacts of a particular disaster after the immediate situation has stabilized.
Many quantitative tools have helped in areas of risk analysis, insurance, logistical preparation and supply management, evacuation planning, and development of communication systems. Recent research has shown that while many strides and discoveries have been made, much research is still needed. Certainly each of the four disaster response areas could benefit from additional research, but recovery seems to be of particular concern and perhaps the most promising for future research. Source: Based on N. Altay and W. Green. “OR/MS Research in Disaster Operations Management,” European Journal of Operational Research 175, 1 (2006): 475–493.
called pilot plants. A schematic model is a picture, drawing, or chart of reality. Automobiles, lawn mowers, gears, fans, typewriters, and numerous other devices have schematic models (drawings and pictures) that reveal how these devices work. What sets quantitative analysis apart from other techniques is that the models that are used are mathematical. A mathematical model is a set of mathematical relationships. In most cases, these relationships are expressed in equations and inequalities, as they are in a spreadsheet model that computes sums, averages, or standard deviations. Although there is considerable flexibility in the development of models, most of the models presented in this book contain one or more variables and parameters. A variable, as the name implies, is a measurable quantity that may vary or is subject to change. Variables can be controllable or uncontrollable. A controllable variable is also called a decision variable. An example would be how many inventory items to order. A parameter is a measurable quantity that is inherent in the problem. The cost of placing an order for more inventory items is an example of a parameter. In most cases, variables are unknown quantities, while parameters are known quantities. All models should be developed carefully. They should be solvable, realistic, and easy to understand and modify, and the required input data should be obtainable. The model developer has to be careful to include the appropriate amount of detail to be solvable yet realistic.
Acquiring Input Data
Garbage in, garbage out means that improper data will result in misleading results.
Once we have developed a model, we must obtain the data that are used in the model (input data). Obtaining accurate data for the model is essential; even if the model is a perfect representation of reality, improper data will result in misleading results. This situation is called garbage in, garbage out. For a larger problem, collecting accurate data can be one of the most difficult steps in performing quantitative analysis. There are a number of sources that can be used in collecting data. In some cases, company reports and documents can be used to obtain the necessary data. Another source is interviews with employees or other persons related to the firm. These individuals can sometimes provide excellent information, and their experience and judgment can be invaluable. A production supervisor, for example, might be able to tell you with a great degree of accuracy the amount of time it takes to produce a particular product. Sampling and direct measurement provide other sources of data for the model. You may need to know how many pounds of raw material are used in producing a new photochemical product. This information can be obtained by going to the plant and actually measuring with scales the amount of raw material that is being used. In other cases, statistical sampling procedures can be used to obtain data.
THE QUANTITATIVE ANALYSIS APPROACH
Developing a Solution
The input data and model determine the accuracy of the solution.
Developing a solution involves manipulating the model to arrive at the best (optimal) solution to the problem. In some cases, this requires that an equation be solved for the best decision. In other cases, you can use a trial and error method, trying various approaches and picking the one that results in the best decision. For some problems, you may wish to try all possible values for the variables in the model to arrive at the best decision. This is called complete enumeration. This book also shows you how to solve very difficult and complex problems by repeating a few simple steps until you find the best solution. A series of steps or procedures that are repeated is called an algorithm, named after Algorismus, an Arabic mathematician of the ninth century. The accuracy of a solution depends on the accuracy of the input data and the model. If the input data are accurate to only two significant digits, then the results can be accurate to only two significant digits. For example, the results of dividing 2.6 by 1.4 should be 1.9, not 1.857142857.
Testing the Solution
Testing the data and model is done before the results are analyzed.
Before a solution can be analyzed and implemented, it needs to be tested completely. Because the solution depends on the input data and the model, both require testing. Testing the input data and the model includes determining the accuracy and completeness of the data used by the model. Inaccurate data will lead to an inaccurate solution. There are several ways to test input data. One method of testing the data is to collect additional data from a different source. If the original data were collected using interviews, perhaps some additional data can be collected by direct measurement or sampling. These additional data can then be compared with the original data, and statistical tests can be employed to determine whether there are differences between the original data and the additional data. If there are significant differences, more effort is required to obtain accurate input data. If the data are accurate but the results are inconsistent with the problem, the model may not be appropriate. The model can be checked to make sure that it is logical and represents the real situation. Although most of the quantitative techniques discussed in this book have been computerized, you will probably be required to solve a number of problems by hand. To help detect both logical and computational mistakes, you should check the results to make sure that they are consistent with the structure of the problem. For example, (1.96)(301.7) is close to (2)(300), which is equal to 600. If your computations are significantly different from 600, you know you have made a mistake.
Analyzing the Results and Sensitivity Analysis
Sensitivity analysis determines how the solutions will change with a different model or input data.
Analyzing the results starts with determining the implications of the solution. In most cases, a solution to a problem will result in some kind of action or change in the way an organization is operating. The implications of these actions or changes must be determined and analyzed before the results are implemented. Because a model is only an approximation of reality, the sensitivity of the solution to changes in the model and input data is a very important part of analyzing the results. This type of analysis is called sensitivity analysis or postoptimality analysis. It determines how much the solution will change if there were changes in the model or the input data. When the solution is sensitive to changes in the input data and the model specification, additional testing should be performed to make sure that the model and input data are accurate and valid. If the model or data are wrong, the solution could be wrong, resulting in financial losses or reduced profits. The importance of sensitivity analysis cannot be overemphasized. Because input data may not always be accurate or model assumptions may not be completely appropriate, sensitivity analysis can become an important part of the quantitative analysis approach. Most of the chapters in the book cover the use of sensitivity analysis as part of the decision-making and problemsolving process.
Implementing the Results The final step is to implement the results. This is the process of incorporating the solution into the company. This can be much more difficult than you would imagine. Even if the solution is optimal and will result in millions of dollars in additional profits, if managers resist the new solution, all of the efforts of the analysis are of no value. Experience has shown that a large
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
MODELING IN THE REAL WORLD Defining the Problem
Developing a Model
Acquiring Input Data
Developing a Solution
Testing the Solution
Analyzing the Results
Implementing the Results
Railroad Uses Optimization Models to Save Millions
Defining the Problem CSX Transportation, Inc., has 35,000 employees and annual revenue of $11 billion. It provides rail freight services to 23 states east of the Mississippi River, as well as parts of Canada. CSX receives orders for rail delivery service and must send empty railcars to customer locations. Moving these empty railcars results in hundreds of thousands of empty-car miles every day. If allocations of railcars to customers is not done properly, problems arise from excess costs, wear and tear on the system, and congestion on the tracks and at rail yards.
Developing a Model In order to provide a more efficient scheduling system, CSX spent 2 years and $5 million developing its Dynamic Car-Planning (DCP) system. This model will minimize costs, including car travel distance, car handling costs at the rail yards, car travel time, and costs for being early or late. It does this while at the same time filling all orders, making sure the right type of car is assigned to the job, and getting the car to the destination in the allowable time.
Acquiring Input Data In developing the model, the company used historical data for testing. In running the model, the DCP uses three external sources to obtain information on the customer car orders, the available cars of the type needed, and the transit-time standards. In addition to these, two internal input sources provide information on customer priorities and preferences and on cost parameters.
Developing a Solution This model takes about 1 minute to load but only 10 seconds to solve. Because supply and demand are constantly changing, the model is run about every 15 minutes. This allows final decisions to be delayed until absolutely necessary.
Testing the Solution The model was validated and verified using existing data. The solutions found using the DCP were found to be very good compared to assignments made without DCP.
Analyzing the Results Since the implementation of DCP in 1997, more than $51 million has been saved annually. Due to the improved efficiency, it is estimated that CSX avoided spending another $1.4 billion to purchase an additional 18,000 railcars that would have been needed without DCP. Other benefits include reduced congestion in the rail yards and reduced congestion on the tracks, which are major concerns. This greater efficiency means that more freight can ship by rail rather than by truck, resulting in significant public benefits. These benefits include reduced pollution and greenhouse gases, improved highway safety, and reduced road maintenance costs.
Implementing the Results Both senior-level management who championed DCP as well as key car-distribution experts who supported the new approach were instrumental in gaining acceptance of the new system and overcoming problems during the implementation. The job description of the car distributors was changed from car allocators to cost technicians. They are responsible for seeing that accurate cost information is entered into DCP, and they also manage any exceptions that must be made. They were given extensive training on how DCP works so they could understand and better accept the new system. Due to the success of DCP, other railroads have implemented similar systems and achieved similar benefits. CSX continues to enhance DCP to make DCP even more customer friendly and to improve car-order forecasts. Source: Based on M. F. Gorman, et al. “CSX Railway Uses OR to Cash in on Optimized Equipment Distribution,” Interfaces 40, 1 (January–February 2010): 5–16.
number of quantitative analysis teams have failed in their efforts because they have failed to implement a good, workable solution properly. After the solution has been implemented, it should be closely monitored. Over time, there may be numerous changes that call for modifications of the original solution. A changing economy, fluctuating demand, and model enhancements requested by managers and decision makers are only a few examples of changes that might require the analysis to be modified.
HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL
The Quantitative Analysis Approach and Modeling in the Real World The quantitative analysis approach is used extensively in the real world. These steps, first seen in Figure 1.1 and described in this section, are the building blocks of any successful use of quantitative analysis. As seen in our first Modeling in the Real World box, the steps of the quantitative analysis approach can be used to help a large company such as CSX plan for critical scheduling needs now and for decades into the future. Throughout this book, you will see how the steps of the quantitative analysis approach are used to help countries and companies of all sizes save millions of dollars, plan for the future, increase revenues, and provide higher-quality products and services. The Modeling in the Real World boxes in every chapter will demonstrate to you the power and importance of quantitative analysis in solving real problems for real organizations. Using the steps of quantitative analysis, however, does not guarantee success. These steps must be applied carefully.
How to Develop a Quantitative Analysis Model Developing a model is an important part of the quantitative analysis approach. Let’s see how we can use the following mathematical model, which represents profit: Profit = Revenue - Expenses
Expenses include fixed and variable costs.
In many cases, we can express revenues as price per unit multiplied times the number of units sold. Expenses can often be determined by summing fixed costs and variable cost. Variable cost is often expressed as variable cost per unit multiplied times the number of units. Thus, we can also express profit in the following mathematical model: Profit = Revenue - (Fixed cost + Variable cost) Profit = (Selling price per unit)(Number of units sold) - 3Fixed cost + (Variable cost per unit)(Number of units sold)4 Profit = sX - 3f + nX4 (1-1) Profit = sX - f - nX where s f n X
= = = =
selling price per unit fixed cost variable cost per unit number of units sold
The parameters in this model are f, n, and s, as these are inputs that are inherent in the model. The number of units sold (X) is the decision variable of interest. EXAMPLE: PRITCHETT’S PRECIOUS TIME PIECES We will use the Bill Pritchett clock repair shop
example to demonstrate the use of mathematical models. Bill’s company, Pritchett’s Precious Time Pieces, buys, sells, and repairs old clocks and clock parts. Bill sells rebuilt springs for a price per unit of $10. The fixed cost of the equipment to build the springs is $1,000. The variable cost per unit is $5 for spring material. In this example, s = 10 f = 1,000 n = 5 The number of springs sold is X, and our profit model becomes Profit = $10X - $1,000 - $5X If sales are 0, Bill will realize a $1,000 loss. If sales are 1,000 units, he will realize a profit of $4,000 ($4,000 = ($10)(1,000) - $1,000 - ($5)(1,000)). See if you can determine the profit for other values of units sold.
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
The BEP results in $0 profits.
In addition to the profit models shown here, decision makers are often interested in the break-even point (BEP). The BEP is the number of units sold that will result in $0 profits. We set profits equal to $0 and solve for X, the number of units at the break-even point: 0 = sX - f - nX This can be written as 0 = (s - n)X - f Solving for X, we have f = (s - n)X f X = s - n This quantity (X) that results in a profit of zero is the BEP, and we now have this model for the BEP: Fixed cost (Selling price per unit) - (Variable cost per unit) f BEP = s - n
For the Pritchett’s Precious Time Pieces example, the BEP can be computed as follows: BEP = $1,000>($10 - $5) = 200 units, or springs, at the break-even point
The Advantages of Mathematical Modeling There are a number of advantages of using mathematical models: 1. Models can accurately represent reality. If properly formulated, a model can be extremely accurate. A valid model is one that is accurate and correctly represents the problem or system under investigation. The profit model in the example is accurate and valid for many business problems. 2. Models can help a decision maker formulate problems. In the profit model, for example, a decision maker can determine the important factors or contributors to revenues and expenses, such as sales, returns, selling expenses, production costs, transportation costs, and so on. 3. Models can give us insight and information. For example, using the profit model from the preceding section, we can see what impact changes in revenues and expenses will have on profits. As discussed in the previous section, studying the impact of changes in a model, such as a profit model, is called sensitivity analysis. 4. Models can save time and money in decision making and problem solving. It usually takes less time, effort, and expense to analyze a model. We can use a profit model to analyze the impact of a new marketing campaign on profits, revenues, and expenses. In most cases, using models is faster and less expensive than actually trying a new marketing campaign in a real business setting and observing the results. 5. A model may be the only way to solve some large or complex problems in a timely fashion. A large company, for example, may produce literally thousands of sizes of nuts, bolts, and fasteners. The company may want to make the highest profits possible given its manufacturing constraints. A mathematical model may be the only way to determine the highest profits the company can achieve under these circumstances. 6. A model can be used to communicate problems and solutions to others. A decision analyst can share his or her work with other decision analysts. Solutions to a mathematical model can be given to managers and executives to help them make final decisions.
Mathematical Models Categorized by Risk Deterministic means with complete certainty.
Some mathematical models, like the profit and break-even models previously discussed, do not involve risk or chance. We assume that we know all values used in the model with complete certainty. These are called deterministic models. A company, for example, might want to
THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS APPROACH
minimize manufacturing costs while maintaining a certain quality level. If we know all these values with certainty, the model is deterministic. Other models involve risk or chance. For example, the market for a new product might be “good” with a chance of 60% (a probability of 0.6) or “not good” with a chance of 40% (a probability of 0.4). Models that involve chance or risk, often measured as a probability value, are called probabilistic models. In this book, we will investigate both deterministic and probabilistic models.
The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach Developing a solution, testing the solution, and analyzing the results are important steps in the quantitative analysis approach. Because we will be using mathematical models, these steps require mathematical calculations. Fortunately, we can use the computer to make these steps easier. Two programs that allow you to solve many of the problems found in this book are provided at the Companion Website for this book: 1. POM-QM for Windows is an easy-to-use decision support system that was developed for use with production/operations management (POM) and quantitative methods or quantitative management (QM) courses. POM for Windows and QM for Windows were originally separate software packages for each type of course. These are now combined into one program called POM-QM for Windows. As seen in Program 1.1, it is possible to display all the modules, only the POM modules, or only the QM modules. The images shown in this textbook will typically display only the QM modules. Hence, in this book, reference will usually be made to QM for Windows. Appendix E at the end of the book and many of the end-of-chapter appendices provide more information about QM for Windows. 2. Excel QM, which can also be used to solve many of the problems discussed in this book, works automatically within Excel spreadsheets. Excel QM makes using a spreadsheet even easier by providing custom menus and solution procedures that guide you through every step. In Excel 2007, the main menu is found in the Add-Ins tab, as shown in Program 1.2. Appendix F provides further details of how to install this add-in program to Excel 2010 and Excel 2007. To solve the break-even problem discussed in Section 1.4, we illustrate Excel QM features in Programs 1.3A and 1.3B.
PROGRAM 1.1 The QM for Windows Main Menu of Quantitative Models
Main menu Toolbar Instruction
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
PROGRAM 1.2 Excel QM Main Menu of Quantitative Models in Excel 2010
Select the Add-Ins tab. Click ClickExcel ExcelQM, QM and the drop-down menu menuopens openswith withthe thelist listof ofmodels models available availableininExcel ExcelQM. QM.
PROGRAM 1.3A Selecting Breakeven Analysis in Excel QM Select the Add-Ins tab.
Select Excel QM. Select Breakeven Analysis and then select Breakeven (Cost vs Revenue).
Add-in programs make Excel, which is already a wonderful tool for modeling, even more powerful in solving quantitative analysis problems. Excel QM and the Excel files used in the examples throughout this text are also included on the Companion Website for this text. There are two other powerful Excel built-in features that make solving quantitative analysis problems easier: 1. Solver. Solver is an optimization technique that can maximize or minimize a quantity given a set of limitations or constraints. We will be using Solver throughout the text to
PROGRAM 1.3B Breakeven Analysis in Excel QM
THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS APPROACH
To see the formula used for the calculations, hold down the Ctrl key and press the ` (grave accent) key. Doing this a second time returns to the display of the results.
Put any value in B13, and Excel will compute the profit in B23.
The break-even point is given in units and also in dollars.
solve optimization problems. It is described in detail in Chapter 7 and used in Chapters 7–12. 2. Goal Seek. This feature of Excel allows you to specify a goal or target (Set Cell) and what variable (Changing Cell) that you want Excel to change in order to achieve a desired goal. Bill Pritchett, for example, would like to determine how many springs must be sold to make a profit of $175. Program 1.4 shows how Goal Seek can be used to make the necessary calculations. PROGRAM 1.4 Using Goal Seek in the Break-Even Problem to Achieve a Specified Profit
Select the Data tab and then select What-If Analysis. Then select Goal Seek. Put the cell that has the profit (B23) into the Set Cell window.
Put in the desired profit and specify the location for the volume cell (B13). Click OK, and Excel will change the value in cell B13. Other cells are changed according to the formulas in those cells.
CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS
Major League Operations Research at the Department of Agriculture
n 1997, the Pittsburgh Pirates signed Ross Ohlendorf because of his 95-mph sinking fastball. Little did they know that Ross possessed operations research skills also worthy of national merit. Ross Ohlendorf had graduated from Princeton University with a 3.8 GPA in operations research and financial engineering. Indeed, after the 2009 baseball season, when Ross applied for an 8-week unpaid internship with the U.S. Department of Agriculture, he didn’t need to mention his full-time employer because the
Secretary of the Department of Agriculture at the time, Tom Vilsack, was born and raised in Pittsburgh and was an avid Pittsburgh Pirates fan. Ross spent 2 months of the ensuing off-season utilizing his educational background in operations research, helping the Department of Agriculture track disease migration in livestock, a subject Ross has a vested interest in as his family runs a cattle ranch in Texas. Moreover, when ABC News asked Ross about his off-season unpaid internship experience, he replied, “This one’s been, I’d say, the most exciting off-season I’ve had.”
Possible Problems in the Quantitative Analysis Approach We have presented the quantitative analysis approach as a logical, systematic means of tackling decision-making problems. Even when these steps are followed carefully, there are many difficulties that can hurt the chances of implementing solutions to real-world problems. We now take a look at what can happen during each of the steps.
Defining the Problem One view of decision makers is that they sit at a desk all day long, waiting until a problem arises, and then stand up and attack the problem until it is solved. Once it is solved, they sit down, relax, and wait for the next big problem. In the worlds of business, government, and education, problems are, unfortunately, not easily identified. There are four potential roadblocks that quantitative analysts face in defining a problem. We use an application, inventory analysis, throughout this section as an example. All viewpoints should be considered before formally defining the problem.
CONFLICTING VIEWPOINTS The first difficulty is that quantitative analysts must often consider
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ VOLUME 04 MARCH 1985 NUMBER 01 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Editor's Notes ..................................... Page 01 Jasper Terry of Montgomery Co. Virginia ............ Page 04 Covering the Terry-Tory ............................ Page 05 Byrd Terry Family .................................. Page 07 James Terrys of Virginia ........................... Page 08 Obituary of Carl Beach Terry ....................... Page 08 Eliphalet Terry .................................... Page 09 Terry Quips ........................................ Page 10 Scouts Give Cemetery Facelift ...................... Page 10 John Terry of Norwich, England 1563 ................ Page 11 Notes on a Terry Family of Michigan ................ Page 12 Terry's of Virginia Past and Present ............... Page 12 Washington Co. Arkansas Terrys ..................... Page 13 Some South Carolina Terry Marriages ................ Page 13 Troubles of a Baptist Minister - 1776 .............. Page 14 Missing Terry ...................................... Page 17 Obituary of William Martin Terry ................... Page 17 Notes on Descendants of Curtis Terry ............... Page 18 Pension Application of James B. Terry .............. Page 19 Terry Line of Joan Crawford ........................ Page 20 Parshall Terry: Father and Son ..................... Page 21 Queries ............................................ Page 22 Terry Line of Mrs. Fay Ray McMurray ........... Page 23 Terry Line of Susan T. Blevins ................ Page 25 Terry Line of Joanna Baker .................... Page 25 Terry Line of Ann (Gibson) Moore .............. Page 26 Terry Line of Sheila (Terry) Spiess ........... Page 29 Terry Line of Virginia (McDaniel) Weede ....... Page 31 Terry Line of Jeff L. Carr .................... Page 33 Terry Line of Lelia (Terry) Morrow ............ Page 34 Terry Line of Rhoena Frances (Brown) Landers .. Page 37 Terry Line of Jack R. Terry ................... Page 39 Terry Line of Mary Sue Inman .................. Page 40Single Copy Price - $4.00; by subscription - $16.00 per year. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Queries are free to Members, otherwise, queries are $1.00 (up to fifty words per issue) for NON-MEMBERS. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Future deadlines for publication will be as follows: 1/15 for March, 4/15 for June, 7/15 for September and 10/15 for December. It is hoped that the publication will be mailed by the 15th of the month. IF YOU DO NOT GET YOUR COPY BY THE LAST DAY OF THE MONTH DUE, DROP ME A CARD.--EDITOR. * * * * EDITOR'S NOTESThe Beginning The TFH was a big idea with a small beginning as I noted in the first few issues. It began as a chain letter which circulated between eight present TFH members who were researching Major Stephen Terry of Atlanta. I became frustrated at the length of time it took the letter to get back and also because it took so long for my queries to come out in the `Roots Cellar' of the Genealogical Helper. [I still take the GH as it is a necessity if you are serious about publishing or researching.] We are beginning the fourth year of the Terry Family Historian and I think we have made some progress. I say we, because I certainly could not have begun to do all of this TERRY research single-handed. I believe we could safely say we have the largest concentration of Terry data in the U.S. I wore out one typewriter and outgrew the computer that I had in the third year and just purchased one with more memory to handle the data I have been receiving. I still have four file drawers full of bits and scraps of paper and a growing inventory of TERRY publications. Some time ago I read a pamphlet by a genealogist who discouraged the use of computers because 'nobody wanted to sit around the Christmas tree with the family and look at computer print outs'. We do have some listings such as these and they do have their place in our research efforts; however, I also love to read those humorous stories like Bob Terry's continuing article "Covering the Terry-Tory". I always know it is forthcoming and can't wait to see the next one. [If I only had his gift for writing.] (1)The Goals The goals I set originally were to be entertaining and also to provide documentation for what was printed. I have always been in awe of Mrs. Bushnell's scholarly style and was influenced greatly by her Terry Records of Virginia. I also am not ashamed to say I modeled the TFH after the Arkansas Family Historian which is an old genealogical publication and I always found it quite entertaining. [Genealogical Publications come and go rather frequently.] In later years I have tried to appeal to those Terry researchers outside of the South to share their research with us but have not been as successful as I would like. [I have not given up!] There is a small core of members who actually do the library and courthouse research required. Others, not unlike my own parents, are more passively interested and are enjoy reading the history of the different Terry Clans. We need both kinds of subscribers to make the publication successful, but the editor would like to see an increase in the "hard core" researchers. I also wanted the TFH to be a place where Terry researchers could meet, in a fashion, and discuss what they have done and ask questions of others. I am so glad I asked questions of the senior members of the family, because some of them are no longer with us.--That information would have been lost. Even though I have increased the original price to cover costs, I think you can agree that the TFH is the best buy for the bucks. [You have a money back guarantee; and if not satisfied I will return your money plus postage for the return of the article in question.] I have been less than pleased with research paid for and done by other researchers on several occasions myself and vowed to give the members a publication they could relate to and feel that it was worthwhile. [I have had one subscription returned in three years so I guess the record speaks for itself.]Problems & Advice At the present time, we have about 200 members. I should note that I do the researching, ordering, typing, advertising and mailing chores myself. And this is just my "part time" duties. I also have family duties and a "full time job." [I should note that Emma helped me lick stamps on the recent postcard mail-outs--she's 4 going on 5. This explains why some of the stamps were upside down and folded over the back of the card. Good help is hard to find!] While I have the paid membership, I also have questions from others about their research problems and am now getting (2)questions about computers and genealogy as well. My time is getting to be very limited and I cannot begin to answer the mail in a timely fashion. I am trying to develop a system that will at least print out names and addresses of those who have made inquiries about your particular Terry Clan. The bottom line is--I will try and get your questions in the TFH Query section and will try and answer eventually. When I get enough information to make an article that might help several people, I usually make a short out of it. If I am short on articles, I print what I have about my own family and this explains some of the South Carolina TERRY information. However, I do not want to give the impression that our publication is only for Southerners. My personal interest lies there as well as a majority of the members it seems. My advice is to do your homework first. Get the census information, talk to senior Terry's relatives, go to the court house or library and copy what there is on TERRY's. Then share it with the membership in the TFH. The Ahnentafel charts in the Query section which are preceded by "Terry Line of ...." will get you more responses I can assure you. But you need dates and places, and par- ticularly counties.Future plans & Possible Solutions If you would like to be a corresponding secretary for one of the Terry Clans please let me know. I would like to farm out some of the correspondence. Should you want to write a regular feature on your particular family, please call or write. If you don't like writing please line up one of the senior members of family and do a tape recording and send that. If you still use a pen and pencil I will accept this as well. If you have a computer, I notice your mailing labels and letters with the little dots, send a disk with your informa- tion and I'll return it. I have access to a machine to read most CPM formats and I work at a Computer store and have access to Big Blue formats and Fruit type computers. If you have a telephone modem hooked to your computer I plan to put all of the Terry data on line for TFH members. The program should be able to run unattended when I get all of the equipment.--Another wonder of the Computer Age. I will have to continue charging for paper copies and will gladly continue to provide what I have. However, I should note I am in the process of changing my text files to another disk format. (3) I'm now getting off of my soapbox and returning to the typing mode and the TFH for March 1985. Mike Terry, Editor N' Chief * * * * * I was notified prior to the December 1984 issue that Mrs. William Still Morris had lost her husband February 18, of last year . The editor has for several years been exchanging Morris-Terry information with Bill and Corrie re: Stephen Terry d. 1769 and his daughter Sarah Terry who m. William Morris of Turkey Creek SC. Most recently, I received a note from Corrie and she indicated she is working on the Morris-Terry genealogy again and may have some leads on the Thomas Morris family. Mrs. William Still Morris, 2580 Utah St., Napa CA 94558. * * * * * JASPER TERRY OF MONTGOMERY CO. VIRGINIA Notes submitted by Mrs. Valerie Whitlow Terry Rt. 3, Box 154, Princeton WV 24740 I was quite pleased to see my Terry lineage published in the December 1984 issue of the Terry Family Historian. Thanks also for your editor's note. However, I was aware of the Jasper Terry will in Montgomery County, Virginia. The problem there is that the wife mentioned is not the mother of the children;, but a widow Jasper married sometime after their births. Jasper was married three or possibly four times and it hasn't been proven which wife or wives were the mothers to the children. Maybe someone else has some information that will bear on this, but so far everyone I have contacted seems to be unsure. I am enclosing a copy of the Jasper Terry will, transcribed to the best of my ability from my copy. You will notice that the third daughter mentioned is not Karen Happuck, but Karon Happuck Rose. She was married to Joseph Rose 21 Dec 1813 in Montgomery County, VA. The unusual first name, Karonhappuch, is probably what caused the confusion. Jasper named his three daughters after Job's three daughters in the Bible (see Job 42:14). I obtained much of this information from Mrs. Jean Deweese Cordts, so I'm not sure exactly how the mix-up came about on the name of Karonhappuch Rose. This may or may not be of help, but I thought you'd want to keep your records straight. (4) JASPER TERRY WILL -- MONTGOMERY COUNTY, VIRGINIA PROBATED JULY 6, 1819 WILL BOOK 3, PAGE 121 In the name of God Amen; I Jasper Terry of Montgomery County and State of Virginia being low in health, and of perfect mind do make this my last will and Testament. That is, I resign my soul to God that gave it and first of all I give to my loving wife Margaret Terry the plantation I now live on during her life to enjoy it peaceably and freely and one cow and one two year heifer, one serviceable horse the price not to exceed sixty dollars, twenty dollars in bank notes and eight dollars in specie, one barrow, one sow and two shoats, one kettle, one pot, one ewe and lamb, one flax wheel, and all the property that she possesed of that she brought with her here, and an equal part of ______ the crop of small grain that is now growing. The cow, heifer, hogs, ewe lamb and wheel is her own property to dispose of as she pleases; he pot and kettle no to ______ carried from the house and to be returned to my heirs after her decease; if she dies possesed of a horse that is to be returned to my heirs also; I desire that my wife shall give my stepdaughter Susannah Snido the privileges on the plantation that she formerly has had. The land I now live is to be sold as soon possible after the decease of my wife Margaret Terry and the money to be equally divided amongst my three daughters; Kezia Grayham, Jemima Deweese and Karon Happuck Rose. My land going James Banks; and my land in Franklin County on Snow Creek to be sold also and divided equally amongst William Terry, Jonathon Terry and my three daughters above mentioned; my perishable property of all kind to be sold the last of November 1819 any part of my household furniture that my wife stands in need of she keep it untill her decease then to be divided between William Terry and Jonathan Terry; I give Silas one dollar. I give Elijah Terry one dollar. I do nominate, and appoint my trusty friends Daniel Shelor and Joshua Young my Executors of my last Will and Testament in witness whereof I Jasper Terry doth hereunto set my hand and seal the seventh day of May in the year of our Lord one Thousand Eight hundred and nineteen. The 43rd year of Independence. Sealed signed and acknowledge in presence of Will Barton, William Shelor, John Hill. Jasper TerryWill proved 6 July 1819 by Oaths of William Shelor and John Hill.[Note: Words underlined were not clear in original. Also, errors in mechanics found in the original have been re- (5)tained]. * * * * * COVERING THE TERRY-TORY By Robert W. Terry 4900 Springdale Rd., Cincinnati OH 45247 Most of us go through life "unsung", and that includes Terrys. Yet, I have evidence that a composer once wrote a song and dedicated it to Captain Robert W. Terry, pilot and later captain of Ohio River steamboats about the time of the War Between the States, or Civil War. The evidence came to me from a thoughtful friend, who saw the song in a current publication for riverboat buffs, persons who treasure accounts of "rollin" down the river" on ornate passenger craft. Title of the song is "Down the River We Swiftly Glide," a melody reminiscent of "Over the River and Through the Woods To Grandmother's House We Go." It is safe to say that it never made whatever "charts" existed in the 1860's. Composer was one Nelson Kneass and the song was published either in Cincinnati by A. C. Peters & Bro. or in St. Louis, MO by J. L. Peters & Bro. Capt. Robt. W., according to an accompanying article with the song, had been a pilot and mate on Ohio River steamboats prior to 1864. Late in that year, he and J. A. Stonebreaker, purser on river craft, bought the side-wheeler Robert Burns, built in Cincinnati at Eversoll's Yard for the original owners, Capt. George W. Ebert and purser Standish Peppard, both of Georgetown, PA. The Robert Burns ran up and down the rivers as an independent, competing with the regularly established Cincinnati & Memphis Packet Co., which operated several boats. In fact, the latter firm acquired the Robert Burns in 1866 and Capt. Robert W. may have retired or found other employment. I have been unable to determine additional information, and I still wonder at the composer`s tribute to Capt. Robert W., who apparently ran the boat for two years or less. (6) Composer Nelson Kneass may not rank with the Bachs, Strauss family, Leroy Anderson or John Williams, but I'll say this for him -- he wrote a piano score that would tax the right hand dexterity of any pianist, living or dead. This incident was one of those blind alleys that sidetrack one's genealogical pursuits. In reply to my request for any additional information on my namesake, the publisher of the riverboat magazine informed me: "Absolutely no information." Since my distant ancestors appear to have tilled the soil as farmers, I see no personal connection to the riverboat captain. I'm still working on their possible employment as fishermen and whalers along the East Coast of the colonies. Yet, each time I cross the Ohio River here in Cincinnati and see the immense tows and other craft, I wonder whether Captain Robert W. might have run away from the farm as a boy, and instead of joining the circus, took to the river. * * * * * BYRD TERRY FAMILY Submitted by Mrs. A. J. Morgan Rt. 2, Box 61 B, Bruce MS 38915 I do not know much about Terry in Texas but have learned some this year. The earliest is of William Terry 1809-1888 who is buried at Prairie Lea, Texas beside Mittie Terry, who was his grandson, Byrd Terry's wife. Byrd was my husband's grandfather and Mittie his grandmother. This William had a son William also, who was Byrd's father. According to information in the 1900 Yalabusha Co., MS Census, Byrd's father was born in NC and mother in SC. Byrd was born in AL as was 1st Mittie King and his 2nd wife Pathenia Chadwick. Byrd came to MS around 1900 and lived near relatives of his 2nd wife. Mittie and "Thenia" were cousins, and I believe 1st cousins. I think Thenia was born in Russell Co. AL.... Byrd had a son William Gary who lived in Yalobusha Co. MS and had a large family. Some of Wm. G.'s grandsons & families still live in Yalabusha Co. MS near Water Valley. Byrd Terry gave Census taker information in 1900 Census that (7)his father was born in NC and mother in SC. Much later he said his father was born in GA (he was old and sick then).... Byrd had a cousin Walter or Uncle. My husband's mother visited cousins in Texas in 1950. She had a cousin Ves Terry who lived in Sudan, TX. He came to MS in 1969 to visit him. Ves & wife Gladys have two sons, Bill & Bob. They live in AR & NM. Cousins here say Texas is full of Terrys....We went to the Cemetery at Prairie Lea and saw the tombs of Wm. Terry 1809-1888 and Mittie Terry 1857-1893. I have finally learned for sure that census info is not always correct but I've had to start with that and many times it is correct. I suspect that Byrd Terry's name may be something other than Byrd. He is "BY" in some church records. Pathenia had four names, I've learned recently. Uncle Wm. (Will) Gary Terry m. Johnny Porter and they had 9 children that lived to be grown & married and had children. His oldest lives near Water Valley about 17 miles from us. She was born in 1900. Others live in Memphis, TN....I hope to hear from you. * * * * * JAMES TERRY'S IN VIRGINIASubmitted by Mrs. Inez Martin, 833 Avocado Ave., El Cajon CA 92020. I paid Amy A. Sabin of Staten Island, NY $10.00 last summer to do Virginia research on the Terry name. I don't know if it is permissible or not to print them in the Historian. She didn't find much, but I will send you what she had.James Terry mentioned in Virginia Council Land Grants 1745- 1769, Nov 9, 1753. Source: Colonial Soldiers of the South 1732-1774 by Clark.James Terry and Thomas Terry, 1707, received land in King William Co. VA.James Terry is named in 1779 as receiving land in Louisa Co., VA.William Terry, James Terry, John Terry, Charles Terry, Mary Terry, had land taxed in 1782 in King William Co. VA.Capt. James Terry had 200 acres of land in King William Co., VA.James M. Terry m. Mrs. Ann Gerald April 26, 1815, Norfolk (8)Co. Marriage Bonds.James Terry, Pvt., served in the Rev. War. Source: Virginians in the Rev., by Gwathmey.(As you can tell, I asked her to research James Terry.) * * * * * I was notified by Mr. Robert R. Hill of 631 S. Echo Drive, Brandon FL 33511 that Mr. Carl Beach Terry of Tampa who furnished information about his Terry family in the December 1984 issue of the TFH passed away. His obituary from the Tampa Tribune (January 15th, 1985) follows:TERRY Mr. Carl B. Terry, Sr., 73, widower of Edenia Delaney Terry, of Tampa, passed away Sunday. Funeral services will be held Wednesday morning at 11:30 from the Chapel of the F. T. Blount Company Funeral Home, 5101 Nebraska Avenue, with The Rev. Timothy C. Trively, Rector of St. Andrew's Episcopal Church, officiating. Interment will follow in Myrtle Hill Memorial Park. The family will receive friends at the funeral home Tuesday night from 5:00 to 9:00 p.m. Mr. Terry was a native and lifetime resident of Tampa. He was a lifetime member of St. Andrew's Church and had retired from Tom's Peanut Company. Survivors include two sons, Carl B. Terry, Jr., Newport News, Va. and Richard D. Terry, Tampa; two grand children Danielle Terry, Tampa and Michael Terry, Newport News, Va.; one brother, Clyde Terry, of Tampa. F. T. BLOUNT CO. Tampa Chapel Note: Mr. Terry's age was given as 73 in the above obit- uary, but he told me he was 75 (that was on October 16th, 1984). Mr. Carl Beach Terry, was the son of Franklin Lanier Terry and wife Katherine Land. He was the grandson of George Washington Terry and his wife Elizabeth Lanier, from Atlanta, Georgia. He was the great grandson of Stephen Terry and Elizabeth Harrison Hill, both of South Carolina.... I am en- closing a copy of the obituary of Mr. Carl B. Terry with some notes for your file...as you say "Get Terryfied..but DON'T GO OVER THE HILL." ....Regards from Robert Hill. * * * * * ELIPHALET TERRY Have you seen a copy of the 1985 "The Hartford" (9)calendar? There is a picture of Eliphalet Terry. The date is Dec 16, 1835, New York City. Paragraph at the bottom reads: "On December 16, 1835, a raging fire destroyed half of New York City. Hartford President Eliphalet Terry set out from Hartford, Ct., in a horse-drawn sleigh to personally pay claims at the scene of the disaster. As a result of the pace-setting performance of President Terry, agent William Walker & others, public confidence in The Hartford blossomed." On June 4, 1835 Eliphalet Terry was elected Hartford President. At the bottom of the page of June 1985 reads: "On June 27, 1810, the first stockholders' meeting of The Hartford Fire Insurance Company was held at Ransom's Inn on the banks of the Connecticut River. Nathaniel Terry was elected presi- dent and Walter Mitchell was elected secretary." Nathaniel's signature is also on page for June. You may have seen the calendar, but just in case you haven't I thought I'd let you know about it. Quite interes- ting to me to see the name TERRY anywhere...Betty Martin. * * * * * TERRY QUIPS ....I intended to send the check for 6 months or more. Like everything else, I wait till I have to make a special trip, so to speak...."Forgetfulness is one of those signs of getting old. I forgot what the other two are". [Picked out from a letter from Earl T. Terry, 888 Nadine Ave., Eugene OR 97404.] I have a computer to check spelling but not grammar. It also does not check words typed twice, words missing, or nonsensical words. It does everything but type itself which still largely involves me, the editor.--Case in point--George A. Terry of Goodlettsville TN has a street address on page 163 of the Dec 84 TFH which should be 304 Highland Heights, Goodlettsville TN 37092. Nothing misspelled, but he won't get the mail. Mr. Harold Sears, 8104 Jefferson, Kansas City MO 66114 was kind enough to point out that his mail was returned in a phone call. Thanks for pointing out my glaring [literally] errors. --The Editor. * * * * * Enclosed is a copy of an article which appeared quite (10)some time ago in the Dallas Morning News (Monday, June 13, 1983). Dorene Blaylock Philen, 3017 Brookview Dr., Plano TX 75074. SCOUTS GIVE CEMETERY A FACE LIFT: Vandals, weeds had spoiled site. by Elizabeth Eckstein, staff writer of The News. MESQUITE -- The old Aunt Abby Frost Cemetery has been given new life. The century-old cemetery, covered for years by bramble and trash, has been cleared and cleaned. Cub Scout Pack 149 has been working since April, when pack leader Barbara Howell noticed the sun glinting off a tombstone obscured by overgrowth and stopped her car to investigate. In the weeks since, the 27 Wolves, Bears and Bobcats in the pack -- with the help of Mrs. Howell, her husband Ben and several concerned residents -- have cleared brush and bramble, pulled down dead trees and righted and repaired the tombstones marking the graves of a dozen Mesquite Pioneers, including a veteran of the Civil War. "We thought, when we first came out here, it'd be just a spooky old cemetery," Tim Duke, 9, said. Behind him, 11-year-old Carl Bowen pantomimed a hand reaching from a grave to clasp Tim's ankle. Both shrieked and laughed. "But we had the courage to clean it up, and it's beautiful now," Charles Jackson, 8, said. Mrs. Howell said some Eastfield College students cleaned up the cemetery eight or nine years ago but that the bramble had retaken the cemetery. Most of the wooden crosses the students placed on the graves rotted, she said. Vandals were responsible for most of the trash and damage to the tombstones, she said, and the Mesquite police have been asked to watch the cemetery more closely. The Scouts ages 8 to 11, found the tombstone of Rachel Beckner --born April 20, 1824; died Aug 28, 1862 broken into two pieces and lying a few feet from the foot marker. It was repaired by Ben Howell, righted and replaced. (11) As part of the cemetery tour, Scouts pointed out the grave of the Civil War veteran: "Isaac Newton Terry -- born Jan 29, 1836; died Oct 12, 1889." Mrs. Howell discovered through genealogy and census records that he fought in the Civil War. Records also showed that those buried in the cemetery were neighbors in what would become the City of Mesquite, and Mrs. Howell likes to speculate that they arrived together in a wagon train from Tennessee or Kentucky. As finishing touches for he cemetery, rose bushes and irises were planted, a fence erected and curb, concrete steps and flagpole base poured. A bare pole stands ready for a historical marker that the pack has requested from the state. During a ceremony at 7 p. m. Tuesday, U.S. and Texas flags will be raised over the cemetery on Belt Line Road near Bruton Road. Old Aunt Abby would be proud. * * * * * JOHN TERRY OF NORWICH, ENGLAND 1523 Peggy Thomas of 1118 Horizon Trail, Richardson TX 75081 wrote: Finally found the information sheet on the brass I copied from Westminister in London. It caught my eye because of my husband's name "John Terry Thomas". He's actually the "cousin" to you. My relation is by marriage only but I feel I'm a "Terry" too. Fondest regards, Peggy.1524 St. John Maddermarket, NorwichA description of the brass indicates that John and Lettys Terry and their two sons and daughters are on the face. It was done in 1524 for John who was the mayor of the City of Norwich in 1523. The plaque shows the coat of arms of the city and of the Mercers of London and the initials I. T. The article indicates that he was not a member of the Mercers Company and had no right to use the arms in the way he did. * * * * * NOTES ON A TERRY FAMILY OF MICHIGAN (12) by Frances Evelyn (Terry) Kelley 306 W. West St., Sturgis MI 49091 I haven't taken the time before this to write about the Terry side of my family. My fathers name was Edwin Frank Terry, born in Coopersville, Michigan May 30, 1875. His father's name was Lyman Terry. His mother's name was Armenia Minerva Mapes or Bostick or both. My mother said she had been married to an Indian before she married Lyman. Lyman had a brother Harvey Terry, he lived in Coopersville too. My father had a sister Etta and a brother Elmer. My father married my mother Sarah Amanda Nayant about 1900. My brother Clarence was born March 4, 1902, my sister Esther October 28, 1904 and my birth date is February 6, 1914. My brother Edwin L. Terry was born Jun 15, 1918. Clarence is deceased. Elmer Terry was married to Margaret, they had a daughter Mable who was married and living in Grand Rapids, but I don't know if she is still alive. Her married name is Merron. I was 16 years old when my mother died and we lost touch with our relatives. I think the Terry's came from the eastern states;, perhaps New York. I had joined a genealogy class recently at our High School, but had to give it up because my husband became ill and is in a hospital. I hope I can get back to it before it ends. We were gong to the Fort Wayne, IN Library where they have many records. I have enjoyed reading the Terry F. Historian, it seems there are lots of Terrys in the Southern States. * * * * * NOTES ON TERRY'S OF VIRGINIA PAST AND PRESENT By W. Sanford Terry, Jr., P. O. Box 13032, Richmond VA 23225. We are anxiously expecting our second child in February and if a boy will name him Barton Harrison Terry. This name may be the key to my line and missing records. Barton Terry was the grandson of Champness Terry of Louisa, VA. but 100 years earlier in 1699, the name appeared on a petition to the Governor of Virginia. Also, the ancestor immigrant 1635 was Andrew Terry (VA) and living one generation after him was Andrew Barton Terry. The Harrison name comes from my wife's family, the James River Harrison's including two Presidents of our country. I have more updated information for you but haven't had the time to write it up properly. In addition, have a lead and contact with individuals with access to Terry research (13)never organized or published. My most interesting recent study has been that of the legendary Col. B. F. (Frank) Terry, C. S. A. organizer and leader of the 8th Texas Cavalry, C. S. A. known as Terry's Texas Rangers! Please find the enclosed renewal for the TFH, which I have thoroughly devoured and enjoyed. * * * * * NOTES ON WASHINGTON COUNTY ARKANSAS TERRY'S Mrs. Bob L. Cook, 306 Butts St. Holdenville, OK 74848 I have a TERRY in my family tree, but am having difficulty trying top find a place to start on her. She was Nancy Terry who married William T. Harp. The first account I find of her is in Fayetteville, Washington Co. AR in 1862 where they owned land. A deed was witnessed by William Terry. Nancy was the mother of my great-grandmother Angelina (Harp) Boyd. [She was married to John B. Boyd in Cedar Vale, Chant? Co. Kansas.] I also have a postal card from Purdy, MO 1880 signed M. M. (Terry) Martin -- mentions her father's dying (Terry?) and her mother still alive. I thought maybe you've run into this name? * * * * * I received the following items from Marguerite Stegall, Rt. 2, Box 24, Strong AR 71765 who is researching Williams/McClure families. She has sent several items on Terry's as well and resides near the vicinity where my Terry's are buried at New London, Union Co. AR.11 Nov 1866 TERRY, Benjamin m. MADDEN, Frances Laurens Dist SC.04 Sep 1856 TERRY, Elizabeth m. GOODING, Wm James Beaufort Dist SC.30 Oct 1855 TERRY, Roland m. SUMMERALL, Jane Edgefield Dist SC.-- --- ---- TERRY, Wm. m. SUMMERALL, Elizabeth Edgefield Dist. SC20 Feb 1793 MCCLURE, Robert m. WALLACE, Margaret Mecklenberg (14)Co. NC.30 Oct 1856 TERRY, James N. m. EVANS, Lydia Jane Chesterfield Dist. SC.05 DEC 1869 TERRY, J. m. WILLIAMS, Eleanor Union Co. SC by Esq. J. Trull.Do you have any information on this couple? We are working on a Williams History--and can't place her in any of our family. * * * * * TROUBLES OF A BAPTIST MINISTER - 1776 Anson County in 1776 was a scene of turmoil. With most of the Tory leaders in jail in Virginia or Philadelphia as a result of the Battle of Moores Creek Bridge and Whig extrem- ists exhorting their views to all who would listen, it was not safe to utter any words or perform any act that would even imply Tory sympathies. In such an atmosphere it was not difficult for one to twist the meaning of another's utter- ances and cause great trouble. Such is what happened to James Terry, Jr. James Terry, Jr., was a Newlight Baptist preacher in Anson County. Terry was an ardent Whig, but he also felt himself a realist. On 1 Sep 1776, while riding through the woods with John Allen, he told Allen the inhabitants of Quebec and Florida were all Tories, that the King had possession of these and had a right to do with them as he felt and that we had to fight it out in the middle between them. He added, "If the King cannot subdue us, he may sell claim to us to some other Nation". Terry thought no more of the conversation until the 14th of October, when he was at the house of William Pickett. There was a gathering of people at the house and sometime in the evening Terry asked Pickett, Capt. Walton Harris, Burwell Lanier and James Allen to go with him to one of the upper rooms. There they met John Allen, who turned on Terry and said he was very prejudiced against Terry, for Terry's comments of September. Terry told John Allen he was sorry Allen was dissatisfied with him on that account. Terry said further, "I did not speak those words out of any disaffection to the American Cause, but that it was the truth. We have gone from the King and not the King from us, our going from the King did not disannul his right to us. For if we had a Negro that runs away, his running away does not disannul our Right to him. WE should have a right to sell the same Negro to any Person that would buy him". Terry continued, "The King (15)has a Right to sell us to the Turks or any other nation, on half for conquering the whole. He has a Right to sell us to the Turks or any other nation for Servants or Slaves". John Allen and Lanier discussed this concept further with Terry. Finally Burwell Lanier acknowledged himself satisfied that there was nothing really hurtful to the American Cause in these statements. John Allen was apparently not satisfied and went to Samuel Spencer who was chairman of the Anson County Committee of Surety, Intelligence and Observation. Concerned that Terry's remarks might cause some people to become disaffected with the American Cause, Spencer held a hearing before the Committee on 26 October. At this hearing they questioned Terry and Capt. Walton Harris as to what had been said. Feeling additional testimony was needed, Spencer adjourned the hearing until the 6th November. At the second hearing Burwell Lanier gave his testimony as to the conversation. Even under intense cross-examination Terry would not change his opinion. At the conclusion of the hearing, which lasted until dark, Spencer felt action in the matter should be handled by the Provincial Congress which was to convene in Halifax, North Carolina, the 10th of November. It is very likely Terry was confined to jail because he obstinately refused to provide any surety that would guarantee his appearance before the Provincial Congress. Being fully cognizant that, with the tenor of the times he would be caused a great deal of injury, James Terry, Jr., procured affidavits from a number of individuals stressing his devotion to the American Cause. Both Shd. Hogan and D. Smith pointed out that in February 1775 John Colson, accompanied by Governor Martin's waiting man, got up before a large crowd in Anson County and read a letter from the Governor applauding Colson's loyalty and protesting the actions of the Provincial Congress and the Committees of Safety. Following this action Colson proceeded to urge the people to sign the protest. At this point, Terry stepped up to Colson and told him, "I think the King and Parliament are both wrong and they are about to open the door to oppress- ion." Terry continued along the same vein emphasizing the justness of the American Cause. Because of his arguments, Terry dissuaded a large number of people from signing the protest. Terry continued to argue on behalf of the cause of Liberty both publicly and privately. In July 1775 a gathering was held at Anson County Courthouse to have a day of Fasting and Prayer at the request of the Committee of South Carolina to implore the Almighty's blessings on the American Cause. In a conversation between Terry and William Moody, Moody stated he was sorry that the (16)present distress of American had happened in this day. Terry immediately rejoined, "I'm glad it happened in my day that I might see what my Posterity has to depend upon". Then, at the request of the people, Terry offered prayer before the gathering praying for the success of America and gave God thanks that the dispute between our Mother Country and America happened in his day. Following the prayer Terry then began to talk to the gathering about the nature of the cause by proving the difficulties and hardships their forebears underwent to obtain the Freedom of America. In early 1776 the Tories began to assemble, prior to their planned march to Wilmington, at Dry Creek. One Sunday while the Tories were encamped at Dry Creek James Terry Jr., was preaching at Little River Meeting House. During the course of the sermon several armed Tories rode up to the Meeting House. After the sermon they asked Terry to ride with them a little way because they wanted his advice concerning the then present disturbances. Terry, in company with James Auldman, rode a short way and advised the Tories not to go to the Scottish camps for Terry believed they were in the wrong. The Tories were not convinced and Terry went on his way. Auldman rode with the Tories a little further when one of the Tories stopped and turning to the others said, "I've a good mind to go back and take Terry and carry him to the King's camp". The Tory finally decided that maybe Terry advised them for their own good and left him alone. On the 23rd November 1776 the Provincial Congress received the signed oath of James Terry, Jr., stating: "I will bear faith and true Allegiance to the Independent State of North Carolina and I will to the Utmost of my Powers maintain, support & defend the same against the forces of Great Britain and all other Enemies of the Independent States of America and this I do most solemnly swear without any Equivocation, mental Evasion or secret Reservation whatsoever". With this Terry was allowed to return to his peaceful ministrations to the people of Anson County.(I should mention that Terry later represented Anson County in the General Assembly, but that is another Story.)Source: The three pages on James Terry was in the Bulletin from the Union Co. Genealogical Society. This Mr. Bennett may have other information--made these copies for you to keep.Compiled and submitted by: William D. Bennett, 415 Bickett Blvd., Raleigh, NC 27608 - Source: NC State Archives, Secretary of State Papers, General Records, Box 302, Provincial Congress 1774-1776, Loose Papers. (17) * * * * * MISSING TERRY Your address was in the Kansas City paper recently, concerning your research into families with the last name Terry. I am looking for the records of a VIRGINIA TERRY who owned property in LaPorte, TX (Harris CO.) in 1923. That is when she bought it. She died, but I don't know when, leaving the property to her child, Ellery Terry, a minor. When Ellery was about 17 years old (1937), the property was sold to my father, Dr. D. R. Aves. Ellery's guardian handled the sale. My father and mother both died more than 30 years ago and now my sisters and I have a chance to sell the property. However, the title company will not issue a guaranteed title unless we can come up with a copy of Virginia Terry's will, leaving the land to Ellery Terry. With the above sketchy information,how can I find out more about Virginia Terry? The Harris County Court house could not help without a date of death. Do you have information that would be useful, such as: 1. Date and place of death of Virginia Terry, born somewhere around 1900, and/or 2. Married name of Ellery Terry, born about 1920, and her present address if still living.[She noted]....I am willing to pay a reasonable fee. Thank you for your time. Laura M. Curry, 4229 Campbell, Kansas City MO 64110. * * * * *The following obituary, of William Martin Terry was submitted by Helen Hobbs, 409 Memorial Dr., Abingdon IL 61410.W. M. TERRY Dies in S. F. Owner of Terry The Cleaner, William Martin Terry, 65, of 2504 South Center Ave., died at a local hospital Thursday evening following a brief Illness. Mr. Terry had resided in Sioux Falls for the past 31 years. Born in Courtland, Ala. August 22, 1885, Mr. Terry moved with his parents to Paris, Tex. at the age of 7. He took his tailoring apprenticeship as a young man in Chicago and Kansas (18)City, MO., and was able to start his own shop while he was in his early 20s in Childress, Tex. Mr. Terry also operated tailor firms in Denver, from 1913 until 1914; in Creston, IA from 1914 until 1919, and in Sidney, NE, from 1919 until 1920, when he came to Sioux Falls and established his shop here. Funeral services will be held at the Miller Funeral home at 11 a.m. Monday with the Rev. Clarence Adams officiating. Mrs. S. S. Steiber will be organist. Interment will be in Mt. Pleasant cemetery. He is survived by five sons, Cleo M., Thomas J., Charles E., Dewey M. and Clyde R., all of Sioux Falls, and four grandchildren. His sons will act as pallbearers. FUNERALS The Rev. Clarence Adams officiated at services at the Miller Funeral home today for William Martin Terry, 65, of 2504 South Center Ave. Owner of Terry the Cleaner, Mr. Terry succumbed at a local hospital Thursday, after a brief illness. He had resided here since 1920. Organist was Mrs. S. S. Steiber. Pallbearers were his five sons, Cleo, Thomas, Charles, Dewey and Clyde. Interment was in Mt. Pleasant cemetery. * * * * * NOTES ON DESCENDANTS OF CURTIS TERRY By Colleen Belk, P. O. Box 25, Duenweg, MO 64841-0025 My great grandmother Eliza Jane Terry was the daughter of Jesse K. Terry. Jesse was killed when she was 9 years old. She witnessed his death---. He was accused of being a Southern sympathizer [which he was!] Eliza spoke of her "Uncle Brazewell"in her late years telling that he was the one in the family that [was] Yankee minded in his talk--and it caused hard feelings. After the War Uncle Brazewell and his wife came to Jasper Co. MO--and stopped briefly--after he learned of Jesse's tragic death he just "went away on to Texas."-- It took some time to find any record of Brazewell and I firmly believe this James B. Terry is that man. Do you think the initials in the corner of the page are V. M. or N. M.? James Brazewell Terry b. 1831 was the son of Curtis Terry and (19)Elizabeth Kuykendall. James married Amanda Pearson. The family story I'd heard was that he had "gone to Texas." I am interested in the record mostly because it gives his description. He was the brother to my great-great grandfather Jesse K. Terry. Eliza Jane Terry Webb Bigger lived in North Enid, OK in the years of the 1930's--with her older son Jesse Thomas Webb and his family. He lived on the Biggs place. * * * *So Division Inv. 6 No. 1100848 DEPARTMENT OF THE INTERIOR, James B. Terry BUREAU OF PENSIONS Co. C, 8 Reg't Tenn Vol. Mtd. Infty Washington, D. C., Dec. 17, 1901 Sir: To aid this Bureau in preventing any one falsely personating you, or otherwise committing fraud in your name, or on account of your service, you are required to answer fully the questions enumerated below: You will please return this circular under cover of the inclosed envelope which requires no postage. Very respectfully H. Clay Evands CommissionerJames B. Terry Bokchito Choctaw Nat.-Ind. Ter.1. When were you born? Answer. Nov 7 - 1831 2. Where were you born? Answer. Close to Cookvill, Putnam Co. Tenn. 3. When did you enlist? Answer. Fore Part of 1865. 4. Where did you enlist? Answer. At Nashville, Tenn. 5. Where had you lived before that? Answer. Cookville, Tenn. 6. What was your post-office address at enlistment? Answer. Cookville Tenn. 7. What was your occupation at enlistment? Answer. Farmer. 8. When were you discharged? Answer. Nashville [Crossed out] Tenn Latter Part of 1862. 9. Where were you discharged? Answer. Nashville Tenn. 10. Where have you lived since discharge? Give dates, as nearly as possible of any changes of residence. Basin Springs Tex -1870 Oakland I.T. 1889. Coalgate I.T. 1893. Bokchito 1901. 11. What is your present occupation? Answer. Nothing (20)12. What is your height? Answer. 5 feet 7 inches. Your weight? 150. The color of your eyes? Dark Brown. The color of your hair? Dark Brown. Your complexion? fair. Are there any permanent marks or scars on your person? If so, describe them. 2 scars in Right Leg. between Ancle & knee. 13. What is your full name? Please write it on the line below, in ink, in the manner in which you are accustomed to sign it,in the presence of two witnesses who can write. James B. TerryWitnesses: 1. T. A. Macleer? Date: Jan 20, 1902 2. N. M. Terry * * * * * LUCILLE LESUEUR **ALIAS** JOAN CRAWFORDBorrowed from Terry and Allied Families, Vol. I, by Frances Terry Ingmire. Second edition. 1983. Page 34. The youthful symbol of Hollywood, was born in San Antonio, Texas, March 23, 1908. Her first marriage was to actor, Douglas Fairbanks, Jr. This marriage lasted four years. Her second marriage was to actor, Franchot Tone. This marriage lasted about four years. She then married husband number three, actor Phillip Terry (relationship, if any, unknown). This marriage ended in about four years. Joan married husband four, on May 10, 1955, the love of her life, Mr. Alfred N. Steel, President of Pepsi-Cola Company. He passed away in 1959, four years after they were married. She is superstitious about the number four from incidents involving the 4's above. Can anyone blame her? Joan quit school at the age of eleven; later, having her high school records forged, so she could attend college, after which, she entered show business, a career which spans some 47 years plus, having made in excess of eighty outstanding films. Joan had four adopted children. Her will left her estate to two twin daughters, the other two children were disinherited. Her will states reason as, "Known only to them". Joan Crawford, was one of our greatest movie actresses and one we can be very proud of. Her great-grandfather and great-grandmother, are buried in the Camp Creek Cemetery, located on Route #615, about 6.5 miles northeast of the town of Floyd, Virginia, on what is (21)known as the Old Christianburg Road. The cemetery is on a hilltop and on the left side of the road. The oldest grave in this cemetery is dated 1887. Joan Crawford, alias, Lucille LeSueur, great- grandparents lived in this neighborhood. Her great- grandfather, Martell LeSueur's son, Bert LeSueur, was Joan Crawford's grandfather. Bert LeSueur, moved to Crawford, Nebraska. He had two children, one son and one daughter. His son, Thomas, is Joan Crawford's father.1. LESUEUR, Lucille b. San Antonio TX 23 Mar 1908 d. CA 10 May 1977.2. LESUEUR, Thomas E. b. 21 Jan 1868 d. 1 Jan 1938 m. ?? 3. JOHNSON, Anna Belle b. 29 Nov 1884 d. 18 Aug 1958.6. JOHNSON, Sylvester 7. SEARLES, Mary Ellen b. 1863 d. 195014. SEARLES, Joseph Allen b. Medera IL 1 Nov 1838 d. Medera IL 5 Jan 1913 m. Macoupin Co. IL 3 Feb 1857. 15. RHOADS, Harriet b. IL 2 Apr 1838 d. Medera, IL 6 Jan 1919.28. SEARLES, William b. KY 10 Mar 1811 d. IL 13 Nov 1888 m. Greene Co. IL 29 Nov 1836. 29. STEVENS, Sarah Ann b. MO 1816 d. ca. 1844.58. STEVENS, Rev. John b. VA 5 Feb 1792 d. Greene Co. IL 12 Mar 1853 m. Hardin Co. KY 2 Dec 1811. 59. TERRY, Elizabeth b. Montgomery Co. VA 12 May 1798 d. Greene Co. IL 28 Feb 1881.118. TERRY, Jasper Morrison, Sr. b. Botetourt Co. VA 6 Jan 1777 d. Montgomery Co. IL 14 Nov 1851 m. Montgomery Co. VA 1 Aug 1797. 119. FULLER, Sarah "Sallie" b. Peeksill, NY 6 Sep 1788 d. Greene Co. IL 17 Sep 1850.236. TERRY, Josiah b. Botetourt Co. VA 2 Apr 1755 d. aft. 1839 m. VA ca. 1775 237. LLOYD, Mary b. ?? d. Greene Co. IL 27 Apr 1844474. TERRY, Jasper 475. MORRISON, Mary948. TERRY, William Sr. d. bf. 1776? 949. _____, RachielSources: Terry and Allied Families, Vol. I, by Frances Terry (22)Ingmire. Second edition. 1983. Pages 24,25,27,32-35. * * * * * PARSHALL TERRY: Father and Son I have always been intrigued by the story of one Parshall Terry Jr. and his father Parshall Terry Sr. Both of whom found themselves on different sides of the fence during the Revolutionary War. Parshall Terry Jr., baptized 22 Feb 1756, was the son of Parshall Terry Sr. and Deborah Clark. He was noted to have been at the battle of Wyoming, known as the Wyoming Massacre, in July, 1778. He is said to have been a member of the First Westmoreland Independent Company in 1776 and served with Washington's army for some time. The story, as it goes, is he stopped to tie his shoe and was reprimanded by an officer. He was struck with a sword by the officer and as a result knocked the officer down and fled. It was noted he deserted January 11, 1777. Later he joined the British Army and became a Lieutenant in Butler's Rangers, Royal Greens. The story further indicates that Parshall Terry, Sr. and his other sons were on the side of the Colonials in the same battle; reports were later generated that he had killed his father, mother and brothers and sisters during the battle. Captain Jonathan Terry, his brother, later testified that these reports were false and his brother, Parshall Jr., had come to the Fort to save their lives..."My father, has survived many years, and died among his friends in this place [Terrytown, PA?] in good old age." His sister, Deborah Terry Horton, spoke of him in less kind words and noted she saw her "Tory" brother stand by while Indians cut her father's shoes off his feet. A more moderate view of the family differences was noted in 1914 by a J. Washington Ingham, a great grandson of Parshall, Jr. who opined: "In justice to him it ought to be said that between him and the rest of the family, there were only political differences." At the close of the Revolutionary War [1783 or 1789 by some accounts] Parshall Terry Jr. moved to Upper Canada, now Ontario, where he was given some large holdings by the Crown. (23)Tradition is, he was a member of the First Parliament for upper Canada, but this has not been verified. Later descendants of this particular Terry Family clan migrated to Michigan, Illinois, and Utah. Several were prominent early members of the Church of Jesus Christ of the Latter Day Saints. Source: Parshall Terry Family History. Reprint 1963. Mr. and Mrs. Terry Lund. Salt Lake City Utah. Page 12-13.*************************************************************