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| Preface | |
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| An Introduction to Model-Building | |
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| An Introduction to Modeling | |
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| The Seven-Step Model-Building Process | |
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| CITGO Petroleum | |
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| San Francisco Police Department Scheduling | |
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| GE Capital | |
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| Basic Linear Algebra | |
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| Matrices and Vectors | |
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| Matrices and Systems of Linear Equations | |
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| The Gauss-Jordan Method for Solving Systems of Linear Equations | |
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| Linear Independence and Linear Dependence | |
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| The Inverse of a Matrix | |
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| Determinants | |
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| Introduction to Linear Programming | |
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| What Is a Linear Programming Problem? | |
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| The Graphical Solution of Two-Variable Linear Programming Problems | |
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| Special Cases | |
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| A Diet Problem | |
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| A Work-Scheduling Problem | |
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| A Capital Budgeting Problem | |
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| Short-Term Financial Planning | |
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| Blending Problems | |
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| Production Process Models | |
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| Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model | |
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| Multiperiod Financial Models | |
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| Multiperiod Work Scheduling | |
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| The Simplex Algorithm and Goal Programming | |
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| How to Convert an LP to Standard Form | |
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| Preview of the Simplex Algorithm | |
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| Direction of Unboundedness | |
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| Why Does an LP Have an Optimal bfs | |
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| The Simplex Algorithm | |
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| Using the Simplex Algorithm to Solve Minimization Problems | |
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| Alternative Optimal Solutions | |
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| Unbounded LPs | |
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| The LINDO Computer Package | |
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| Matrix Generators, LINGO, and Scaling of LPs | |
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| Degeneracy and the Convergence of the Simplex Algorithm | |
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| The Big M Method | |
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| The Two-Phase Simplex Method | |
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| Unrestricted-in-Sign Variables | |
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| Karmarkar's Method for Solving LPs | |
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| Multiattribute Decision Making in the Absence of Uncertainty: Goal Programming | |
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| Using the Excel Solver to Solve LPs | |
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| Sensitivity Analysis: An Applied Approach | |
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| A Graphical Introduction to Sensitivity Analysis | |
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| The Computer and Sensitivity Analysis | |
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| Managerial Use of Shadow Prices | |
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| What Happens to the Optimal z-Value If the Current Basis Is No Longer Optimal? | |
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| Sensitivity Analysis and Duality | |
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| A Graphical Introduction to Sensitivity Analysis | |
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| Some Important Formulas | |
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| Sensitivity Analysis | |
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| Sensitivity Analysis When More Than One Parameter Is Changed: The 100% Rule | |
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| Finding the Dual of an LP | |
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| Economic Interpretation of the Dual Problem | |
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| The Dual Theorem and Its Consequences | |
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| Shadow Prices | |
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| Duality and Sensitivity Analysis | |
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| Complementary Slackness | |
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| The Dual Simplex Method | |
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| Data Envelopment Analysis | |
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| Transportation, Assignment, and Transshipment Problems | |
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| Formulating Transportation Problems | |
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| Finding Basic Feasible Solutions for Transportation Problems | |
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| The Transportation Simplex Method | |
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| Sensitivity Analysis for Transportation Problems | |
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| Assignment Problems | |
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| Transshipment Problems | |
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| Network Models | |
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| Basic Definitions | |
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| Shortest Path Problems | |
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| Maximum Flow Problems | |
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| CPM and PERT | |
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| Minimum Cost Network Flow Problems | |
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| Minimum Spanning Tree Problems | |
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| The Network Simplex Method | |
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| Integer Programming | |
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| Introduction to Integer Programming | |
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| Formulating Integer Programming Problems | |
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| The Branch-and-Bound Method for Solving Pure Integer Programming Problems | |
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| The Branch-and-Bound Method for Solving Mixed Integer Programming Problems | |
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| Solving Knapsack Problems by the Branch-and-Bound Method | |
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| Solving Combinatorial Optimization Problems by the Branch-and-Bound Method | |
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| Implicit Enumeration | |
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| The Cutting Plane Algorithm | |
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| Advanced Topics in Linear Programming | |
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| The Revised Simplex Algorithm | |
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| The Product Form of the Inverse | |
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| Using Column Generation to Solve Large-Scale LPs | |
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| The Dantzig-Wolfe Decomposition Algorithm | |
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| The Simplex Method for Upper-Bounded Variables | |
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| Karmarkar's Method for Solving LPs | |
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| Game Theory | |
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| Two-Person Zero-Sum and Constant-Sum Games: Saddle Points | |
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| Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution | |
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| Linear Programming and Zero-Sum Games | |
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| Two-Person Nonconstant-Sum Games | |
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| Introduction to n-Person Game Theory | |
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| The Core of an n-Person Game | |
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| The Shapley Value | |
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| Nonlinear Programming | |
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| Review of Differential Calculus | |
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| Introductory Concepts | |
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| Convex and Concave Functions | |
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| Solving NLPs with One Variable | |
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| Golden Section Search | |
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| Unconstrained Maximization and Minimization with Several Variables | |
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| The Method of Steepest Ascent | |
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| Lagrange Multipliers | |
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| The Kuhn-Tucker Conditions | |
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| Quadratic Programming | |
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| Separable Programming | |
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| The Method of Feasible Directions | |
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| Pareto Optimality and Tradeoff Curves | |
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| Deterministic Dynamic Programming | |
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| Two Puzzles | |
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| A Network Problem | |
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| An Inventory Problem | |
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| Resource Allocation Problems | |
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| Equipment Replacement Problems | |
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| Formulating Dynamic Programming Recursions | |
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| Using EXCEL to Solve Dynamic Programming Problems | |
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| Heuristic Techniques | |
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| Complexity Theory | |
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| Introduction to Heuristic Procedures | |
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| Simulated Annealing | |
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| Genetic Search | |
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| Tabu Search | |
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| Comparison of Heuristics | |
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| Solving Optimization Problems with the Evolutionary Solver | |
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| Price Bundling, Index Function, Match Function, and Evolutionary Solver | |
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| More Nonlinear Pricing Models | |
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| Locating Warehouses | |
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| Solving Other Combinatorial Problems | |
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| Production Scheduling at John Deere | |
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| Assigning Workers to Jobs with the Evolutionary Solver | |
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| Cluster Analysis | |
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| Fitting Curves | |
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| Discriminant Analysis | |
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| Neural Networks | |
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| Introduction to Neural Networks | |
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| Examples of the Use of Neural Networks | |
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| Why Neural Nets Can Beat Regression: The XOR Example | |
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| Estimating Neural Nets with PREDICT | |
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| Using Genetic Algorithms to Optimize a Neural Network | |
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| Using Genetic Algorithms to Determine Weights for a Back Propagation Network | |
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| Cases | |
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| Help, I'm Not Getting Any Younger | |
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| Solar Energy for Your Home | |
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| Golf-Sport: Managing Operations | |
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| Vision Corporation: Production Planning and Shipping | |
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| Material Handling in a General Mail-Handling Facility | |
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| Selecting Corporate Training Programs | |
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| Best Chip: Expansion Strategy | |
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| Emergency Vehicle Location in Springfield | |
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| System Design: Project Management | |
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| Modular Design for the Help-You Company | |
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| Brite Power: Capacity Expansion | |
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| Index | |