A
Analysis
ement
GLOBAL EDITION
ELEVENTH EDITION
Charles Harwood Professor of Management Science
Graduate School of Business, Rollins College
Professor of Information and Management Sciences,
Florida State University
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
CONTENTS
PREFACE 1 5
CHAPTER 1
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 25
The Quantitative Analysis Approach and
Modeling in the Real World 27
How to Develop a Quantitative Analysis
Model 27
,
The Advantages of Mathematical Modeling 28
Mathematical Models Categorized by Risk 28
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 33
Acquiring Input Data 33
Developing a Solution 34
Testing the Solution 34
Analyzing the Results 34
Implementation—Not Just the Final Step 35
Lack of Commitment and Resistance to Change 35
Lack of Commitment by Quantitative Analysts 35
Summary 36 Glossary 36 Key Equations 36
Self-Test 37 Discussion Questions and Problems
37 Case Study: Food and Beverages at Southwestern
University Football Games 39 Bibliography 39
CHAPTER 2
2.1
2.2
2.3
Probability Concepts and Applications 41
Introduction 42
Fundamental Concepts 42
Types of Probability 43
Mutually Exclusive and Collectively
Exhaustive Events 44
Appendix 2.1
Appendix 2.2
Adding Mutually Exclusive Events 46
Law of Addition for Events That Are Not
Mutually Exclusive 46
Statistically Independent Events 47
Statistically Dependent Events 48
Revising Probabilities with Bayes'Theorem 49
General Form of Bayes' Theorem 51
Further Probability Revisions 52
Random Variables 53
Probability Distributions 54
Probability Distribution of a Discrete Random
Variable 54
Expected Value of a Discrete Probability
Distribution 55
Variance of a Discrete Probability Distribution 56
Probability Distribution of a Continuous
Random Variable 56
The Binomial Distribution 58
Solving Problems with the Binomial Formula 59
Solving Problems with Binomial Tables 60
The Normal Distribution 61
Area Under the Normal Curve 62
Using the Standard Normal Table 62 s
Haynes Construction Company Example 64
The Empirical Rule 68
The F Distribution 68
The Exponential Distribution 70
Arnold's Muffler Example 71
The Poisson Distribution 72
Summary 74 Glossary 74 Key Equations 75
Solved Problems 76 Self-Test 79 Discussion
Questions and Problems 80 Case Study:
WTVX 85 Bibliography 86
Derivation of Bayes' Theoreni 86
Basic Statistics Using Excel 86
CIWTIIR3
3.1
3.2
3.3
3.4
Decision Analysis 89
Introduction 90
The Six Steps in Decision Making 90
Types of Decision-Making Environments 91
Decision Making Under Uncertainty 92
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
Optimistic 92
Pessimistic 93
Criterion of Realism (Hurwicz Criterion) 93
CONTENTS
3.5
Equally Likely (Laplace) 94
Minimax Regret 94
Appendix 4.2
Decision Making Under Risk 96
Appendix 4.3
Expected Monetary Value 96
Expected Value of Perfect Information 97
Expected Opportunity Loss 98
Sensitivity Analysis 99
3.6
3.7
3.8
Appendix 3.1
Appendix 3.2
Using Excel QM to Solve Decision Theory
Problems 100
Decision Trees 101
Efficiency of Sample Information 106
Sensitivity Analysis 106
How Probability Values are Estimated by
Bayesian Analysis 107
Calculating Revised Probabilities 107
Potential Problem in Using Survey Results 109
Utility Theory 110
Measuring Utility and Constructing a Utility
Curve 111
Utility as a Decision-Making Criterion 113
Summary 115 Glossary 115 Key Equations 116
Solved Problems 117 Self-Test 122 Discussion
Questions and Problems 123 Case Study:
Starting Right Corporation 130 Case Study:
Blake Electronics 131 Bibliography 133
CHAPTER 5
5.1
5.2
5.3
5.4
5.5
Decision Models with QM for Windows 133
Decision Trees with QMfor Windows 134
5.6
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
Appendix 4.1
Regression Models 135
Introduction 136
Scatter Diagrams 136
Simple Linear Regression 137
Measuring the Fit of the Regression Model 139
Coefficient of Determination 140
Correlation Coefficient 141
Using Computer Software for Regression 142
Assumptions of the Regression Model 143
Estimating the Variance 145
Testing the Model for Significance 145
Triple A Construction Example 147
The Analysis of Variance (ANOVA) Table 147
Triple A Construction ANOVA Example 148
Multiple Regression Analysis 148
Evaluating the Multiple Regression Model 149
Jenny Wilson Realty Example 150
Binary or Dummy Variables 151
Model Building 152 •
Nonlinear Regression 153
Cautions and Pitfalls in Regression
Analysis 156
Summary 156 Glossary 157 Key Equations 157
Solved Problems 158 Self-Test 160 Discussion
Questions and Problems 160 Case Study:
North-South Airline 165 Bibliography 166
Formulas for Regression Calculations 166
Regression Models Using QMfor
Windows 168
Regression Analysis in Excel QM or
Excel 2007 170
Forecasting 173
Introduction 174
Types of Forecasts 174
Time-Series Models 174
Causal Models 174
Qualitative Models 175
Scatter Diagrams and Time Series 176
Measures of Forecast Accuracy 178
Time-Series Forecasting Models 180
Components of a Time Series 180
Moving Averages 181
Exponential Smoothing 184
Using Excel QM for Trend-Adjusted Exponential
Smoothing 189
Trend Projections' 189
Seasonal Variations 191
Seasonal Variations with Trend 193
The Decomposition Method of Forecasting with
Trend and Seasonal Components 195
Using Regression with Trend and Seasonal
Components 197
Monitoring and Controlling Forecasts 199
Adaptive Smoothing 201
Summary 201 Glossary 202 Key Equations 202
Solved Problems 203 Self-Test 204 Discussion
Questions and Problems 205 Case Study:
Forecasting Attendance at SWU Football
Games 209
Case Study: Forecasting Monthly Sales 210
Bibliography 211
Appendix 5.1
Forecasting with QMfor Windows 211
CHAPITER 6
6.1
6.2
Inventory Control Models 215
Introduction 216
Importance of Inventory Control 216
Decoupling Function 217
Storing Resources 217
Irregular Supply and Demand 217
Quantity Discounts 217
Avoiding Stockouts and Shortages 217
6.3
6.4
6.5
Inventory Decisions 217
Economic Order Quantity: Determining How
Much to Order 219
Inventory Costs in the EOQ Situation 220
Finding the EOQ 222
Sumco Pump Company Example 222
Purchase Cost of Inventory Items 223
Sensitivity Analysis with the EOQ Model 224
Reorder Point: Determining When to Order 225
CONTENTS
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
EOQ Without the Instantaneous Receipt
Assumption 226
Annual Carrying Cost for Production Run
Model 227
Annual Setup Cost or Annual Ordering Cost 228
Determining the Optimal Production Quantity 228
Brown Manufacturing Example 228
Quantity Discount Models 230
Brass Department Store Example 232
Use of Safety Stock 233
Single-Period Inventory Models 240
Marginal Analysis with Discrete Distributions 241
Cafe du Donut Example 242
Marginal Analysis with the Normal
Distribution 242
Newspaper Example 243
ABC Analysis 245
Dependent Demand: The Case for Material
Requirements Planning 246
Material Structure Tree 246
Gross and Net Material Requirements Plan 247
Two or More End Products 249
Just-in-Time Inventory Control 250
Enterprise Resource Planning 252
Summary 252 Glossary 252 Key Equations 253
Solved Problems 254 Self-Test 257 Discussion
Questions and Problems -258 Case Study:
Martin-Pullin Bicycle Corporation 265
Bibliography 266
Appendix 6.1
Inventory Control with QMfor Windows 266
CHAPTER 7
7.1
Linear Programming Models: Graphical
and Computer Methods 269
Introduction 270
7.2
Requirements of a Linear Programming
7.8
Appendix 7.1
CHAPTERS
8.1
8.2
8.3
8.4
8.5
8.6
Prnhlem ?7fl
iiuuieiii
7.3
7.4
7.5
z./u
Formulating LP Problems 271
Flair Furniture Company 272
Graphical Solution to an LP Problem 273
Graphical Representation of Constraints 273
Isoprofit Line Solution Method 277
Corner Point Solution Method 280
Slack and Surplus 282
Solving Flair Furniture's LP Problem Using
QMFor Windows and Excel 283
Using QM for Windows 283
Using Excel's Solver Command to Solve
1 P Prr»hlpmc 784
Lr
7.6
7.7
rlOUlCIlla
8.7
Linear Programming Applications 327
Introduction 328
Marketing Applications 328
Media Selection 328
Marketing Research 329
Manufacturing Applications 332
Production Mix 332
Production Scheduling 333
Employee Scheduling Applications 337
Labor Planning 337
Financial Applications 339
Portfolio Selection 339
Truck Loading Problem 342
Ingredient Blending Applications 344
Diet Problems 344
Ingredient Mix and Blending Problems 345
Transportation Applications 347
Shipping Problem 347
Summary 350 Self-Test 350 Problems 351
Case Study: Chase Manhattan Bank 359
Bibliography 359
CHAPTER 9
9.1
9.2
^1O4
Solving Minimization Problems 290
Holiday Meal Turkey Ranch 290
Four Special Cases in LP 294
No Feasible Solution 294
Unboundedness 295
Redundancy 295
Alternate Optimal Solutions 296
Sensitivity Analysis 296
High Note Sound Company 298
Changes in the Objective Function Coefficient 298
QM for Windows and Changes in Objective
Function Coefficients 299
Excel Solver and Changes in Objective Function
Coefficients 300
Changes in the Technological Coefficients 300
Changes in the Resources or Right-Hand-Side
Values 302
QM for Windows and Changes in Right-HandSide Values 303
Excel Solver and Changes in Right-Hand-Side
Values 305
Summary 305 Glossary 305 Solved
Problems 306 Self-Test 311 Discussion
Questions and Problems 312 Case Study:
Mexicana Wire Works 320 Bibliography 322
Excel QM 322
9.3
9.4
Transportation and Assignment
Models 361
Introduction 362
The Transportation Problem 362
Linear Program for the Transportation
Example 362
A General LP Model for Transportation
Problems 363
The Assignment Problem 364
Linear Program for Assignment Example 365
The Transshipment Problem 366
Linear Program for Transshipment Example 367
10
CONTENTS
9.5
Linear Objective Function with Nonlinear
Constraints 434
Summary 435 Glossary 435
Solved Problems 436 Self-Test 439 Discussion
Questions and Problems 439 Case Study:
Schank Marketing Research 445 Case Study:
Oakton River Bridge 445 Bibliography 446
The Transportation Algorithm 368
Developing an Initial Solution: Northwest
Corner Rule 370
Stepping-Stone Method: Finding a Least-Cost
Solution 372
9.6
9.7
9.8
9.9
Appendix 9.1
CHAPTER 10
10.1
10.2
10.3
10.4
10.5
Special Situations with the Transportation
Algorithm 378
Unbalanced Transportation Problems 378
Degeneracy in Transportation Problems 379
More Than One Optimal Solution 382
Maximization Transportation Problems 382
Unacceptable or Prohibited Routes 382
Other Transportation Methods 382
Facility Location Analysis 383
Locating a New Factory for Hardgrave Machine
Company 383
The Assignment Algorithm 385
The Hungarian Method (Flood's Technique) 386
Making the Final Assignment 389
Special Situations with the Assignment
Algorithm 391
Unbalanced Assignment Problems 391
Maximization Assignment Problems 391
Summary 393 Glossary 393 Solved
Problems 394 Self-Test 400 Discussion
Questions and Problems 401 Case Study:
Andrew-Carter, Inc. 411 Case Study: Old
Oregon Wood Store 412 Bibliography 413
Using QM for Windows 413
Integer Programming, Goal Programming,
and Nonlinear Programming 415
Introduction 416
Integer Programming 416
Harrison Electric Company Example of Integer
Programming 416
Using Software to Solve the Harrison Integer
Programming Problem 418
Mixed-Integer Programming Problem
Example 420
Modeling with 0-1 (Binary) Variables 422
Capital Budgeting Example 422
Limiting the Number of Alternatives Selected 424
Dependent Selections 424
Fixed-Charge Problem Example 424
Financial Investment Example 425
Goal Programming 426
Example of Goal Programming: Harrison Electric
Company Revisited 428
Extension to Equally Important Multiple Goals 429
Ranking Goals with Priority Levels 429
Goal Programming with Weighted Goals 430
Nonlinear Programming 431
Nonlinear Objective Function and Linear
Constraints 432
Both Nonlinear Objective Function and
Nonlinear Constraints 433
11.1
11.2
11.3
11.4
12.1
12.2
12.3
12.4
12.5
Appendix 12.1
Network Models 449
Introduction 450
Minimal-Spanning Tree Problem 450
Maximal-Flow Problem 453
Maximal-Flow Technique 453
Linear Program for Maximal Flow 458
Shortest-Route Problem 459
Shortest-Route Technique 459
Linear Program for Shortest-Route Problem 461
Summary 464 Glossary 464
Solved Problems 465 Self-Test 467
Discussion Questions and Problems 468
Case Study: Binder's Beverage 475 Case Study:
Southwestern University Traffic Problems 476
Bibliography 477
Project Management 479
Introduction 480
PERT/CPM 480
General Foundry Example of PERT/CPM 481
Drawing the PERT/CPM Network 482
Activity Times 483
How to Find the Critical Path 484
Probability of Project Completion 489
What PERT Was Able to Provide 491
Using Excel QM for the General Foundry
Example 491
Sensitivity Analysis and Project Management 491
PERT/Cost 493
Planning and Scheduling Project Costs:
Budgeting Process 493
Monitoring and Controlling Project Costs 497
Project Crashing 499
General Foundary Example 500
Project Crashing with Linear Programming 500
Other Topics in Project Management 504
Subprojects 504
Milestones 504
Resource Leveling 504
Software 504
Summary 504 Glossary 505
Key Equations 505 Solved Problems 506
Self-Test 507 Discussion Questions and
Problems 508 Case Study: Project Management:
Cost, Quality and Time Trade-Off in a Thai
Construction Company 514 Case Study: Family
Planning Research Center of Nigeria 515
Bibliography 516
Project Management with QMfor Windows 517
CONTENTS
CHAPTER 13
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
Waiting Lines and Queuing Theory
Models 519
Introduction 520
Waiting Line Costs 520
Three Rivers Shipping Company Example 521
Characteristics of a Queuing System 521
Arrival Characteristics 521
Waiting Line Characteristics 522
Service Facility Characteristics 523
Identifying Models Using Kendall Notation 523
Single-Channel Queuing Model with Poisson
Arrivals and Exponential Service Times
(M/M/l) 526
Assumptions of the Model 526
Queuing Equations 526
Arnold's Muffler Shop Case 527
Enhancing the Queuing Environment 531
Multichannel Queuing Model with Poisson
Arrivals and Exponential Service Times
(M/M/m) 531
Equations for the Multichannel Queuing
Model 532
Arnold's Muffler Shop Revisited 532
Constant Service Time Model (M/D/l)
534
Equations for the Constant Service Time
Model 535
Garcia-Golding Recycling, Inc. 535
Finite Population Model (M/M/l with Finite
Source) 536
Equations for the Finite Population Model 537
Department of Commerce Example 537
Some General Operating Characteristic
Relationships 539
More Complex Queuing Models and
the Use of Simulation 539
Summary 540 Glossary 540 Key Equations
541 Solved Problems 542 Self-Test 544
Discussion Questions and Problems 545 Case
Study: New England Foundry 550 Case Study:
Winter Park Hotel 551 Bibliography 552
Appendix 13.1
Using QMfor Windows 552
CHAPTER 1 4
Simulation Modeling 553
14.1
14.2
14.3
14.4
14.5
Introduction 554
Advantages and Disadvantages
of Simulation 555
Monte Carlo Simulation 556
Harry's Auto Tire Example 556
Using QM for Windows for Simulation 561
Simulation with Excel Spreadsheets 561
14.6
14.7
B
15.1
15.2
15.3
15.4
15.5
15.6
15.7
Markov Analysis 593
Introduction 594
States and State Probabilities 594
The Vector of State Probabilities for Three
Grocery Stores Example 595
Matrix of Transition Probabilities 596
Transition Probabilities for the Three Grocery
Stores 597
Predicting Future Market Shares 597
Markov Analysis of Machine Operations 598
Equilibrium Conditions 599
Absorbing States and the Fundamental
Matrix: Accounts Receivable Application 602
Summary 606 Glossary 607 Key Equations
607 Solved Problems 607 Self-Test 611
'
Discussion Questions and Problems 611
Case Study: Rentall Trucks 615 Bibliography 617
Markov Analysis with QMfor Windows 6\
Markov Analysis With Excel 619
CHAPTER 1 6
16.1
16.2
16.3
Statistical Quality Control 621
Introduction 622
Defining Quality and TQM 622
Statiscal Process Control 623
16.5
Variability in the Process 623
Control Charts for Variables 625
The Central Limit Theorem 625
Setting x-Chart Limits 626
Setting Range Chart Limits 629
Control Charts for Attributes 630
p-Charts 630
c-Charts 633
Summary 634 Glossary 634 Key Equations
634 Solved Problems 635 Self-Test 636
Discussion Questions and Problems 637
Bibliography 639
Simulation and Inventory Analysis 565
Simkin's Hardware Store 565
Analyzing Simkin's Inventory Costs 568
Simulation of a Queuing Problem 570
Port of New Orleans 570
Using Excel to Simulate the Port of New Orleans
Queuing Problem 571
Simulation Model for a Maintenance
Policy 573
Three Hills Power Company 573
Cost Analysis of the Simulation 577
Other Simulation Issues 577
Two Other Types of Simulation Models 577
Verification and Validation 579
Role of Computers in Simulation 580
Summary 580 Glossary 580
Solved Problems 581 Self-Test 584
Discussion Questions and Problems 585
Case Study: Alabama Airlines 590 Case Study:
Statewide Development Corporation 591
Bibliography 592
Appendix 15.1
Appendix 15.2
16.4
Appendix 16.1
11
Using QMfor Windows for SPC 639
12
CONTENTS
APPENDICES 6 4 1
APPENDIX A
Areas Under the Standard
Normal Curve 642
APPENDIX B
Binomial Probabilities 644
APPENDIX C
Values of e~A for use in the Poisson
Distribution 649
APPENDIX D
^Distribution Values 650
APPENDIX E
Using POM-QM for Windows 652
APPENDIX f
Using Excel QM and Excel Add-Ins 655
APPENDIX G
Solutions to Selected Problems 656
APPENDIX H
Solutions to Self-Tests 659
MODULE 3
M3.1
M3.2
M3.3
~
INDEX 661
ONLINE MODULES
MODULE 1
Ml.l
Ml.2
Ml.3
Ml.4
Appendix Ml. 1
MODULE 2
M2.1
M2.2
M2.3
M2.4
M2.5
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 M1 -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 SelfTest 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 using 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
Appendix M3.1
Appendix M3.2
Decision Theory and the Normal
Distribution M3-1
Introduction M3-2
Break-Even Analysis and the Normal
Distribution 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
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
MODULI 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
Appendix M4.1
Game Theory
with QM for Windows M4-12
MODULE 5
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
M5.1
M5.2
M5.3
M5.4
/
CONTENTS
AppendixM5.1
MODULE 6
M6.1
M6.2
M6.3
M6.4
M6.5
M6.6
MODULE 7
M7.1
M7.2
M7.3
M7.4
M7.5
M7.6
M7.7
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
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
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
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
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
M7.8
M7.9
M7.10
M7.11
M7.12
M7.13
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
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 Glossary M7-39 Key
Equation M7-40 Solved Problems M7-40
Self-Test M7-42 Discussion Questions and
Problems M7-45 Bibliography M7-54
13