Introduction to mathematical programming

摘要: 1. INTRODUCTION TO MODEL BUILDING. An Introduction to Modeling. The Seven-Step Model-Building Process. Examples. 2. BASIC LINEAR ALGEBRA. Matrices and Vectors. Systems of Linear Equations. Gauss-Jordan Method for Solving Independence Dependence. Inverse a Matrix. Determinants. 3. PROGRAMING. What is Programming Problem? Graphical Solution Two-Variable Problems. Special Cases. A Diet Problem. Work-Scheduling Capital Budgeting Short-term Financial Planning. Blending Production Process Models. Using Solve Multiperiod Decision Problems: Inventory Model. Work Scheduling. 4. THE SIMPLEX ALGORITM AND GOAL How Convert an LP Standard Form. Preview the Simplex Algorithm. Algorithm Minimization Alternative Optimal Solutions. Unbounded LPs. LINDO Computer Package. Matrix Generators, LINGO, Scaling Degeneracy Convergence Big M Method. Two-Phase Unrestricted-in-Sign Variables. Karmarkar?s Multiattribute Decision-Making in Absence Uncertainty: Goal Programming. LPs with Spreadsheets. 5. SENSITIVITY ANALYSIS: AN APPLIED APPROACH. Sensitivity Analysis. Managerial Use Shadow Prices. Happens z-value if Current Basis no Longer Optimal? 6. ANALYSIS DUALITY. Some Important Formulas. Analysis When More Than One Parameter Changed: 100% Rule. Finding Dual LP. Economic Interpretation Theorem Its Consequences. Duality 7. TRANSPORTATION, ASSIGNMENT, TRANSSHIPMENT PROBLEMS. Formulating Transportation Basic Feasible Solutions Assignment Transshipment 8. NETWORK MODELS. Definitions. Shortest Path Maximum Flow CPM PERT. Minimum Cost Network Spanning Tree 9. INTEGER PROGRAMMING. Integer Formulation Branch-and-Bound Pure Mixed Knapsack Problems by Combinatorial Optimization Implicit Enumeration. Cutting Plane 10. ADVANCED TOPICS IN Revised Product Form Inverse. Column Generation Large-Scale Dantzig-Wolfe Decomposition Upper-Bounded 11. GAME THEORY. Two-Person Zero-Sum Constant-Sum Games: Saddle Points. Randomized Str4ategies, Domination, Solution. Games. Nonconstant-Sum n-Person Game Theory. Core o f Game. Shapely Value. 12. NONLINEAR Review Differential Calculus. Introductory Concepts. Convex Concave Functions. NLPs Variable. Golden Section Search. Unconstrained Maximization Several Steepest Ascent. Lagrange Multiples. Kuhn-Tucker Conditions. Quadratic Separable Directions. Pareto Optimality Tradeoff Curves. 13. DETERMINISTIC DYNAMIC Two Puzzles. Resource Allocation Equipment Replacement Dynamic Recursions. Spreadsheets 14. HEURISTIC METHODS. 15. NEURAL NETWORKS. Answers To Selected Index.