Linear Programming and Extensions

Description

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. Frontmatter Preface Contents 1. The Linear Programming Concept 2. Origins and Influences 3. Formulating a Linear Programming Model 4. Linear Equation and Inequality Systems 5. The Simplex Method 6. Proof of the Simplex Algorithm and the Duality Theorem 7. The Geometry of Linear Programs 8. Pivoting, Vector Spaces, Matrices, and Inverses 9. The Simplex Method Using Multipliers 10. Finiteness of the Simplex Method under Perturbation 11. Variants of the Simplex Algorithm 12. The Price Concept in Linear Programming 13. Games And Linear Programs 14. The Classical Transportation Problem 15. Optimal Assignment and Other Distribution Problems 16. The Transshipment Problem 17. Networks and the Transshipment Problem 18. Variables with Upper Bounds 19. Maximal Flows in Networks 20. The Primal-Dual Method for Transportation Problems 21. The Weighted Distribution Problem 22. Programs with Variable Coefficients 23. A Decomposition Principle for Linear Programs 24. Convex Programming 25. Uncertainty 26. Discrete-Variable Extremum Problems 27. Stigler’s Nutrition Model. An Example of Formulation and Solution 28. The Allocation of Aircraft to Routes under Uncertain Demand Bibliography Subject Index Name Index Selected Rand Books.pdf