Preface 

ix  

An Introduction to ModelBuilding 


1  (10) 

An Introduction to Modeling 


1  (4) 

The SevenStep ModelBuilding Process 


5  (1) 


6  (1) 

San Francisco Police Department Scheduling 


7  (2) 


9  (2) 


11  (38) 


11  (9) 

Matrices and Systems of Linear Equations 


20  (2) 

The GaussJordan Method for Solving Systems of Linear Equations 


22  (10) 

Linear Independence and Linear Dependence 


32  (4) 


36  (6) 


42  (7) 

Introduction to Linear Programming 


49  (78) 

What Is a Linear Programming Problem? 


49  (7) 

The Graphical Solution of TwoVariable Linear Programming Problems 


56  (7) 


63  (5) 


68  (4) 

A WorkScheduling Problem 


72  (4) 

A Capital Budgeting Problem 


76  (6) 

ShortTerm Financial Planning 


82  (3) 


85  (10) 

Production Process Models 


95  (5) 

Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model 


100  (5) 

Multiperiod Financial Models 


105  (4) 

Multiperiod Work Scheduling 


109  (18) 

The Simplex Algorithm and Goal Programming 


127  (100) 

How to Convert an LP to Standard Form 


127  (3) 

Preview of the Simplex Algorithm 


130  (4) 

Direction of Unboundedness 


134  (2) 

Why Does an LP Have an Optimal bfs 


136  (4) 


140  (9) 

Using the Simplex Algorithm to Solve Minimization Problems 


149  (3) 

Alternative Optimal Solutions 


152  (2) 


154  (4) 

The LINDO Computer Package 


158  (5) 

Matrix Generators, LINGO, and Scaling of LPs 


163  (5) 

Degeneracy and the Convergence of the Simplex Algorithm 


168  (4) 


172  (6) 

The TwoPhase Simplex Method 


178  (6) 

UnrestrictedinSign Variables 


184  (6) 

Karmarkar's Method for Solving LPs 


190  (1) 

Multiattribute Decision Making in the Absence of Uncertainty: Goal Programming 


191  (11) 

Using the Excel Solver to Solve LPs 


202  (25) 

Sensitivity Analysis: An Applied Approach 


227  (35) 

A Graphical Introduction to Sensitivity Analysis 


227  (5) 

The Computer and Sensitivity Analysis 


232  (14) 

Managerial Use of Shadow Prices 


246  (2) 

What Happens to the OptimalzValue If the Current Basis Is No Longer Optimal? 


248  (14) 

Sensitivity Analysis and Duality 


262  (98) 

A Graphical Introduction to Sensitivity Analysis 


262  (5) 


267  (8) 


275  (14) 

Sensitivity Analysis When More Than One Parameter Is Changed: The 100% Rule 


289  (6) 

Finding the Dual of an LP 


295  (7) 

Economic Interpretation of the Dual Problem 


302  (2) 

The Dual Theorem and Its Consequences 


304  (9) 


313  (10) 

Duality and Sensitivity Analysis 


323  (2) 


325  (4) 


329  (6) 

Data Envelopment Analysis 


335  (25) 

Transportation, Assignment, and Transshipment Problems 


360  (53) 

Formulating Transportation Problems 


360  (13) 

Finding Basic Feasible Solutions for Transportation Problems 


373  (9) 

The Transportation Simplex Method 


382  (8) 

Sensitivity Analysis for Transportation Problems 


390  (3) 


393  (7) 


400  (13) 


413  (62) 


413  (1) 


414  (5) 


419  (12) 


431  (19) 

Minimum Cost Network Flow Problems 


450  (6) 

Minimum Spanning Tree Problems 


456  (3) 

The Network Simplex Method 


459  (16) 


475  (87) 

Introduction to Integer Programming 


475  (2) 

Formulating Integer Programming Problems 


477  (35) 

The BranchandBound Method for Solving Pure Integer Programming Problems 


512  (11) 

The BranchandBound Method for Solving Mixed Integer Programming Problems 


523  (1) 

Solving Knapsack Problems by the BranchandBound Method 


524  (3) 

Solving Combinatorial Optimization Problems by the BranchandBound Method 


527  (13) 


540  (5) 

The Cutting Plane Algorithm 


545  (17) 

Advanced Topics in Linear Programming 


562  (48) 

The Revised Simplex Algorithm 


562  (5) 

The Product Form of the Inverse 


567  (3) 

Using Column Generation to Solve LargeScale LPs 


570  (6) 

The DantzigWolfe Decomposition Algorithm 


576  (17) 

The Simplex Method for UpperBounded Variables 


593  (4) 

Karmarkar's Method for Solving LPs 


597  (13) 


610  (43) 

TwoPerson ZeroSum and ConstantSum Games: Saddle Points 


610  (4) 

TwoPerson ZeroSum Games: Randomized Strategies, Domination, and Graphical Solution 


614  (9) 

Linear Programming and ZeroSum Games 


623  (11) 

TwoPerson NonconstantSum Games 


634  (5) 

Introduction to nPerson Game Theory 


639  (2) 

The Core of anPerson Game 


641  (3) 


644  (9) 


653  (97) 

Review of Differential Calculus 


653  (6) 


659  (14) 

Convex and Concave Functions 


673  (7) 

Solving NLPs with One Variable 


680  (12) 


692  (6) 

Unconstrained Maximization and Minimization with Several Variables 


698  (5) 

The Method of Steepest Ascent 


703  (3) 


706  (7) 

The KuhnTucker Conditions 


713  (10) 


723  (8) 


731  (5) 

The Method of Feasible Directions 


736  (2) 

Pareto Optimality and Tradeoff Curves 


738  (12) 

Deterministic Dynamic Programming 


750  (50) 


750  (1) 


751  (7) 


758  (5) 

Resource Allocation Problems 


763  (11) 

Equipment Replacement Problems 


774  (4) 

Formulating Dynamic Programming Recursions 


778  (12) 

Using EXCEL to Solve Dynamic Programming Problems 


790  (10) 


800  (23) 


800  (4) 

Introduction to Heuristic Procedures 


804  (1) 


805  (3) 


808  (7) 


815  (6) 


821  (2) 

Solving Optimization Problems with the Evolutionary Solver 


823  (43) 

Price Bundling, Index Function, Match Function, and Evolutionary Solver 


823  (7) 

More Nonlinear Pricing Models 


830  (6) 


836  (3) 

Solving Other Combinatorial Problems 


839  (2) 

Production Scheduling at John Deere 


841  (5) 

Assigning Workers to Jobs with the Evolutionary Solver 


846  (5) 


851  (6) 


857  (3) 


860  (6) 


866  (25) 

Introduction to Neural Networks 


866  (4) 

Examples of the Use of Neural Networks 


870  (1) 

Why Neural Nets Can Beat Regression: The XOR Example 


871  (3) 

Estimating Neural Nets with PREDICT 


874  (8) 

Using Genetic Algorithms to Optimize a Neural Network 


882  (2) 

Using Genetic Algorithms to Determine Weights for a Back Propagation Network 


884  (7) 
Appendix: Cases 

891  (22) 

Case 1 Help, I'm Not Getting Any Younger 


892  (1) 

Case 2 Solar Energy for Your Home 


892  (1) 

Case 3 GolfSport: Managing Operations 


893  (3) 

Case 4 Vision Corporation: Production Planning and Shipping 


896  (1) 

Case 5 Material Handling in a General MailHandling Facility 


897  (3) 

Case 6 Selecting Corporate Training Programs 


900  (3) 

Case 7 Best Chip: Expansion Strategy 


903  (2) 

Case 8 Emergency Vehicle Location in Springfield 


905  (1) 

Case 9 System Design: Project Management 


906  (1) 

Case 10 Modular Design for the HelpYou Company 


907  (2) 

Case 11 Brite Power: Capacity Expansion 


909  (4) 
Index 

913  