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| 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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| Examples | |
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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? 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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| 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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| Solving LPs with Spreadsheets | |
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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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| 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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| Formulation 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 Methods for Upper-Bounded Variables | |
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| Karmarkar''s Method for Solving LPs | |
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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 Multiples | |
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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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| Review of calculus and probability | |
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| Review of Integral Calculus | |
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| Differentiation of Integrals | |
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| Basic Rules of Probability | |
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| Bayes'' Rule | |
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| Random Variables | |
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| Mean Variance and Covariance | |
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| The Normal Distribution | |
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| Z-Transforms | |
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| Review Problems | |
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| Decision making under uncertainty | |
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| Decision Criteria | |
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| Utility Theory | |
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| Flaws in Expe | |