ContentsCHAPTER ONE Introduction 1
F Answers to Even-Numbered Problems F- 1
E References and Bibliography E- 1
D Matnx Notation and Operations D- 1
C Values of e-λC- 1
B Random Digits B- 1
Appendixes A- 1
G Solutions to Self-Test Problems G- 1
A Areas for the Standard Normal Distribution A- 2
1.1 Problem Sotving and Decision Making 2
1.2 Quantitative Analvsis and Decision Making 3
1.3 Guantitative Analysis 5
Model Development 6
Data Preparation 9
Model Solution 10
Report Generation 11
A Note Regarding Implementation 11
Revenue and Volume Models 12
Cost and Volume Models 12
1.4 Models of Cost,Revenue,and Profit 12
Profit and Volume Models 13
Break-Even Analysis 13
1.5 Management Science in Practice 14
Management Science Techniques 14
Methods Used Most Frequently 15
Glossary 17
Summary 17
Problems 18
Appendix 1.1 Spreadsheets for Management Science 21
Appendix 1.2 The Management Scientist Software Package 22
Management Science in Practice:Mead Corporation 25
CHAPTER TWO Linear Programming:The Graphical Method 27
2.1 A Simple Maximization Problem 28
The Objective Function 29
The Constraints 30
Mathematical Statement of the Par,Inc.,Problem 31
2.2 Graphical Solution 32
A Note on Graphing Lines 41
Summary of the Graphical Solution Procedure for Maximization Problems 43
Slack Variables 43
2.3 Extreme Points and the Optimal Solution 45
2.4 A Simple Minimization Problem 47
Surplus Variables 50
Summary of the Graphical Solution Procedure for Minimization Problems 50
Alternative Optimal Solutions 52
2.5 Special Cases 52
Infeasibility 53
Unbounded 54
2.6 Introduction to Sensitivity Analysis 56
Obiective Function Coefficients 57
2.7 Graphical Sensitivity Analysis 57
Right-Hand Sides 62
Glossary 64
Summary 64
Problems 65
Case Problem:Production Strategy 79
Case Problem:Advertising Strategy 79
CHAPTER THREE Linear Programming:Formulation,Computer Solution,and Interpretation 81
3.1 Computer Solution of Linear Programs 81
Interpretation of Computer Output 82
Simultaneous Changes 85
Interpretation of Computer Output—A Second Example 87
Cautionary Note on the Interpretation of Dual Prices 89
3.2 More Than Two Decision Variables 90
The Modified Par,Inc.,Problem 90
The Bluegrass Farms Problem 95
Formulation of the Bluegrass Farms Problem 95
Computer Solution and Interpretation for the Bluegrass Farms Problem 97
Guidelines for Model Formulation 99
3.3 Modeling 99
Management Science in Action:An Optimal Wood Procurement Policy 100
The Electronic Communications Problem 101
Formulation of the Electronic Communications Problem 102
Computer Solution and Interpretation for the Electronic Communications Problem 103
Management Science in Action:Using Linear Programming for Traffic Control 106
Glossary 107
Summary 107
Problems 108
case Problem:Product Mix 121
Case Problem:Truck Leasing Strategy 122
Appendix 3.2:Solving Linear Programs with LINDO/PC 123
Appendix 3.1:Solving Linear Programs with The Management Scientist 123
Appendix 3.3:Spreadsheet Solution of Linear Programs 126
Management Science in Practice:Eastman Kodak 130
CHAPTER FOUR Linear Programming Applications 132
4.1 Marketing Applications 132
Media Selection 132
Marketing Research 136
Portfolio Selection 139
4.2 Financial Applications 139
Financial Planning 143
Management Science in Action:Using Linear Programming for Optimal Lease Structuring 143
A Make-or-Buy Decision 147
4.3 Production Management Applications 147
Production Scheduling 150
Management Science in Action:Libbey-Owens-Ford 157
Work-Force Assignment 157
4.4 Blending Problems 161
Evaluating the Performance of Hospitals 166
4.5 Data Envelopment Analvsis 166
An Overview of the DEA Approach 167
The DEA Linear Programming Model 168
Summary of the DEA Approach 172
Summary 173
Problems 174
Case Problem:Environmental Protection 187
Case Problem:Investment Strategy 189
Case Problem:Textile Mill Scheduling 190
Appendix 4.1 Spreadsheet Solution of Linear Programs 191
Management Science in Practice:Marathon Oil Company 193
CHAPTET FIVE Linear Programming:The Simplex Method 195
5.1 An Algebraic Overview of the Simplex Method 195
Management Science in Action:Fleet Assignment at Delta Air Lines 196
Algebraic Properties of the Simplex Method 197
Determining a Basic Solution 197
5.2 Tableau Form 198
Basic Feasible Solutions 198
5.3 Setting Up the Initial Simplex Tableau 200
5.4 Improving the Solution 203
5.5 Calculating the Next Tableau 205
Interpreting the Results of an Iteration 207
Moving toward a Better Solution 208
Interpreting the Optimal Solution 210
Summary of the Simplex Method 211
5.6 Tableau Form:The General Case 212
Greater-Than-or-Equal-to Constraints 213
Equality Constraints 217
Eliminating Negative Right-Hand-Side Values 217
Summary of the Steps to Create Tableau Form 218
5.7 Solving a Minimization Problem 220
5.8 Special Cases 222
Infeasibility 222
Unboundedness 223
Altemative Optimal Solutions 224
Degeneracy 226
Summary 227
Problems 229
Glossary 229
Objective Function Coefficients 239
6.1 Sensitivity Analysis with the Simplexrableau 239
CHAPTER SIX Simplex-Based Sensitivity Analysis and Duality 239
Right-Haod-Side Values 244
Simultaneous Changes 250
6.2 Duality 251
Economic Interpretation of the Dual Variables 254
Using the Dual to Identify the Primal Solution 255
Findingthe Dual of Anv Primal Problem 256
Glossary 258
Summary 258
Problems 259
Management Science in Practice:Performance Analysis Corporation 266
CHAPTER SEVEN Transportation,Assignment,and Transshipment Problems 268
7.1 The Transportation Problem:The Network Model and a Linear Programming Formulation 268
Problem Variations 273
A General Linear Programming Model of the Transportation Problem 274
7.2 The Assignment Problem:The Network Model and a Linear Programming Formulation 276
Management Science in Action:Marine Corps Mobilization 276
Problem Variations 279
Multiple Assignments 280
A General Linear Programming Model of the Assignment Problem 280
7.3 The Transshipment Problem:The Nelwork Model and a Linear Programming Formulation 281
Problem Variations 286
A General Linear Programming Model of the Transshipment Problem 287
7.4 A Production and Inventory Application 288
7.5 The Transportation Simplex Method:A Special-Purpose Solution Procedure(Optional) 291
Phase Ⅰ:Finding an Initial Feasible Solution 292
Phase Ⅱ:Iterating to the Optimal Solution 296
Summary of the Transportation Simplex Method 305
Problem Variations 306
7.6 The Assignment Problem:A Special-Purpose Solution Procedure(Optional) 307
Finding the Minimum Number of Lines 310
Problem Variations 310
Summary 313
Glossary 314
Problems 315
Case Problem:Assigning Umpire Crews 330
Case Problem:Distribution System Design 332
Management Science jn Practice:Procter Gamble 334
CHAPTER EIGHT Integer Linear Programming 335
Management Science in Action:Scheduling Employees at McDonald's Restaurant 336
8.1 Types of Integer Linear Programming Models 336
8.2 Graphicaland Computer Solution for an All-Integer Linear Program 338
Graphical Solution Procedure 338
Computer Solution 341
Management Science in Action:Cutting Photographic Color Paper Rolls 341
8.3 Applications 342
Capital Budgeting 342
Models Involving Fixed Costs 344
Distribution System Design 346
ABank Location Application 350
8.4 Modeling Flexibility Provided by 0-1 Integer Variables 354
Multiple-Choice and Mutually Exclusive Constraints 355
Management Science in Action:Analyzing Price Quotations Under Business Volume Discounts 355
k Out of n Alternatives Constraint 356
Conditional and Corequisite Constraints 356
Summary 357
A Cautionary Note on Sensitivity Analysis 357
Problems 358
Glossary 358
Case Problem:Textbook Publishing 367
Case Problem:Production Scheduling with Changeover Costs 369
Management Science in Practice:Ketron 370
CHAPTER NINE Network Models 372
9.1 The Shortest-Route Problem 372
A Shortest-Route Algorithm 373
A Minimal Spanning Tree Algorithm 381
9.2 The Minimal Spanning Tree Problem 381
9.3 The Maximal Flow Problem 384
A Maximal Flow Algorithm 385
Glossary 390
Problems 390
Summary 390
Case Problem:Ambulance Routing 397
Management Science in Practice:EDS 399
CHAPTER TEN Project Scheduling:PERT/CPM 401
10.1 Project Scheduling with Known Activity Times 402
The Concepts of a Critical Path 403
Determining the Critical Path 404
Contributions of PERT/CPM 409
Management Science in Action:Project Management on the PC 410
Summary of the PERT/CPM Critical Path Procedure 411
The Daugherty Porta-Vac Project 412
10.2 Project Scheduling with Uncertain Activity Times 412
Uncertain Activity Times 413
The Critical Path 415
Variability in Project Completion Time 418
10.3 Considering Time-Cost Trade-Offs 420
Crashing Activity Times 421
A Linear Programming Model for Crashing Decisions 423
Summary 425
Glossary 425
Problems 426
Case Problem:Warehouse Expansion 435
Management Science in Practice:Seasongood Mayer 436
CHAPTER ELEVEN Inventory Models 439
11.1 Economic Order Quantity(EOQ)Model 440
The How-Much-to-Order Decision 443
The When-to-Order Decision 445
Sensitivity Analysis in the EOQ Model 446
The Manager's Use of the EOQ Model 446
A Summary of the EOQ Model Assumptions 447
How Has the EOQ Decision Model Helped? 447
11.2 Economic Production Lot Size Model 448
The Total Cost Model 449
Finding the Economic Production Lot Size 451
11.4 Quantity Discounts for the EOQ Model 452
11.3 An Inventory Model with Planned Shortages 452
11.5 A Single-Period lnventory Model with Probabilistic Demand 458
The Johnson Shoe Company Problem 459
The Kremer Chemical Company Problem 462
11.6 An Order-Quantity,Reorder-Point Model with Probabilistic Demand 464
The When-to-Order Decision 466
The How-Much-to-Order Decision 466
11.7 A Periodic-Review Model with Probabilistic Demand 468
Management Science in Action:Information from a Netherlands Supplier Lowers Inventory Cost 468
More Complex Periodic-Review Models 471
Management Science in Action:Inventory Model Helps Hewlett-Packard's Product Design for Worldwide Markets 471
11.8 Material Requirements Planning 472
Dependent Demand and the MRP Concept 473
Information System for MRP 474
MRP Calculations 476
11.9 The Just-in-Time Approach to Inventory Management 478
Summary 479
Glossary 479
Problems 481
Case Problem:A Make-or-Buy Analysis 485
Appendix 11.1:Inventory Models with Spreadsheets 489
Appendix 11.3 Development of the Optimal Lot Size(Q)Formula for the Production Lot Size Model 492
Appendix 11.2 Development of the Optimal Order-Quantity(Q)Formula for the EOQ Model 492
Appendix 11.4 Development of the Optimal Order-Quantity(Q)and Optimal Backorder(S)Formulas for the Planned Shortage Model 493
Management Science in Practice:SupeRx.Inc. 495
CHAPTER TWELVE Waiting Line Models 497
12.1 The Structure of a Waiting Line System 498
The Single-Channel Waiting Line 498
The Distribution of Arrivals 498
The Distribution of Service Times 499
Queue Discipline 500
Steady-State Operation 500
The Operating Characteristics 501
12.2 The Single-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times 501
Operating Characteristics for the Burger Dome Problem 502
The Manager's Use of Waiting Line Models 503
Improving the Waiting Line Operation 503
12.3 The Multiple-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times 504
The Operatinig Characteristics 505
Operating Characteristics for the Burger Dome Problem 506
Management Science in Action:Hospital Staffing Based on a Multiple-Channel Waiting Line Model 509
12.4 Some General Relationships for Waiting Line Models 509
12.5 Economic Analysis of Waiting Lines 511
12.6 Other Waiting Line Models 513
Operating Characteristics for the M/G/l Model 514
12.7 The Single-Channel Waiting Line Model with Poisson Arrivals and Arbitrary Service Times 514
Constant Service Times 515
12.8 A Multiple-Channel Model with Poisson Arrivals,Arbitrary Service Times,and No Waiting Line 516
The Operating Characteristics for the M/G/K Model with Blocked Customers Cleared 517
The Operating Characteristics for the M/M/l Model with a Finite Calling Population 519
12.9 Waiting Line Models with Finite Calling Populations 519
Summary 522
Management Science in Action:Improving Fire Department Productivity 522
Glossary 523
Problems 523
Case Problem:Airline Reservations 530
Appendix 12.1:Waiting Line Models with Spreadsheets 531
Management Science in Practice:CITIBANK 533
CHAPER THIRETTEN Simulation 535
13.1 Using Simulation for Risk Analysis 536
The PortaCom Project 536
The PortaCom Simulation Model 537
Random Numbers and Simulating Values of Random Variables 539
Using the Simulation Model 541
Risk Analysis Conclusions 542
Simulation Results 542
13.2 An Inventory Simulation Model 543
Some Simulation Terminology 543
13.3 A Waiting Line Simulation Model 546
The Hammondsport Savings and Loan Waiting Line 546
Customer Arrival Times 546
Customer Service Times 547
The Simulation Model 548
Simulation Results 551
Management Science in Action:Red Cross Uses Simulation to Improve Bloodmobile Services 553
Selecting a Simulation Language 554
13.4 Other lssues 554
Verification and Validation 555
Keeping Track of Time 556
Advantages and Disadvantages 556
Management Science in Action:Simulation at Mexico's Vilpac Truck Company 557
Summary 557
Glossary 558
Problems 558
Case Problem:County Beverage Drive-Thru 567
Case Problem:Machine Repair 568
Appendix 13.1 Simulation with Spreadsheets 569
Management Science in Practice:The Upjohn Company 573
CHAPTER FOURTEEN Decision Analysis 575
Payoff Tables 576
14.1 Structuring the Decision Problem 576
Decision Trees 577
14.2 Decision Making Without Probabilities 578
Optimistic Approach 579
Conservative Approach 579
Minimax Regret Approach 580
14.3 Decision Making with Probabilities 581
14.4 Sensitivity Analvsis 584
Management Science in Action:Decision Analysis and the Selection of Home Mortgages 584
14.5 Expected Value of Perfect Information 587
14.6 Decision Analvsis with Sample Information 589
14.7 Developing a Decision Strategy 591
Computing Branch Probabilities 592
An Optimal Decision Strategy 594
Management Science in Action:Decision Analysis and Drug Testing for Student Athletes 596
14.8 Expected Value of Sample Information 597
Efficiency of Sample Information 598
The Meaning of Utility 599
14.9 Utility and Decision Making 599
Developing Utilities for Payoffs 600
The Expected Utility Approach 603
Glossary 605
Summary 605
Problems 606
Case Problem:Property Purchase Strategy 622
Appendix 14.1:Decision Analysis and Spreadsheets 623
Management Science in Practice:Ohio Edison Company 627
CHAPTET FIFTEEN Multicriteria Decision Problems 630
15.1 Goal Programming:Formulation and Graphical Solution 631
Developing the Constraints and the Goal Equations 632
Developing an Objective Function with Preemptive Priorities 633
The Graphical Solution Procedure 634
The Goal Programming Model 638
15.2 Goal Programming:Solving More Complex Problems 639
The Suncoast Office Supplies Problem 639
Formulating the Goal Equations 640
Formulating the Objective Function 641
Computer Solution 643
15.3 The Analytic Hierarchy Process 646
Management Science in Action:Using AHP and Goal Programming to Plan Facility Locations 647
Developing the Hierarchy 648
15.4 Establishing Priorities Using AHP 648
The Pairwise Comparison Matrix 649
Pairwise Comparisons 649
Procedure for Synthesizing Judgments 650
Synthesis 650
Consistency 651
Estimating the Consistency Ratio 652
Other Pairwise Comparisons for the Car-Selection Problem 653
15.5 Using AHP to Develop an Overall Priority Ranking 655
15.6 Using Expert Choice to Implement AHP 656
Summary 659
Glossary 660
Problems 661
Case Problem:Production Scheduling 668
CHAPTER XIXTEEN Forecasting 669
16.1 The Components of a Time Series 670
Trend Component 671
Cyclical Component 672
Seasonal Component 672
Irregular Component 673
16.2 Smoothing Methods 673
Moving Averages 673
Weighted Moving Averages 676
Exponential Smoothing 676
16.3 Trend Projection 681
16.4 Trend and Seasonal Components 684
The Multiplicative Model 685
Calculating the Seasonal Indexes 685
Deseasonalizing the Time Series 689
Using the Deseasonalized Time Series to Identify Trend 690
Seasonal Adjustments 692
Models Based on Monthy Data 692
Cyclical Component 692
16.5 Forecasting Using Regression Models 693
Management Science in Action:Spare Parts Forecasting at American Airlines 693
Using Regression Analysis When Time Series Data Are Not Available 694
Using Regression Analysis with Time Series Data 698
Delphi Method 700
16.6 Qualitative Approaches to Forecasting 700
Scenario Writing 701
Expert Judgment 701
Management Science in Action:The Business Week Industry Outlook 70lIntuitive Approaches 702
Summary 702
Glossary 702
Problems 703
Case Problem:Forecasting Sales 712
Case Problem:Forecasting Lost Sales 713
Appendix 16.1 Forecasting with Spreadsheets 714
Management Science in Practice:The Cincinnati Gas Electric Company 716
CHAPTER SEVENTEEN Markov Processes 718
17.1 Market Share Analysis 718
17.2 Accounts Receivable Analysis 726
The Fundamental Matrix and Associated Calculations 727
Establishing the Allowance for Doubtful Accounts 729
Problems 731
Glossary 731
Summary 731
Management Science in Practice:U.S.General Accounting Office 735
18.1 A Shortest-Route Problem 737
CHAPTER ELGHTEEN Dynamic Programming 737
18.2 Dynamic Programming Notation 742
18.3 The Knapsack Problem 745
18.4 A Production and Inventory Control Problem 751
Summary 755
Glossary 755
Problems 756
Management Science in Practice:The U.S.Environmental Protection Agency 762