Preface xiii
Chapter 1 Introduction to Quantitative Analysis 1
1.1 What Is Quantitative Analysis? 2
1.2 Business Analytics 2
1.3 The Quantitative Analysis Approach 3
Defining the Problem 4
Developing a Model 4
Acquiring Input Data 4
Developing a Solution 5
Testing the Solution 5
Analyzing the Results and Sensitivity Analysis 6
Implementing the Results 6
The Quantitative Analysis Approach and Modeling in the Real World 6
1.4 How to Develop a Quantitative Analysis Model 6
The Advantages of Mathematical Modeling 9
Mathematical Models Categorized by Risk 9
1.5 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach 9
1.6 Possible Problems in the Quantitative Analysis Approach 12
Defining the Problem 12
Developing a Model 13
Acquiring Input Data 14
Developing a Solution 14
Testing the Solution 14
Analyzing the Results 15
1.7 Implementation—Not Just the Final Step 15
Lack of Commitment and Resistance to Change 16
Lack of Commitment by Quantitative Analysts 16
Summary 16
Glossary 16
Key Equations 17
Self-Test 17
Discussion Questions and Problems 18
Case Study: Food and Beverages at Southwestern University Football Games 19
Bibliography 20
Chapter 2 Probability Concepts and Applications 21
2.1 Fundamental Concepts 22
Two Basic Rules of Probability 22
Types of Probability 22
Mutually Exclusive and Collectively Exhaustive Events 23
Unions and Intersections of Events 25
Probability Rules for Unions, Intersections, and Conditional Probabilities 25
2.2 Revising Probabilities with Bayes’ Theorem 27
General Form of Bayes’ Theorem 28
2.3 Further Probability Revisions 29
2.4 Random Variables 30
2.5 Probability Distributions 32
Probability Distribution of a Discrete Random Variable 32
Expected Value of a Discrete Probability Distribution 32
Variance of a Discrete Probability Distribution 33
Probability Distribution of a Continuous Random Variable 34
2.6 The Binomial Distribution 35
Solving Problems with the Binomial Formula 36
Solving Problems with Binomial Tables 37
2.7 The Normal Distribution 38
Area Under the Normal Curve 40
Using the Standard Normal Table 40
Haynes Construction Company Example 41
The Empirical Rule 44
2.8 The F Distribution 44
2.9 The Exponential Distribution 46
Arnold’s Muffler Example 47
2.10 The Poisson Distribution 48
Summary 50
Glossary 50
Key Equations 51
Solved Problems 52
Self-Test 54
Discussion Questions and Problems 55
Case Study: WTVX 61
Bibliography 61
Appendix 2.1: Derivation of Bayes’ Theorem 61
Chapter 3 Decision Analysis 63
3.1 The Six Steps in Decision Making 63
3.2 Types of Decision-Making Environments 65
3.3 Decision Making Under Uncertainty 65
Optimistic 66
Pessimistic 66
Criterion of Realism (Hurwicz Criterion) 67
Equally Likely (Laplace) 67
Minimax Regret 67
3.4 Decision Making Under Risk 69
Expected Monetary Value 69
Expected Value of Perfect Information 70
Expected Opportunity Loss 71
Sensitivity Analysis 72
A Minimization Example 73
3.5 Using Software for Payoff Table Problems 75
QM for Windows 75
Excel QM 75
3.6 Decision Trees 77
Efficiency of Sample Information 82
Sensitivity Analysis 82
3.7 How Probability Values Are Estimated by Bayesian Analysis 83
Calculating Revised Probabilities 83
Potential Problem in Using Survey Results 85
3.8 Utility Theory 86
Measuring Utility and Constructing a Utility Curve 86
Utility as a Decision-Making Criterion 88
Summary 91
Glossary 91
Key Equations 92
Solved Problems 92
Self-Test 97
Discussion Questions and Problems 98
Case Study: Starting Right Corporation 107
Case Study: Toledo Leather Company 107
Case Study: Blake Electronics 108
Bibliography 110
Chapter 4 Regression Models 111
4.1 Scatter Diagrams 112
4.2 Simple Linear Regression 113
4.3 Measuring the Fit of the Regression Model 114
Coefficient of Determination 116
Correlation Coefficient 116
4.4 Assumptions of the Regression Model 117
Estimating the Variance 119
4.5 Testing the Model for Significance 119
Triple A Construction Example 121
The Analysis of Variance (ANOVA) Table 122
Triple A Construction ANOVA Example 122
4.6 Using Computer Software for Regression 122
Excel 2016 122
Excel QM 123
QM for Windows 125
4.7 Multiple Regression Analysis 126
Evaluating the Multiple Regression Model 127
Jenny Wilson Realty Example 128
4.8 Binary or Dummy Variables 129
4.9 Model Building 130
Stepwise Regression 131
Multicollinearity 131
4.10 Nonlinear Regression 131
4.11 Cautions and Pitfalls in Regression Analysis 134
Summary 135
Glossary 135
Key Equations 136
Solved Problems 137
Self-Test 139
Discussion Questions and Problems 139
Case Study: North–South Airline 144
Bibliography 145
Appendix 4.1: Formulas for Regression Calculations 145
Chapter 5 Forecasting 147
5.1 Types of Forecasting Models 147
Qualitative Models 147
Causal Models 148
Time-Series Models 149
5.2 Components of a Time-Series 149
5.3 Measures of Forecast Accuracy 151
5.4 Forecasting Models—Random Variations Only 154
Moving Averages 154
Weighted Moving Averages 154
Exponential Smoothing 156
Using Software for Forecasting Time Series 158
5.5 Forecasting Models—Trend and Random Variations 160
Exponential Smoothing with Trend 160
Trend Projections 163
5.6 Adjusting for Seasonal Variations 164
Seasonal Indices 165
Calculating Seasonal Indices with No Trend 165
Calculating Seasonal Indices with Trend 166
5.7 Forecasting Models—Trend, Seasonal, and Random Variations 167
The Decomposition Method 167
Software for Decomposition 170
Using Regression with Trend and Seasonal Components 170
5.8 Monitoring and Controlling Forecasts 172
Adaptive Smoothing 174
Summary 174
Glossary 174
Key Equations 175
Solved Problems 176
Self-Test 177
Discussion Questions and Problems 178
Case Study: Forecasting Attendance at SWU Football Games 182
Case Study: Forecasting Monthly Sales 183
Bibliography 184
Chapter 6 Inventory Control Models 185
6.1 Importance of Inventory Control 186
Decoupling Function 186
Storing Resources 187
Irregular Supply and Demand 187
Quantity Discounts 187
Avoiding Stockouts and Shortages 187
6.2 Inventory Decisions 187
6.3 Economic Order Quantity: Determining How Much to Order 189
Inventory Costs in the EOQ Situation 189
Finding the EOQ 191
Sumco Pump Company Example 192
Purchase Cost of Inventory Items 193
Sensitivity Analysis with the EOQ Model 194
6.4 Reorder Point: Determining When to Order 194
6.5 EOQ Without the Instantaneous Receipt Assumption 196
Annual Carrying Cost for Production Run Model 196
Annual Setup Cost or Annual Ordering Cost 197
Determining the Optimal Production Quantity 197
Brown Manufacturing Example 198
6.6 Quantity Discount Models 200
Brass Department Store Example 202
6.7 Use of Safety Stock 203
6.8 Single-Period Inventory Models 209
Marginal Analysis with Discrete Distributions 210
Café du Donut Example 210
Marginal Analysis with the Normal Distribution 212
Newspaper Example 212
6.9 ABC Analysis 214
6.10 Dependent Demand: The Case for Material Requirements Planning 214
Material Structure Tree 215
Gross and Net Material Requirements Plans 216
Two or More End Products 218
6.11 Just-In-Time Inventory Control 219
6.12 Enterprise Resource Planning 220
Summary 221
Glossary 221
Key Equations 222
Solved Problems 223
Self-Test 225
Discussion Questions and Problems 226
Case Study: Martin-Pullin Bicycle Corporation 234
Bibliography 235
Appendix 6.1: Inventory Control with QM for Windows 235
Chapter 7 Linear Programming Models: Graphical and Computer Methods 237
7.1 Requirements of a Linear Programming Problem 238
7.2 Formulating LP Problems 239
Flair Furniture Company 240
7.3 Graphical Solution to an LP Problem 241
Graphical Representation of Constraints 241
Isoprofit Line Solution Method 245
Corner Point Solution Method 248
Slack and Surplus 250
7.4 Solving Flair Furniture’s LP Problem Using QM for Windows, Excel 2016, and Excel QM 251
Using QM for Windows 251
Using Excel’s Solver Command to Solve LP Problems 252
Using Excel QM 255
7.5 Solving Minimization Problems 257
Holiday Meal Turkey Ranch 257
7.6 Four Special Cases in LP 261
No Feasible Solution 261
Unboundedness 261
Redundancy 262
Alternate Optimal Solutions 263
7.7 Sensitivity Analysis 264
High Note Sound Company 265
Changes in the Objective Function Coefficient 266
QM for Windows and Changes in Objective Function Coefficients 266
Excel Solver and Changes in Objective Function Coefficients 267
Changes in the Technological Coefficients 268
Changes in the Resources or Right-Hand-Side Values 269
QM for Windows and Changes in Right-Hand-Side Values 270
Excel Solver and Changes in Right-Hand-Side Values 270
Summary 272
Glossary 272
Solved Problems 273
Self-Test 277
Discussion Questions and Problems 278
Case Study: Mexicana Wire Winding, Inc. 286
Bibliography 288
Chapter 8 Linear Programming Applications 289
8.1 Marketing Applications 289
Media Selection 289
Marketing Research 291
8.2 Manufacturing Applications 293
Production Mix 293
Production Scheduling 295
8.3 Employee Scheduling Applications 299
Labor Planning 299
8.4 Financial Applications 300
Portfolio Selection 300
Truck Loading Problem 303
8.5 Ingredient Blending Applications 305
Diet Problems 305
Ingredient Mix and Blending Problems 306
8.6 Other Linear Programming Applications 308
Summary 310
Self-Test 310
Problems 311
Case Study: Cable & Moore 318
Bibliography 318
Chapter 9 Transportation, Assignment, and Network Models 319
9.1 The Transportation Problem 320
Linear Program for the Transportation Example 320
Solving Transportation Problems Using Computer Software 321
A General LP Model for Transportation Problems 322
Facility Location Analysis 323
9.2 The Assignment Problem 325
Linear Program for Assignment Example 325
9.3 The Transshipment Problem 327
Linear Program for Transshipment Example 327
9.4 Maximal-Flow Problem 330
Example 330
9.5 Shortest-Route Problem 332
9.6 Minimal-Spanning Tree Problem 334
Summary 337
Glossary 338
Solved Problems 338
Self-Test 340
Discussion Questions and Problems 341
Case Study: Andrew–Carter, Inc. 352
Case Study: Northeastern Airlines 353
Case Study: Southwestern University Traffic Problems 354
Bibliography 355
Appendix 9.1: Using QM for Windows 355
Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming 357
10.1 Integer Programming 358
Harrison Electric Company Example of Integer Programming 358
Using Software to Solve the Harrison Integer Programming Problem 360
Mixed-Integer Programming Problem Example 360
10.2 Modeling with 0–1 (Binary) Variables 363
Capital Budgeting Example 364
Limiting the Number of Alternatives Selected 365
Dependent Selections 365
Fixed-Charge Problem Example 366
Financial Investment Example 367
10.3 Goal Programming 368
Example of Goal Programming: Harrison Electric Company Revisited 369
Extension to Equally Important Multiple Goals 370
Ranking Goals with Priority Levels 371
Goal Programming with Weighted Goals 371
10.4 Nonlinear Programming 372
Nonlinear Objective Function and Linear Constraints 373
Both Nonlinear Objective Function and Nonlinear Constraints 373
Linear Objective Function with Nonlinear Constraints 374
Summary 375
Glossary 375
Solved Problems 376
Self-Test 378
Discussion Questions and Problems 379
Case Study: Schank Marketing Research 384
Case Study: Oakton River Bridge 385
Bibliography 385
Chapter 11 Project Management 387
11.1 PERT/CPM 389
General Foundry Example of PERT/CPM 389
Drawing the PERT/CPM Network 390
Activity Times 391
How to Find the Critical Path 392
Probability of Project Completion 395
What PERT Was Able to Provide 398
Using Excel QM for the General Foundry Example 398
Sensitivity Analysis and Project Management 399
11.2 PERT/Cost 400
Planning and Scheduling Project Costs: Budgeting Process 400
Monitoring and Controlling Project Costs 403
11.3 Project Crashing 405
General Foundry Example 406
Project Crashing with Linear Programming 407
11.4 Other Topics in Project Management 410
Subprojects 410
Milestones 410
Resource Leveling 410
Software 410
Summary 410
Glossary 410
Key Equations 411
Solved Problems 412
Self-Test 414
Discussion Questions and Problems 415
Case Study: Southwestern University Stadium Construction 422
Case Study: Family Planning Research Center of Nigeria 423
Bibliography 424
Appendix 11.1: Project Management with QM for Windows 424
Chapter 12 Waiting Lines and Queuing Theory Models 427
12.1 Waiting Line Costs 428
Three Rivers Shipping Company Example 428
12.2 Characteristics of a Queuing System 429
Arrival Characteristics 429
Waiting Line Characteristics 430
Service Facility Characteristics 430
Identifying Models Using Kendall Notation 431
12.3 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M /1) 434
Assumptions of the Model 434
Queuing Equations 434
Arnold’s Muffler Shop Case 435
Enhancing the Queuing Environment 438
12.4 Multichannel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/m) 439
Equations for the Multichannel Queuing Model 439
Arnold’s Muffler Shop Revisited 440
12.5 Constant Service Time Model (M/D/1) 442
Equations for the Constant Service Time Model 442
Garcia-Golding Recycling, Inc. 443
12.6 Finite Population Model (M/M/1 with Finite Source) 443
Equations for the Finite Population Model 444
Department of Commerce Example 444
12.7 Some General Operating Characteristic Relationships 445
12.8 More Complex Queuing Models and the Use of Simulation 446
Summary 446
Glossary 447
Key Equations 447
Solved Problems 449
Self-Test 451
Discussion Questions and Problems 452
Case Study: New England Foundry 457
Case Study: Winter Park Hotel 459
Bibliography 459
Appendix 12.1: Using QM for Windows 460
Chapter 13 Simulation Modeling 461
13.1 Advantages and Disadvantages of Simulation 462
13.2 Monte Carlo Simulation 463
Harry’s Auto Tire Example 464
Using QM for Windows for Simulation 468
Simulation with Excel Spreadsheets 469
13.3 Simulation and Inventory Analysis 471
Simkin’s Hardware Store 472
Analyzing Simkin’s Inventory Costs 475
13.4 Simulation of a Queuing Problem 476
Port of New Orleans 476
Using Excel to Simulate the Port of New Orleans Queuing Problem 478
13.5 Simulation Model for a Maintenance Policy 479
Three Hills Power Company 479
Cost Analysis of the Simulation 481
13.6 Other Simulation Issues 484
Two Other Types of Simulation Models 484
Verification and Validation 485
Role of Computers in Simulation 485
Summary 486
Glossary 486
Solved Problems 487
Self-Test 489
Discussion Questions and Problems 490
Case Study: Alabama Airlines 496
Case Study: Statewide Development Corporation 497
Case Study: FB Badpoore Aerospace 498
Bibliography 500
Chapter 14 Markov Analysis 501
14.1 States and State Probabilities 502
The Vector of State Probabilities for Grocery Store Example 503
14.2 Matrix of Transition Probabilities 504
Transition Probabilities for Grocery Store Example 504
14.3 Predicting Future Market Shares 505
14.4 Markov Analysis of Machine Operations 506
14.5 Equilibrium Conditions 507
14.6 Absorbing States and the Fundamental Matrix: Accounts Receivable Application 510
Summary 514
Glossary 514
Key Equations 514
Solved Problems 515
Self-Test 518
Discussion Questions and Problems 519
Case Study: Rentall Trucks 523
Bibliography 525
Appendix 14.1: Markov Analysis with QM for Windows 525
Appendix 14.2: Markov Analysis with Excel 526
Chapter 15 Statistical Quality Control 529
15.1 Defining Quality and TQM 529
15.2 Statistical Process Control 531
Variability in the Process 531
15.3 Control Charts for Variables 532
The Central Limit Theorem 533
Setting x¯x¯-Chart Limits 534
Setting Range Chart Limits 536
15.4 Control Charts for Attributes 537
p-Charts 537
c-Charts 539
Summary 541
Glossary 541
Key Equations 541
Solved Problems 542
Self-Test 543
Discussion Questions and Problems 543
Bibliography 546
Appendix 15.1: Using QM for Windows for SPC 547
Appendices 549
Appendix A Areas Under the Standard Normal Curve 550
Appendix B Binomial Probabilities 552
Appendix C Values of e−λ for Use in the Poisson Distribution 557
Appendix D F Distribution Values 558
Appendix E Using POM-QM for Windows 560
Appendix F Using Excel QM and Excel Add-Ins 563
Appendix G Solutions to Selected Problems 564
Appendix H Solutions to Self-Tests 568
Index 571
Online Modules
Module 1 Analytic Hierarchy Process M1-1
M1.1 Multifactor Evaluation Process M1-2
M1.2 Analytic Hierarchy Process M1-3
Judy Grim’s Computer Decision M1-3
Using Pairwise Comparisons M1-5
Evaluations for Hardware M1-5
Determining the Consistency Ratio M1-6
Evaluations for the Other Factors M1-7
Determining Factor Weights M1-8
Overall Ranking M1-9
Using the Computer to Solve Analytic Hierarchy Process Problems M1-9
M1.3 Comparison of Multifactor Evaluation and Analytic Hierarchy Processes M1-9
Summary M1-10
Glossary M1-10
Key Equations M1-10
Solved Problems M1-11
Self-Test M1-12
Discussion Questions and Problems M1-12
Bibliography M1-14
Appendix M1.1: Using Excel for the Analytic Hierarchy Process M1-14
Module 2 Dynamic Programming M2-1
M2.1 Shortest-Route Problem Solved Using Dynamic Programming M2-2
M2.2 Dynamic Programming Terminology M2-5
M2.3 Dynamic Programming Notation M2-7
M2.4 Knapsack Problem M2-8
Types of Knapsack Problems M2-8
Roller’s Air Transport Service Problem M2-8
Summary M2-13
Glossary M2-14
Key Equations M2-14
Solved Problem M2-14
Self-Test M2-16
Discussion Questions and Problems M2-17
Case Study: United Trucking M2-19
Bibliography M2-20
Module 3 Decision Theory and the Normal Distribution M3-1
M3.1 Break-Even Analysis and the Normal Distribution M3-1
Barclay Brothers Company’s New Product Decision M3-1
Probability Distribution of Demand M3-2
Using Expected Monetary Value to Make a Decision M3-4
M3.2 Expected Value of Perfect Information and the Normal Distribution M3-5
Opportunity Loss Function M3-5
Expected Opportunity Loss M3-5
Summary M3-7
Glossary M3-7
Key Equations M3-7
Solved Problems M3-7
Self-Test M3-8
Discussion Questions and Problems M3-9
Bibliography M3-10
Appendix M3.1: Derivation of the Break-Even Point M3-10
Appendix M3.2: Unit Normal Loss Integral M3-11
Module 4 Game Theory M4-1
M4.1 Language of Games M4-2
M4.2 The Minimax Criterion M4-2
M4.3 Pure Strategy Games M4-3
M4.4 Mixed Strategy Games M4-4
M4.5 Dominance M4-6
Summary M4-7
Glossary M4-7
Solved Problems M4-14
Self-Test M4-8
Discussion Questions and Problems M4-9
Bibliography M4-10
Module 5 Mathematical Tools: Determinants and Matrices M5-1
M5.1 Matrices and Matrix Operations M5-1
Matrix Addition and Subtraction M5-2
Matrix Multiplication M5-2
Matrix Notation for Systems of Equations M5-5
Matrix Transpose M5-5
M5.2 Determinants, Cofactors, and Adjoints M5-5
Determinants M5-5
Matrix of Cofactors and Adjoint M5-7
M5.3 Finding the Inverse of a Matrix M5-9
Summary M5-10
Glossary M5-10
Key Equations M5-10
Self-Test M5-11
Discussion Questions and Problems M5-11
Bibliography M5-12
Appendix M5.1: Using Excel for Matrix Calculations M5-13
Module 6 Calculus-Based Optimization M6-1
M6.1 Slope of a Straight Line M6-1
M6.2 Slope of a Nonlinear Function M6-2
M6.3 Some Common Derivatives M6-5
Second Derivatives M6-6
M6.4 Maximum and Minimum M6-6
M6.5 Applications M6-8
Economic Order Quantity M6-8
Total Revenue M6-8
Summary M6-9
Glossary M6-10
Key Equations M6-10
Solved Problems M6-10
Self-Test M6-11
Discussion Questions and Problems M6-11
Bibliography M6-12
Module 7 Linear Programming: The Simplex Method M7-1
M7.1 How to Set Up the Initial Simplex Solution M7-2
Converting the Constraints to Equations M7-2
Finding an Initial Solution Algebraically M7-3
The First Simplex Tableau M7-4
M7.2 Simplex Solution Procedures M7-7
The Second Simplex Tableau M7-8
Interpreting the Second Tableau M7-11
The Third Simplex Tableau M7-12
Review of Procedures for Solving LP Maximization Problems M7-14
M7.3 Surplus and Artificial Variables M7-15
Surplus Variables M7-15
Artificial Variables M7-15
Surplus and Artificial Variables in the Objective Function M7-16
M7.4 Solving Minimization Problems M7-16
The Muddy River Chemical Corporation Example M7-16
Graphical Analysis M7-17
Converting the Constraints and Objective Function M7-18
Rules of the Simplex Method for Minimization Problems M7-18
First Simplex Tableau for the Muddy River Chemical Corporation Problem M7-19
Developing a Second Tableau M7-20
Developing a Third Tableau M7-22
Fourth Tableau for the Muddy River Chemical Corporation Problem M7-23
Review of Procedures for Solving LP Minimization Problems M7-24
M7.5 Special Cases M7-25
Infeasibility M7-25
Unbounded Solutions M7-25
Degeneracy M7-26
More Than One Optimal Solution M7-27
M7.6 Sensitivity Analysis with the Simplex Tableau M7-27
High Note Sound Company Revisited M7-27
Changes in the Objective Function Coefficients M7-28
Changes in Resources or RHS Values M7-30
M7.7 The Dual M7-32
Dual Formulation Procedures M7-33
Solving the Dual of the High Note Sound Company Problem M7-33
M7.8 Karmarkar’s Algorithm M7-34
Summary M7-35
Glossary M7-35
Key Equations M7-36
Solved Problems M7-36
Self-Test M7-40
Discussion Questions and Problems M7-41
Bibliography M7-50
Module 8 Transportation, Assignment, and Network Algorithms M8-1
M8.1 The Transportation Algorithm M8-1
Developing an Initial Solution: Northwest Corner Rule M8-2
Stepping-Stone Method: Finding a Least-Cost Solution M8-3
Special Situations with the Transportation Algorithm M8-9
Unbalanced Transportation Problems M8-9
Degeneracy in Transportation Problems M8-10
More Than One Optimal Solution M8-12
Maximization Transportation Problems M8-13
Unacceptable or Prohibited Routes M8-13
Other Transportation Methods M8-13
M8.2 The Assignment Algorithm M8-13
The Hungarian Method (Flood’s Technique) 14
Making the Final Assignment M8-18
Special Situations with the Assignment Algorithm M8-18
Unbalanced Assignment Problems M8-18
Maximization Assignment Problems M8-19
M8.3 Maximal-Flow Problem M8-20
Maximal-Flow Technique M8-20
M8.4 Shortest-Route Problem M8-24
Shortest-Route Technique M8-24
Summary M8-26
Glossary M8-26
Solved Problems M8-26
Self-Test M8-33
Discussion Questions and Problems M8-33
Bibliography M8-43