Authors Wayne Winston and Munirpallam Venkataramanan emphasize model-formulation and model-building skills as well as interpretation of computer software output. Focusing on deterministic models, this book is designed for the first half of an operations research sequence. A subset of Winston's best-selling OPERATIONS RESEARCH, INTRODUCTION TO MATHEMATICAL PROGRAMMING offers self-contained chapters that make it flexible enough for one- or two-semester courses ranging from advanced beginning to intermediate in level. The book has a strong computer orientation and emphasizes model-formulation and model-building skills. Every topic includes a corresponding computer-based modeling and solution method and every chapter presents the software tools needed to solve realistic problems. LINDO, LINGO, and Premium Solver for Education software packages are available with the book.

 

Preface

p. ix

 

An Introduction to Model-Building

p. 1

 

An Introduction to Modeling

p. 1

 

The Seven-Step Model-Building Process

p. 5

 

CITGO Petroleum

p. 6

 

San Francisco Police Department Scheduling

p. 7

 

GE Capital

p. 9

 

Basic Linear Algebra

p. 11

 

Matrices and Vectors

p. 11

 

Matrices and Systems of Linear Equations

p. 20

 

The Gauss-Jordan Method for Solving Systems of Linear Equations

p. 22

 

Linear Independence and Linear Dependence

p. 32

 

The Inverse of a Matrix

p. 36

 

Determinants

p. 42

 

Introduction to Linear Programming

p. 49

 

What Is a Linear Programming Problem?

p. 49

 

The Graphical Solution of Two-Variable Linear Programming Problems

p. 56

 

Special Cases

p. 63

 

A Diet Problem

p. 68

 

A Work-Scheduling Problem

p. 72

 

A Capital Budgeting Problem

p. 76

 

Short-Term Financial Planning

p. 82

 

Blending Problems

p. 85

 

Production Process Models

p. 95

 

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

p. 100

 

Multiperiod Financial Models

p. 105

 

Multiperiod Work Scheduling

p. 109

 

The Simplex Algorithm and Goal Programming

p. 127

 

How to Convert an LP to Standard Form

p. 127

 

Preview of the Simplex Algorithm

p. 130

 

Direction of Unboundedness

p. 134

 

Why Does an LP Have an Optimal bfs

p. 136

 

The Simplex Algorithm

p. 140

 

Using the Simplex Algorithm to Solve Minimization Problems

p. 149

 

Alternative Optimal Solutions

p. 152

 

Unbounded LPs

p. 154

 

The LINDO Computer Package

p. 158

 

Matrix Generators, LINGO, and Scaling of LPs

p. 163

 

Degeneracy and the Convergence of the Simplex Algorithm

p. 168

 

The Big M Method

p. 172

 

The Two-Phase Simplex Method

p. 178

 

Unrestricted-in-Sign Variables

p. 184

 

Karmarkar's Method for Solving LPs

p. 190

 

Multiattribute Decision Making in the Absence of Uncertainty: Goal Programming

p. 191

 

Using the Excel Solver to Solve LPs

p. 202

 

Sensitivity Analysis: An Applied Approach

p. 227

 

A Graphical Introduction to Sensitivity Analysis

p. 227

 

The Computer and Sensitivity Analysis

p. 232

 

Managerial Use of Shadow Prices

p. 246

 

What Happens to the Optimal z-Value If the Current Basis Is No Longer Optimal?

p. 248

 

Sensitivity Analysis and Duality

p. 262

 

A Graphical Introduction to Sensitivity Analysis

p. 262

 

Some Important Formulas

p. 267

 

Sensitivity Analysis

p. 275

 

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

p. 289

 

Finding the Dual of an LP

p. 295

 

Economic Interpretation of the Dual Problem

p. 302

 

The Dual Theorem and Its Consequences

p. 304

 

Shadow Prices

p. 313

 

Duality and Sensitivity Analysis

p. 323

 

Complementary Slackness

p. 325

 

The Dual Simplex Method

p. 329

 

Data Envelopment Analysis

p. 335

 

Transportation, Assignment, and Transshipment Problems

p. 360

 

Formulating Transportation Problems

p. 360

 

Finding Basic Feasible Solutions for Transportation Problems

p. 373

 

The Transportation Simplex Method

p. 382

 

Sensitivity Analysis for Transportation Problems

p. 390

 

Assignment Problems

p. 393

 

Transshipment Problems

p. 400

 

Network Models

p. 413

 

Basic Definitions

p. 413

 

Shortest Path Problems

p. 414

 

Maximum Flow Problems

p. 419

 

CPM and PERT

p. 431

 

Minimum Cost Network Flow Problems

p. 450

 

Minimum Spanning Tree Problems

p. 456

 

The Network Simplex Method

p. 459

 

Integer Programming

p. 475

 

Introduction to Integer Programming

p. 475

 

Formulating Integer Programming Problems

p. 477

 

The Branch-and-Bound Method for Solving Pure Integer Programming Problems

p. 512

 

The Branch-and-Bound Method for Solving Mixed Integer Programming Problems

p. 523

 

Solving Knapsack Problems by the Branch-and-Bound Method

p. 524

 

Solving Combinatorial Optimization Problems by the Branch-and-Bound Method

p. 527

 

Implicit Enumeration

p. 540

 

The Cutting Plane Algorithm

p. 545

 

Advanced Topics in Linear Programming

p. 562

 

The Revised Simplex Algorithm

p. 562

 

The Product Form of the Inverse

p. 567

 

Using Column Generation to Solve Large-Scale LPs

p. 570

 

The Dantzig-Wolfe Decomposition Algorithm

p. 576

 

The Simplex Method for Upper-Bounded Variables

p. 593

 

Karmarkar's Method for Solving LPs

p. 597

 

Game Theory

p. 610

 

Two-Person Zero-Sum and Constant-Sum Games: Saddle Points

p. 610

 

Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution

p. 614

 

Linear Programming and Zero-Sum Games

p. 623

 

Two-Person Nonconstant-Sum Games

p. 634

 

Introduction to n-Person Game Theory

p. 639

 

The Core of an n-Person Game

p. 641

 

The Shapley Value

p. 644

 

Nonlinear Programming

p. 653

 

Review of Differential Calculus

p. 653

 

Introductory Concepts

p. 659

 

Convex and Concave Functions

p. 673

 

Solving NLPs with One Variable

p. 680

 

Golden Section Search

p. 692

 

Unconstrained Maximization and Minimization with Several Variables

p. 698

 

The Method of Steepest Ascent

p. 703

 

Lagrange Multipliers

p. 706

 

The Kuhn-Tucker Conditions

p. 713

 

Quadratic Programming

p. 723

 

Separable Programming

p. 731

 

The Method of Feasible Directions

p. 736

 

Pareto Optimality and Tradeoff Curves

p. 738

 

Deterministic Dynamic Programming

p. 750

 

Two Puzzles

p. 750

 

A Network Problem

p. 751

 

An Inventory Problem

p. 758

 

Resource Allocation Problems

p. 763

 

Equipment Replacement Problems

p. 774

 

Formulating Dynamic Programming Recursions

p. 778

 

Using EXCEL to Solve Dynamic Programming Problems

p. 790

 

Heuristic Techniques

p. 800

 

Complexity Theory

p. 800

 

Introduction to Heuristic Procedures

p. 804

 

Simulated Annealing

p. 805

 

Genetic Search

p. 808

 

Tabu Search

p. 815

 

Comparison of Heuristics

p. 821

 

Solving Optimization Problems with the Evolutionary Solver

p. 823

 

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

p. 823

 

More Nonlinear Pricing Models

p. 830

 

Locating Warehouses

p. 836

 

Solving Other Combinatorial Problems

p. 839

 

Production Scheduling at John Deere

p. 841

 

Assigning Workers to Jobs with the Evolutionary Solver

p. 846

 

Cluster Analysis

p. 851

 

Fitting Curves

p. 857

 

Discriminant Analysis

p. 860

 

Neural Networks

p. 866

 

Introduction to Neural Networks

p. 866

 

Examples of the Use of Neural Networks

p. 870

 

Why Neural Nets Can Beat Regression: The XOR Example

p. 871

 

Estimating Neural Nets with PREDICT

p. 874

 

Using Genetic Algorithms to Optimize a Neural Network

p. 882

 

Using Genetic Algorithms to Determine Weights for a Back Propagation Network

p. 884

 

Cases

p. 891

 

Help, I'm Not Getting Any Younger

p. 892

 

Solar Energy for Your Home

p. 892

 

Golf-Sport: Managing Operations

p. 893

 

Vision Corporation: Production Planning and Shipping

p. 896

 

Material Handling in a General Mail-Handling Facility

p. 897

 

Selecting Corporate Training Programs

p. 900

 

Best Chip: Expansion Strategy

p. 903

 

Emergency Vehicle Location in Springfield

p. 905

 

System Design: Project Management

p. 906

 

Modular Design for the Help-You Company

p. 907

 

Brite Power: Capacity Expansion

p. 909

 

Index

p. 913

 

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