Introduction to model building | |
An Introduction to Modeling | |
The Seven-Step Model-Building Process | |
Examples | |
Basic linear algebra | |
Matrices and Vectors | |
Matrices and Systems of Linear Equations | |
The Gauss-Jordan Method for Solving Systems of Linear Equations | |
Linear Independence and Linear Dependence | |
The Inverse of a Matrix | |
Determinants | |
Introduction to linear programming | |
What is a Linear Programming Problem? The Graphical Solution of Two-Variable Linear Programming Problems | |
Special Cases | |
A Diet Problem | |
A Work-Scheduling Problem | |
A Capital Budgeting Problem | |
Short-term Financial Planning | |
Blending Problems | |
Production Process Models | |
Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model | |
Multiperiod Financial Models | |
Multiperiod Work Scheduling | |
The simplex algorithm and goal programming | |
How to Convert an LP to Standard Form | |
Preview of the Simplex Algorithm | |
The Simplex Algorithm | |
Using the Simplex Algorithm to Solve Minimization Problems | |
Alternative Optimal Solutions | |
Unbounded LPs | |
The LINDO Computer Package | |
Matrix Generators, LINGO, and Scaling of LPs | |
Degeneracy and the Convergence of the Simplex Algorithm | |
The Big M Method | |
The Two-Phase Simplex Method | |
Unrestricted-in-Sign Variables | |
Karmarkar''s Method for Solving LPs | |
Multiattribute Decision-Making in the Absence of Uncertainty: Goal Programming | |
Solving LPs with Spreadsheets | |
Sensitivity analysis: an applied approach | |
A Graphical Introduction to Sensitivity Analysis | |
The Computer and Sensitivity Analysis | |
Managerial Use of Shadow Prices | |
What Happens to the Optimal z-value if the Current Basis is No Longer Optimal? | |
Sensitivity analysis and duality | |
A Graphical Introduction to Sensitivity Analysis | |
Some Important Formulas | |
Sensitivity Analysis | |
Sensitivity Analysis When More Than One Parameter is Changed: The 100% Rule | |
Finding the Dual of an LP | |
Economic Interpretation of the Dual Problem | |
The Dual Theorem and Its Consequences | |
Shadow Prices | |
Duality and Sensitivity Analysis | |
Transportation, assignment, and transshipment problems | |
Formulating Transportation Problems | |
Finding Basic Feasible Solutions for Transportation Problems | |
The Transportation Simplex Method | |
Sensitivity Analysis for Transportation Problems | |
Assignment Problems | |
Transshipment Problems | |
Network models | |
Basic Definitions | |
Shortest Path Problems | |
Maximum Flow Problems | |
CPM and PERT | |
Minimum Cost Network Flow Problems | |
Minimum Spanning Tree Problems | |
The Network Simplex Method | |
Integer programming | |
Introduction to Integer Programming | |
Formulation Integer Programming Problems | |
The Branch-and-Bound Method for Solving Pure Integer Programming Problems | |
The Branch-and-Bound Method for Solving Mixed Integer Programming Problems | |
Solving Knapsack Problems by the Branch-and-Bound Method | |
Solving Combinatorial Optimization Problems by the Branch-and-Bound Method | |
Implicit Enumeration | |
The Cutting Plane Algorithm | |
Advanced topics in linear programming | |
The Revised Simplex Algorithm | |
The Product Form of the Inverse | |
Using Column Generation to Solve Large-Scale LPs | |
The Dantzig-Wolfe Decomposition Algorithm | |
The Simplex Methods for Upper-Bounded Variables | |
Karmarkar''s Method for Solving LPs | |
Nonlinear programming | |
Review of Differential Calculus | |
Introductory Concepts | |
Convex and Concave Functions | |
Solving NLPs with One Variable | |
Golden Section Search | |
Unconstrained Maximization and Minimization with Several Variables | |
The Method of Steepest Ascent | |
Lagrange Multiples | |
The Kuhn-Tucker Conditions | |
Quadratic Programming | |
Separable Programming | |
The Method of Feasible Directions | |
Pareto Optimality and Tradeoff Curves | |
Review of calculus and probability | |
Review of Integral Calculus | |
Differentiation of Integrals | |
Basic Rules of Probability | |
Bayes'' Rule | |
Random Variables | |
Mean Variance and Covariance | |
The Normal Distribution | |
Z-Transforms | |
Review Problems | |
Decision making under uncertainty | |
Decision Criteria | |
Utility Theory | |
Flaws in Expe | |
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