HuilTIl
IT
T?
T?
n (5)'
Barry Render
Charles Harwood Professor of Management Science
Graduate School of Business, Rollins College
Ralph l o St'ajr, J L
Professor of Information and Management Sciences
Florida State University
Michael E.-Hanna
Professor of Decision Sciences
University of Houston—Clear Lake
Prentice
Pearson Education International
2
I
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Introduction to Quantitative
Analysis 21
Introduction 22
What Is Quantitative Analysis? 22,
The Quantitative Analysis Approach 23
Defining the Problem 23
Developing a Model 23
Acquiring Input Data 24
Developing a Solution 25
Testing the Solution 25
Analyzing the Results and Sensitivity
Analysis 25
Implementing the Results 27
The Quantitative Analysis Approach
and Modeling in the Real World 27
How to Develop a Quantitative Analysis
Model 27
The Advantages of Mathematical
Modeling 29
Mathematical Models Categorized by Risk 29
The Role of Computers and Spreadsheet
Models in the Quantitative Analysis
Approach 29
Possible Problems in the Quantitative
Analysis Approach 32
Defining the Problem 32
- Developing a Model 34
Acquiring Input Data 35
Developing a Solution 35
Testing the Solution 36
Analyzing the Results 36
Implementation—Not Just the Final
Step 37
Lack of Commitment and Resistance
to Change 37
Lack of Commitment by Quantitative
Analysts 37
Summary 38 Glossary 38 Key
Equations 38 Self-Test 38 Discussion
Questions and Problems 39 Case Study:
Food and Beverages at Southwestern
University Football Games 40
Bibliography 41
Probability Concepts
and Applications 43
2.1
Introduction 44
2.2 •-• Fundamental Concepts 44
Types of Probability 45
2.3
Mutually Exclusive and Collectively
Exhaustive Events 46
Adding Mutually Exclusive Events 48
Law of Addition for Events That Are Not
Mutually Exclusive 48
2.4
Statistically Independent Events 49
2.5
Statistically Dependent Events 50
2.6
Revising Probabilities with Bayes'
Theorem 52
General Form of Bayes' Theorem 54
2.7
Further Probability Revisions 54
2.8
Random Variables 56
2.9
Probability Distributions 57
Probability Distribution of a Discrete
Random Variable 57
s*
Expected Value of a Discrete Probability
Distribution 58
Variance of a Discrete Probability
Distribution 59
Probability Distribution of a Continuous
Random Variable 60
2.10
The Binomial Distribution 61
Solving Problems with the Binomial
Formula 62
Solving Problems with Binomial Tables 62
2.11
The Normal Distribution 64
Area Under the Normal Curve 64
Using the Standard Normal Table 66
Haynes Construction Company
Example 69
2.12
The F Distribution 71
2.13
The Exponential Distribution 72
2.14
The Poisson Distribution 73
Summary 74 Glossary 74 Key
Equations 75 Solved Problems 75
Self-Test 79 Discussion Questions and
Problems 80 Internet Homework
Problems 84 Case Study: WTVX 85
Bibliography 85
Contents
Appendix 2.1
Appendix 2.2
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Derivation of Bayes' Theorem 85
Basic Statistics Using Excel 86
4.4
Decision Analysis 89
Introduction 90
The Six Steps in Decision Making 90
Types of Decision-Making
'' •
Environments 92
Decision Making Under Uncertainty 93
4.5
Maximax 93
Maximin 94
Criterion of Realism (Hurwicz Criterion) 94
Equally Likely (Laplace) 96
Minimax Regret 96
Decision Making Under Risk 97
Expected Monetary Value 97
Expected Value of Perfect Information 98
Expected Opportunity Loss 99
Sensitivity Analysis 100
Using Excel QM to Solve Decision Theory
Problems 101
Decision Trees 103
Sensitivity Analysis 108
How Probability Values Are Estimated
by Bayesian Analysis 109
Calculating Revised Probabilities 109
Potential Problem in Using Survey
Results 111
Utility Theory 112
Measuring Utility and Constructing a Utility
Curve 112
Utility as a Decision-Making Criterion 115
Summary 118 Glossary 118 Key
Equations 119 Solved Problems 119
Self-Test 124 Discussion Questions and
Problems 125 Internet Homework Problems
131 Case Study: Starting Right Corporation
131 Case Study: Blake Electronics 132
Internet Case Studies 134 Bibliography 134
Appendix 3.1
Appendix 3.2
Appendix 3.3
4.1
4.2
4.3
Decision Models with QMfor
Windows 134
Decision Trees with QM
for Windows 135
Using Excel for Bayes' Theorem 135
Regression Models 137
Introduction 138
Scatter Diagrams 138
Simple Linear Regression 139
4.6
4.7
4.8
4.9
4.10
4.11
4.12
Appendix 4.1
Appendix 4.2
Appendix 4.3
CHAPTER s
5.1
5.2
5.3
5.4
5.5
Measuring the Fit of the Regression
Model 141
Coefficient of Determination 143
Correlation Coefficient 143
Using Computer Software
for Regression 144
Assumptions of the Regression
Model 146
Estimating the Variance 147
Testing the Model for Significance 148
Triple A Construction Example 149
The Analysis of Variance (ANOVA)
Table 150
Triple A Construction ANOVA Example 151
Multiple Regression Analysis 151
Evaluating the Multiple Regression
Model 152
Jenny Wilson Realty Example 153
Binary or Dummy Variables 154
Model Building 155
Nonlinear Regression 156
Cautions and Pitfalls in Regression
Analysis 159
Summary 160 Glossary 160 Key
Equations 160 Solved Problems 161
Self-Test 163 Discussion Questions and
Problems 164 Case Study: North-South
Airline 168 'Bibliography 169
Formulas for Regression
Calculations 169
Regression Models Using QM
for Windows 170
Accessing Regression Analysis
in Excel 2007 172
Forecasting 177
Introduction 178
Types of Forecasts 178
Time-Series Models 178
Causal Models 179
Qualitative Models 179
Scatter Diagrams and Time Series 180
Measures of Forecast Accuracy 182
Time-Series Forecasting Models 184
Decomposition of a Time Series 184
Moving Averages 185
Exponential Smoothing 188
Trend Projections 192
Seasonal Variations 194
Seasonal Variations with Trend 197
Contents
5.6
5.7
Appendix 5.1
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
The Decomposition Method of Forecasting
with Trend and Seasonal Components 199
Using Regression with Trend and Seasonal
Components 201
Monitoring and Controlling
Forecasts 204
Adaptive Smoothing 205
Using the Computer to Forecast 206
Summary 206 Glossary 207 Key
Equations 207 Solved Problems 208
Self-Test 210 Discussion Questions and
Problems 211 Internet Homework Problems
214 Case Study: Forecasting Attendance at
SWU Football Games 214 Internet Case
Study 215 Bibliography 215
6.9
Forecasting with QMfor Windows 215
6.12
6.13
Inventory Control Models 219
Introduction 220
Importance of Inventory Control 221
Decoupling Function 221
Storing Resources 221
Irregular Supply and Demand 221
Quantity Discounts 221
Avoiding Stockouts and Shortages 222
Inventory Decisions 222
Economic Order Quantity: Determining
How Much to Order 223
Inventory Costs in the EOQ Situation 225
Finding the EOQ 226
Sumco Pump Company Example 227
Purchase Cost of Inventory Items 228
Sensitivity Analysis with the EOQ
Model 229
Reorder Point: Determining When
to Order 230
EOQ Without the Instantaneous Receipt
Assumption 231 •
Annual Carrying Cost for Production Run
Model 232
Annual Setup Cost or Annual Ordering
l
Cost 232 '
Determining the Optimal Production
Quantity 233 *
Brown Manufacturing Example 233
Quantity Discount Models 236
Brass Department Store Example 237
Use of Safety Stock 240
ROP with Known Stockout Costs 241
Safety Stock with Unknown Stockout
Costs 244
6.10
6.11
Appendix 6.1
7.1
7.2
7.3
7.4
7.5
7.6
7.7
Single-Period Inventory Models 246
Marginal Analysis with Discrete
Distributions 247
Cafe du Donut Example 248
Marginal Analysis with the Normal
Distribution 249
Newspaper Example 249
ABC Analysis 251
Dependent Demand: The Case for
Material Requirements Planning 252
Material Structure Tree 252
Gross and Net Material Requirements
Plan 253
Two or More End Products 255
Just-in-Time Inventory Control 257
Enterprise Resource Planning 258
Summary 259 Glossary 259 Key
Equations 260 Solved Problems 261
Self-Test 263 Discussion Questions and
Problems 264 Internet Homework Problems
270 Case Study: Martin-Pullin Bicycle
Corporation 271 Internet Case Studies 271
Bibliography 271
Inventory Control with QM
for Windows 272
Linear Programming Models:
Graphical and Computer Methods 275
Introduction 276
Requirements of a Linear Programming
Problem 276
Basic Assumptions of LP 277
Formulating LP Problems 278
Flair Furniture Company 278
Graphical Solution to an LP Problem 280
Graphical Representation
of Constraints 280
Isoprofit Line Solution Method 285
Corner Point Solution Method 288
Solving Flair Furniture's LP Problem
Using QMfor Windows and Excel 290
Using QMfor Windows 290
Using ExcePs Solver Command to Solve LP
Problems 291
Solving Minimization Problems 296
Holiday Meal Turkey Ranch 296
Four Special Cases in LP 299
No Feasible Solution 299
Unboundedness 301
Redundancy 302
Alternate Optimal Solutions 302
10
Contents
7.8
Sensitivity Analysis 304
High Note Sound Company 304
r
Changes in the Objective Function
Coefficient 305
QM for Windows and Changes in Objective
Function Coefficients 306
Excel Solver and Changes in Objective
Function Coefficients 307
Changes in the Technological Coefficients 308
Changes in the Resources or Right-HandSide Values 309
QM for Windows and Changes in RightHand-Side Values 310
Excel Solver and Changes in Right-HandSide Values 310
Summary 312 Glossary 312 Solved
Problems 313 Self-Test 317 Discussion
Questions and Problems 318 Internet
Homework Problems 326 Case Study:
Mexicana Wire Works 326 Internet Case
Study 327 Bibliography 327
Appendix 7.1
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
Installing the Solver Add-in in Excel 2007 328
Linear Programming Modeling
Applications with Computer Analyses
in Excel and QM for Windows 331
Introduction 332
Marketing Applications 332
Media Selection 332
Marketing Research 334
Manufacturing Applications 336
Production Mix 336
Production Scheduling 337
Employee Scheduling Applications 341
Assignment Problems 341
Labor Planning 343
Financial Applications 345
Portfolio Selection 345
Transportation Applications 346
Shipping Problem 346
Truck Loading Problem 349
Transshipment Applications 351
Distribution Centers 351
Ingredient Blending Applications 353
Diet Problems 353
Ingredient Mix and Blending Problems 354
Summary 357 Self-Test 358 Problems
358 Internet Homework Problems 366
Case Study: Red Brand Canners 366
Case Study: Chase Manhattan Bank 368
Bibliography 369
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
Linear Programming: The Simplex
Method 371
Introduction 372
How to Set Up the Initial Simplex
Solution 372
Converting the Constraints to Equations 373
Finding an Initial Solution Algebraically 373
The First Simplex Tableau 374
Simplex Solution Procedures 378
The Second Simplex Tableau 379
Interpreting the Second Tableau 382
Developing the Third Tableau 383
Review of Procedures for Solving LP
Maximization Problems 386
Surplus and Artificial Variables 386
Surplus Variables 387
Artificial Variables 387
Surplus and Artificial Variables in the
Objective Function 388
Solving Minimization Problems 388
The Muddy River Chemical Company
Example 388
Graphical Analysis 389
Converting the Constraints and Objective
Function 390
Rules of the Simplex Method for
Minimization Problems 391
First Simplex Tableau for the Muddy River
Chemical Corporation Problem 391
Developing a Second Tableau 393
Developing a Third Tableau 394
Fourth Tableau for the Muddy River
Chemical Corporation Problem 396
Review of Procedures for Solving LP
Minimization Problems 397
Special Cases 398
Infeasibility 398
Unbounded Solutions 398
Degeneracy 399
More Than One Optimal Solution 400
Sensitivity Analysis with the Simplex
Tableau 400
High Note Sound Company Revisited 400
Changes inthe Objective Function
Coefficients 401
Changes in Resources or RHS Values 403
Sensitivity Analysis by Computer 405
The Dual 406
Dual Formulation Procedures 408
Solving the Dual of the High Note Sound
Company Problem 408
Contents
9.13
1©
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
10.15
Summary 466 Glossary 466 Key
Equations 467 Solved Problems 467
Self-Test 474 Discussion Questions and
Problems 474 Internet Homework Problems
483 Case Study: Andrew-Carter, Inc. 484
Case Study: Old Oregon Wood Store 485
Internet Case Studies 486 Bibliography 486
Karmarkar's Algorithm 410
Summary 410 Glossary 410 Key
Equation 411 Solved Problems 411
Self-Test 418 Discussion Questions and
Problems 419 Internet Homework Problems
427 Bibliography 427
Transportation and Assignment
Models 429
Introduction 430
Transportation Model 430
Assignment Model 430
Special-Purpose Algorithms 430
Setting Up a Transportation
Problem 431
Developing an Initial Solution: Northwest
Corner Rule 432
Stepping-Stone Method: Finding
a Least-Cost Solution 434
Testing the Solution for Possible
Improvement 435
Obtaining an Improved Solution 438
MODI Method 443
How to Use the MODI Approach 443
Solving the Executive Furniture Corporation
Problem with MODI 444
Vogel's Approximation Method: Another
Way to Find an Initial Solution 446
Unbalanced Transportation
Problems 449
Demand Less Than Supply 449
Demand Greater Than Supply 449
Degeneracy in Transportation
Problems 451
Degeneracy in an Initial Solution 451
Degeneracy During Later Solution
Stages 452
More Than One Optimal Solution 453
Maximization Transportation
Problems 453
Unacceptable.or Prohibited Routes 453
Facility Location Analysis 454
Locating a New Factory for Hardgrave
Machine Company 454
Assignment Model Approach 457
The Hungarian Method (Flood's
Technique) 458
Making the Final Assignment 462
Unbalanced Assignment Problems 464
Maximization Assignment
Problems 464
11
Appendix 10.1
Appendix 10.2
H
11.1
11.2
Using QM for Windows 486
Comparison of Simplex Algorithm
and Transportation Algorithm 488
Integer Programming, Goal
Programming, and Nonlinear
Programming 489
Introduction 490..
Integer Programming 490
Harrison Electric Company Example
of Integer Programming 491
Branch-and-Bound Method 492
Harrison Electric Company Revisited 493
Using Software to Solve the Harrison Integer
Programming Problem 496
Mixed-Integer Programming Problem
Example 498
11.3
Modeling with 0-1 (Binary) Variables 502
Capital Budgeting Example 502
Limiting the Number of Alternatives
Selected 503
Dependent Selections 503
Fixed-Charge Problem Example 503
Financial Investment Example 505
11.4
Goal Programming 507
Example of Goal Programming: Harrison
Electric Company Revisited 508
Extension to Equally Important Multiple
Goals 509
Ranking Goals with Priority Levels 510
Solving Goal Programming Problems
Graphically 511
Modified Simplex Method for Goal
Programming 514
Goal Programming with Weighted
Goals 516
11.5
Nonlinear Programming 518
Nonlinear Objective Function and Linear
Constraints 518
Both Nonlinear Objective Function and
Nonlinear Constraints 520
Linear Objective Function with Nonlinear
Constraints 520
12
Contents
Computational Procedures for Nonlinear
Programming 521
Summary 522 Glossary 522 Solved
Problems 523 Self-Test 525 Discussion
Questions and Problems 526 Internet
Homework Problems 531 Case Study:
Schank Marketing Research 531 Case
Study: Oakton River Bridge 531 Case
Study: Puyallup Mall 532 Bibliography 533
Appendix 13.1
12
12.1
12.2
12.3
12.4
Appendix 12.1
Network Models 535
Introduction 536
Minimal-Spanning Tree Technique 536
Maximal-Flow Technique 539
Shortest-Route Technique 543
Summary 547 Glossary 547 Solved
Problems 547 Self-Test 550 Discussion
Questions and Problems 551 Internet
Homework Problems 557 Case Study:
Binder's Beverage 557 Case Study:
Southwestern University Traffic Problems 558
Internet Case Study 559 Bibliography 559
4
14.1
14.2
14.3
Network Models with QM
for Windows 559
14.4
3
13.1
13.2
13.3
13.4
13.5
Project Management 563
Introduction 564
PERT/CPM 564
General Foundry Example of PERT/CPM
565
Drawing the PERT/CPM Network 567
Activity Times 567
How to Find the Critical Path 569
Probability of Project Completion 574
What PERT Was Able to Provide 576
Sensitivity Analysis and Project
Management 576
PERT/Cost 577
Planning and Scheduling Project Costs:
Budgeting Process 578
Monitoring and Controlling Project
Costs 581
. Project Crashing 583
General Foundary Example 584
Project Crashing with Linear
Programming 585
Other Topics in Project Management 588
Subprojects 589
Milestones 589
Resource Leveling 589
Software 589
14.5
14.6
14.7
14.8
14.9
Summary 589 Glossary 590 Key
Equations 590 Solved Problems 591
Self-Test 593 Discussion Questions and
Problems 594 Internet Homework Problems
599 Case Study: Southwestern University
Stadium Construction 599 Case Study:
Family Planning Research Center of Nigeria
600 Internet Case Studies 602
Bibliography 602
Project Management with QM
for Windows 602
Waiting Lines and Queuing Theory
Models 605
Introduction 606
Waiting Line Costs 606
Three Rivers Shipping Company Example 607
Characteristics of a Queuing System 608
Arrival Characteristics 608
Waiting Line Characteristics 610
Service Facility Characteristics 610
Identifying Models Using Kendall Notation
612
Single-Channel Queuing Model with
Poisson Arrivals and Exponential Service
Times (M/M/l) 614
Assumptions of the Model 614
Queuing Equations 615
Arnold's Muffler Shop Case 616
Enhancing the Queuing Environment 620
Multichannel Queuing Model with
Poisson Arrivals and Exponential Service
Times (M/M/m) 620
Equations for the Multichannel Queuing
"Model 621
Arnold's Muffler Shop Revisited 622
Constant Service Time Model
(M/D/l) 624
Equations for the Constant Service Time
Model 625
Garcia-Golding Recycling, Inc. 626
Finite Population Model (M/M/l with
Finite Source) 627
Equations for the Finite Population Model 627
Department of Commerce Example 628
Some General Operating Characteristic
Relationships 630
More Complex Queuing Models and the
Use of Simulation 630
Summary 631 Glossary 631 Key
Equations 632 Solved Problems 633
Self-Test 636 Discussion Questions and
Contents
Appendix 14.1
15
15.1
15.2
15.3
15.4
15.5
Problems 637 Internet Homework Problems
640 CaseStudy: New England Foundry 640
Case Study: Winter Park Hotel 642 Internet
CaseStudy 642 Bibliography 642
Using QMfor Windows 643
Simulation Modeling 645
Introduction, 646
Advantages and Disadvantages
of Simulation 646
Monte Carlo Simulation 648
Harry's Auto Tire Example 649
Using QM for Windows for Simulation 654
Simulation with Excel Spreadsheets 655
Simulation and Inventory Analysis 657
Simkin's Hardware Store 657
Analyzing Simkin's Inventory Costs 661
Simulation of a Queuing Problem 663
Port of New Orleans 663
16.4
Predicting Future Market Shares 694
16.5
Markov Analysis of Machine
Operations 695
16.6
Equilibrium Conditions 695
16.7
Absorbing States and the Fundamental
Matrix: Accounts Receivable
Application 699
Summary 704 Glossary 704
Key Equations 704 Solved Problems 705
Self-Test 709 Discussion Questions and
Problems 709 Internet Homework Problems
713 Case Study: Rentall Trucks 713
Internet Case Studies 714 Bibliography 714
Appendix 16.1
Appendix 16.2
Markov Analysis with QM
for Windows 715
Markov Analysis with Excel 716
CHAPTER u
Statistical Quality Control 719
Using Excel to Simulate the Port of New
Orleans Queuing Problem 665
17.1
17.2
17.3
15.6
Fixed Time Increment and Next Event
Increment Simulation Models 666
17.4
15.7
Simulation Model for a Maintenance
Policy 666
Three Hills Power Company 667
Cost Analysis of the Simulation 671
17.5
Building an Excel Simulation Model
for Three Hills Power Company 672
15.8
Two Other Types of Simulation Models 672
Operational Gaming 672
Systems Simulation 674
15.9
Verification and Validation 674
15.10
Role of Computers in Simulation 675
Summary 676 Glossary 676 Solved
Problems 676 Self-Test 680 Discussion
Questions and Problems 681 Internet
Homework Problems 686 CaseStudy:
Alabama Airlines 686 CaseStudy:
Statewide Development Corporation 687
Internet Case Studies 688 Bibliography 688
Appendix 17.1
16.2
Values of e~^ for Use in the Poisson
Distribution 747
F Distribution Values 748
Introduction 690
States and State Probabilities 690
Using POM-QM for Windows 750
Using Excel QM 754
Matrix of Transition Probabilities 693
Transition Probabilities for the Three
Grocery Stores 693
Using QMfor Windows for SPC 738
Areas under the Standard Normal
Curve 740
Binomial Probabilities 742
The Vector of State Probabilities for Three
Grocery Stores Example 691
16.3
Introduction 720
Defining Quality and TQM 720
Statistical Process Control 721
Variability in the Process 721
Control Charts for Variables 723
The Central Limit Theorem 723
Setting x -Chart Limits 724
Setting Range Chart Limits 726
Conrol Charts for Attributes 728
p-Charts 728
c-Charts 731
Summary 732 Glossary 732
Key Equations 732 Solved Problems 733
Self-Test 735 Discussion Questions and
Problems 735 Internet Homework
Problems 737 Internet Case Study 737
Bibliography 738
739
Markov Analysis 689
16.1
13
APPENDIX cs
Solutions to Selected Problems 755
Solutions to Self-Tests 759
14
Contents
M3.3
1
Ml.l
Ml.2
Ml.3
M1.4
Appendix Ml.l
2
M2.1
M2.2
M2.3
M2.4
M2.5
M3.1
M3.2
Analytic Hierarchy Process Ml-1
Introduction Ml-2
Multifactor Evaluation Process Ml -2
Analytic Hierarchy Process Ml -4
Judy Grim's Computer Decision Ml-4
Using Pairwise Comparisons Ml-5
Evaluations for Hardware Ml-7
Determining the Consistency Ratio Ml-7
Evaluations for the Other Factors Ml-9
Determining Factor Weights Ml-10
Overall Ranking Ml-10
Using the Computer to Solve Analytic
Hierarchy Process Problems Ml-10
Comparison of Multif actor Evaluation
and Analytic Hierarchy Processes Ml-11
Summary Ml-12 Glossary Ml-12 Key
Equations Ml-12 Solved Problems Ml-12
Self-Test Ml-14 Discussion Questions and
Problems Ml-14 Bibliography Ml-16
Using Excel for the Analytic Hierarchy
Process Ml-16
Dynamic Programming M2-1
Introduction M2-2
Shortest-Route Problem Solved by
Dynamic Programming M2-2
Dynamic Programming
Terminology M2-6
Dynamic Programming Notation M2-8 „
Knapsack Problem M2-9
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
Decision Theory and the Normal
Distribution M3-1
Introduction M3-2
Break-Even Analysis and the Normal
Distribution M3-2
Barclay Brothers' New Product
Decision M3-2
Probability Distribution of Demand M3-3
Appendix M3.1
Appendix M3.2
M4.1
M4.2
M4.3
M4.4
M4.5
M4.6
Appendix M4.1
M5.1
M5.2
M5.3
M5.4
Appendix M5.1
Using Expected Monetary Value to Make a
Decision M3-5
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
Derivation of the Break-Even
Point M3-12
Unit Normal Loss Integral M3-13
Game Theory M4-1
Introduction M4-2
Language of Games M4-2
The Minimax Criterion M4-3
Gross and Net Material Requirements
Plan 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
Game Theory
with QMfor Windows M4-12
Mathematical Tools: Determinants
and Matrices M5-1
Introduction M5-2
Matrices and Matrix
Operations M5-2
Matrix Addition and Subtraction M5-2
Matrix Multiplication M5-3
Matrix Notation for Systems
of Equations M5-6
Matrix Transpose M5-6
Determinants, Cofactors,
andAdjoints
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
Contents
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
Second Derivatives M6-6
M6.5
Maximum and Minimum M6-6
M6.6
15
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