Preface 

xii  
About the Author 

xvi  

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 Optimal zValue 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) 

MinimumCost 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  (97) 

Review of Differential Calculus 


610  (6) 


616  (14) 

Convex and Concave Functions 


630  (7) 

Solving NLPs with One Variable 


637  (12) 


649  (6) 

Unconstrained Maximization and Minimization with Several Variables 


655  (5) 

The Method of Steepest Ascent 


660  (3) 


663  (7) 

The KuhnTucker Conditions 


670  (10) 


680  (8) 


688  (5) 

The Method of Feasible Directions 


693  (2) 

Pareto Optimality and Tradeoff Curves 


695  (12) 

Review of Calculus and Probability 


707  (30) 

Review of Integral Calculus 


707  (3) 

Differentiation of Integrals 


710  (1) 

Basic Rules of Probability 


710  (3) 


713  (2) 

Random Variables, Mean, Variance, and Covariance 


715  (7) 


722  (8) 


730  (7) 

Decision Making under Uncertainty 


737  (66) 


737  (4) 


741  (14) 

Flaws in Expected Maximization of Utility: Prospect Theory and Framing Effects 


755  (3) 


758  (9) 

Bayes' Rule and Decision Trees 


767  (6) 

Decision Making with Multiple Objectives 


773  (12) 

The Analytic Hierarchy Process 


785  (18) 


803  (43) 

TwoPerson ZeroSum and ConstantSum Games: Saddle Points 


803  (4) 

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


807  (9) 

Linear Programming and ZeroSum Games 


816  (11) 

TwoPerson NonconstantSum Games 


827  (5) 

Introduction to nPerson Game Theory 


832  (2) 

The Core of an nPerson Game 


834  (3) 


837  (9) 

Deterministic EOQ Inventory Models 


846  (34) 

Introduction to Basic Inventory Models 


846  (2) 

The Basic Economic Order Quantity Model 


848  (11) 

Computing the Optimal Order Quantity When Quantity Discounts Are Allowed 


859  (6) 

The Continuous Rate EOQ Model 


865  (3) 

The EOQ Model with Back Orders Allowed 


868  (4) 


872  (1) 

MultipleProduct EOQ Models 


873  (7) 

Probabilistic Inventory Models 


880  (43) 

SinglePeriod Decision Models 


880  (1) 

The Concept of Marginal Analysis 


880  (1) 

The News Vendor Problem: Discrete Demand 


881  (5) 

The News Vendor Problem: Continuous Demand 


886  (2) 


888  (2) 

The EOQ with Uncertain Demand: The (r, q) and (s, S) Models 


890  (8) 

The EOQ with Uncertain Demand: The Service Level Approach to Determining Safety Stock Level 


898  (9) 

(R, S) Periodic Review Policy 


907  (4) 

The ABC Inventory Classification System 


911  (2) 


913  (10) 


923  (38) 

What Is a Stochastic Process? 


923  (1) 


924  (4) 

nStep Transition Probabilities 


928  (3) 

Classification of States in a Markov Chain 


931  (3) 

SteadyState Probabilities and Mean First Passage Times 


934  (8) 


942  (8) 

WorkForce Planning Models 


950  (11) 

Deterministic Dynamic Programming 


961  (55) 


961  (1) 


962  (7) 


969  (5) 

ResourceAllocation Problems 


974  (11) 

EquipmentReplacement Problems 


985  (4) 

Formulating Dynamic Programming Recursions 


989  (12) 

The WagnerWhitin Algorithm and the SilverMeal Heuristic 


1001  (5) 

Using Excel to Solve Dynamic Programming Problems 


1006  (10) 

Probabilistic Dynamic Programming 


1016  (35) 

When Current Stage Costs Are Uncertain, but the Next Period's State Is Certain 


1016  (3) 

A Probabilistic Inventory Model 


1019  (4) 

How to Maximize the Probability of a Favorable Event Occurring 


1023  (6) 

Further Examples of Probabilistic Dynamic Programming Formulations 


1029  (7) 

Markov Decision Processes 


1036  (15) 


1051  (94) 


1051  (2) 

Modeling Arrival and Service Processes 


1053  (1) 


1053  (19) 

The M/M/1/GD/∞/∞ Queuing System and the Queuing Formula L = λW 


1072  (11) 

The M/M/1/GD/c/∞ Queuing System 


1083  (4) 

The M/M/s/GD/∞/∞ Queuing System 


1087  (8) 

The M/G/∞/GD/∞/∞ and GI/G/∞/GD/∞/∞ Models 


1095  (2) 

The M/G/∞/GD/∞/∞ Queuing System 


1097  (2) 

Finite Source Models: The Machine Repair Model 


1099  (5) 

Exponential Queues in Series and Open Queuing Networks 


1104  (8) 

The M/G/s/GD/s/∞ System (Blocked Customers Cleared) 


1112  (3) 

How to Tell Whether Interarrival Times and Service Times Are Exponential 


1115  (4) 


1119  (5) 

An Approximation for the G/G/m Queuing System 


1124  (2) 


1126  (5) 

Transient Behavior of Queuing Systems 


1131  (14) 


1145  (46) 


1145  (1) 

An Example of a DiscreteEvent Simulation 


1146  (7) 

Random Numbers and Monte Carlo Simulation 


1153  (5) 

An Example of Monte Carlo Simulation 


1158  (4) 

Simulations with Continuous Random Variables 


1162  (11) 

An Example of a Stochastic Simulation 


1173  (7) 

Statistical Analysis in Simulations 


1180  (3) 


1183  (1) 


1184  (7) 

Simulation with Process Model 


1191  (21) 

Simulating an M/M/1 Queuing System 


1191  (4) 

Simulating an M/M/2 System 


1195  (4) 

Simulating a Series System 


1199  (4) 

Simulating Open Queuing Networks 


1203  (4) 

Simulating Erlang Service Times 


1207  (3) 

What Else Can Process Model Do? 


1210  (2) 

Simulation with the Excel Addin @Risk 


1212  (63) 

Introduction to @Risk: The News Vendor Problem 


1212  (10) 

Modeling Cash Flows from a New Product 


1222  (10) 

Product Scheduling Models 


1232  (6) 

Reliability and Warranty Modeling 


1238  (6) 


1244  (4) 

The RISKCUMULATIVE Random Variable 


1248  (1) 

The RISKTRIGEN Random Variable 


1249  (1) 

Creating a Distribution Based on a Point Forecast 


1250  (2) 

Forecasting the Income of a Major Corporation 


1252  (4) 

Using Data to Obtain Inputs for New Product Simulations 


1256  (11) 


1267  (2) 


1269  (2) 

Simulating the NBA Finals 


1271  (4) 


1275  (61) 

MovingAverage Forecast Methods 


1275  (6) 

Simple Exponential Smoothing 


1281  (2) 

Holt's Method: Exponential Smoothing with Trend 


1283  (3) 

Winter's Method: Exponential Smoothing with Seasonality 


1286  (6) 


1292  (10) 


1302  (10) 

Fitting Nonlinear Relationships 


1312  (5) 


1317  (19) 

Appendix 1: @Risk Crib Sheet 


1336  (14) 


1350  (20) 

Case 1 Help, I'm Not Getting Any Younger 


1351  (1) 

Case 2 Solar Energy for Your Home 


1351  (1) 

Case 3 GolfSport: Managing Operations 


1352  (3) 

Case 4 Vision Corporation: Production Planning and Shipping 


1355  (1) 

Case 5 Material Handling in a General MailHandling Facility 


1356  (3) 

Case 6 Selecting Corporate Training Programs 


1359  (3) 

Case 7 Best Chip: Expansion Strategy 


1362  (2) 

Case 8 Emergency Vehicle Location in Springfield 


1364  (1) 

Case 9 System Design: Project Management 


1365  (1) 

Case 10 Modular Design for the HelpYou Company 


1366  (2) 

Case 11 Brite Power: Capacity Expansion 


1368  (2) 

Appendix 3: Answers to Selected Problems 


1370  (32) 
Index 

1402  