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Introduction To Mathematical Programming, Volume I / With CD (4TH 03 Edition)by Wayne L. Winston
Synopses & ReviewsPublisher Comments:Authors Wayne Winston and Munirpallam Venkataramanan emphasize modelformulation and modelbuilding 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 bestselling OPERATIONS RESEARCH, INTRODUCTION TO MATHEMATICAL PROGRAMMING offers selfcontained chapters that make it flexible enough for one or twosemester courses ranging from advanced beginning to intermediate in level. The book has a strong computer orientation and emphasizes modelformulation and modelbuilding skills. Every topic includes a corresponding computerbased 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.
Book News Annotation:This textbook describes the model building process for analyzing operations research questions and the tools of linear programming for solving optimization problems. The CDROM contains student editions of Lindo, Lingo, Predict, and Premium Solver. The fourth edition adds chapters on simulated annealing, genetic algorithms, Tabu search, and neural networks.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:This textbook describes the model building process for analyzing operations research questions and the tools of linear programming for solving optimization problems. The CDROM contains student editions of Lindo, Lingo, Predict, and Premium Solver. The fourth edition adds chapters on simulated annea
About the AuthorWayne L. Winston is Professor of Operations and Decision Technologies in the Kelley School of Business at Indiana University, where he has taught since 1975. Wayne received his B.S. degree in mathematics from MIT and his Ph.D. degree in operations researc
Table of Contents1. INTRODUCTION TO MODEL BUILDING. An Introduction to Modeling. The SevenStep ModelBuilding Process. Examples. 2. BASIC LINEAR ALGEBRA. Matrices and Vectors. Matrices and Systems of Linear Equations. The GaussJordan Method for Solving Systems of Linear Equations. Linear Independence and Linear Dependence. The Inverse of a Matrix. Determinants. 3. INTRODUCTION TO LINEAR PROGRAMING. What is a Linear Programming Problem? The Graphical Solution of TwoVariable Linear Programming Problems. Special Cases. A Diet Problem. A WorkScheduling Problem. A Capital Budgeting Problem. Shortterm Financial Planning. Blending Problems. Production Process Models. Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model. Multiperiod Financial Models. Multiperiod Work Scheduling. 4. THE SIMPLEX ALGORITM AND GOAL PROGRAMING. 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 TwoPhase Simplex Method. UnrestrictedinSign Variables. Karmarkars Method for Solving LPs. Multiattribute DecisionMaking in the Absence of Uncertainty: Goal Programming. Solving LPs with Spreadsheets. 5. 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 zvalue if the Current Basis is no Longer Optimal? 6. 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. 7. 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. 8. 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. 9. INTEGER PROGRAMMING. Introduction to Integer Programming. Formulation Integer Programming Problems. The BranchandBound Method for Solving Pure Integer Programming Problems. The BranchandBound Method for Solving Mixed Integer Programming Problems. Solving Knapsack Problems by the BranchandBound Method. Solving Combinatorial Optimization Problems by the BranchandBound Method. Implicit Enumeration. The Cutting Plane Algorithm. 10. ADVANCED TOPICS IN LINEAR PROGRAMMING. The Revised Simplex Algorithm. The Product Form of the Inverse. Using Column Generation to Solve LargeScale LPs. The DantzigWolfe Decomposition Algorithm. The Simplex Method for UpperBounded Variables. Karmarkars Method for Solving LPs. 11. GAME THEORY. TwoPerson ZeroSum and ConstantSum Games: Saddle Points. TwoPerson ZeroSum Games: Randomized Str4ategies, Domination, and Graphical Solution. Linear Programming and ZeroSum Games. TwoPerson NonconstantSum Games. Introduction to nPerson Game Theory. The Core o f an nPerson Game. The Shapely Value. 12. 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 KuhnTucker Conditions. Quadratic Programming. Separable Programming. The Method of Feasible Directions. Pareto Optimality and Tradeoff Curves. 13. DETERMINISTIC DYNAMIC PROGRAMMING. Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems. Formulation Dynamic Programming Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. 14. HEURISTIC METHODS. 15. NEURAL NETWORKS. Answers To Selected Problems. Index.
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