Introduction to Modeling
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Introduction 2
A Waiting-Line Example 3
Modeling versus Models 6
The Seven-Step Modeling Process 7
A Successful Management Science Application
Why Study Mangement Science? 15
Software Included in This Book 16
Conclusion 18
12
2.1 Introduction 20
2.2
2.3
2.4
2.5
2.6
2.7
Basic Spreadsheet Modeling: Concepts and Best Practices 20
Cost Projections 25
Breakeven Analysis 30
Ordering with Quantity Discounts and Demand Uncertainty 38
Decisions Involving the Time Value of Money 44
Conclusion 50
A P P E N D I X Tips for Editing and Documenting Spreadsheets 54
3.1 Introduction 58
3.2 Introduction to Optimization 58
3.3 A Two-Variable Model 60
3.4 Sensitivity Analysis 70
3.5 Properties of Linear Models 78
3.6 Infeasibility and Unboundedness 81
VIII
3.7 A Product Mix Model 83
3.8 A Multiperiod Production Model 93
3.9 A Comparison of Algebraic and Spreadsheet Models
3.10 A Decision Support System 102
3.11 Conclusion 104
A P P E N D I X Information on Solvers 110
C A S E 3.1 Shelby Shelving 111
C A S E 3 . 2 Sonoma Valley Wines 113
Linear Programming Models
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
115
Introduction 116
Advertising Models 117
Static Workforce Scheduling Models
Aggregate Planning Models 134
Blending Models 143
Production Process Models 149
Financial Models 155
Conclusion 166
126
CASE 4. I Amarco, Inc. 177
CASE 4 . 2 American Office Systems, Inc.
Network Models
180
185
5.1 Introduction 186
5.2 Transportation Models 187
5.3 Assignment Models 199
5.4 Minimum Cost Network Flow Models 205
5.5 Shortest Path Models 213
5.6 Project Scheduling Models 222
5.7 Conclusion 234
C A S E 5.1
International Textile Company, Ltd.
6
101
242
Optimization Models with Integer Variables
245
6.1 Introduction 246
6.2 Overview of Optimization with Integer Variables 247
6.3 Capital Budgeting Models 248
6.4 Fixed-Cost Models 255
6.5 Set Covering and Location-Assignment Models 267
6.6 Conclusion 285
C A S E 6.1
Giant Motor Company 293
Contents
ix
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Introduction 296
Basic Ideas of Nonlinear Optimization 297
Pricing Models 301
Advertising Response and Selection Models 317
Facility Location Models 327
Models for Rating Sports Teams 331
Portfolio Optimization Models 336
Conclusion 345
CASE 7.1
GMS Stock Hedging
351
8 I Decision Making under Uncertainty 353
8
Introduction 354
Elements of a Decision Analysis 355
The PrecisionTree Add-in 368
Bayes' Rule 380
Multistage Decision Problems 384
Incorporating Attitudes Toward Risk 399
Conclusion 405
CASE 8.1
Jogger Shoe Company
418
CASE 8.2
Westhouser Paper Company
CASE 8.3
Biotechnical Engineering
419
420
9.1 Introduction 424
9.2 Real Applications of Simulation 425
9.3 Probability Distributions for Input Variables 426
9.4 Simulation with Built-in Excel Tools 444
9.5 Introduction to @Risk 455
9.6 The Effects of Input Distributions on Results 470
9.7 Conclusion 478
APPENDIX
X
Contents
Creating Histograms with Excel Tools
CASE 9.1
Ski Jacket Production
CASE 9.2
Ebony Bath Soap
488
487
485
10.1 Introduction 490
10.2 Operations Models 491
10.3 Financial Models 510
10.4 Marketing Models 524
10.5 Simulating Games of Chance 537
10.6 Conclusion 544
C A S E I 0 . I College Fund Investment 550
C A S E 1 0 . 2 Bond Investment Strategy 551
11
Queueing Models
553
11.1 Introduction 554
11.2 Elements of Queueing Models 556
11.3 The Exponent! al Distribution 559
11.4 Important Queueing Relationships 564
11.5 Analytical Queueing Models 566
11.6 Queueing Simulation Models 587
11.7 Conclusion 596
CASE M . I
Catalog Company Phone Orders
C A S E 1 1 . 2 Pacific National Bank 603
12
Regression and Forecasting Models
601
605
12.1 Introduction 606
12.2 Overview of Regression Models 607
12.3 Simple Regression Models 611
12.4 Multiple Regression Models 622
12.5 Overview of Time Series Models 632
12.6 Moving Averages Models 637
12.7 Exponential Smoothing Models 642
12.8 Conclusion 657
CASE 12.1
Demand for French Bread at Howie's
663
CASE
12.2
Forecasting Overhead at Wagner Printers
CASE
12.3
Arrivals at the Credit Union
664
665
References 666
Index 669
Contents
XI