Linear Programming and Extensions
eBook - PDF

Linear Programming and Extensions

  1. 651 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Linear Programming and Extensions

About this book

The influential book that established the mathematical discipline of linear programming

In the worlds of finance, business, and management, mathematicians and economists frequently encounter problems of optimization. In this classic book, George Dantzig shows how the methods of linear programming can provide solutions. Drawing on a wealth of examples, he introduces the basic theory of linear inequalities and describes the powerful simplex method used to solve them. He discusses the price concept, the transportation problem, and matrix methods, and covers key mathematical concepts such as the properties of convex sets and linear vector spaces. Dantzig demonstrates how linear programming can be applied to a host of optimization problems, from minimizing traffic congestion to maximizing the scheduling of airline flights.

An invaluable resource for students and practitioners alike, Linear Programming and Extensions is an extraordinary account of the development and uses of this versatile mathematical technique, blending foundational research in mathematical theory with computation, economic analysis, and applications to industrial problems.

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Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. CONTENTS
  6. Preface
  7. CHAPTER 1 THE LINEAR PROGRAMMING CONCEPT
  8. CHAPTER 2 ORIGINS AND INFLUENCES
  9. CHAPTER 3 FORMULATING A LINEAR PROGRAMMING MODEL
  10. CHAPTER 4 LINEAR EQUATION AND INEQUALITY SYSTEMS
  11. CHAPTER 5 THE SIMPLEX METHOD
  12. CHAPTER 6 PROOF OF THE SIMPLEX ALGORITHM AND THE DUALITY THEOREM
  13. CHAPTER 7 THE GEOMETRY OF LINEAR PROGRAMS
  14. CHAPTER 8 PIVOTING, VECTOR SPACES, MATRICES, AND INVERSES
  15. CHAPTER 9 THE SIMPLEX METHOD USING MULTIPLIERS
  16. CHAPTER 10 FINITENESS OF THE SIMPLEX METHOD UNDER PERTURBATION
  17. CHAPTER 11 VARIANTS OF THE SIMPLEX ALGORITHM
  18. CHAPTER 12 THE PRICE CONCEPT IN LINEAR PROGRAMMING
  19. CHAPTER 13 GAMES AND LINEAR PROGRAMS
  20. CHAPTER 14 THE CLASSICAL TRANSPORTATION PROBLEM
  21. CHAPTER 15 OPTIMAL ASSIGNMENT AND OTHER DISTRIBUTION PROBLEMS
  22. CHAPTER 16 THE TRANSSHIPMENT PROBLEM
  23. CHAPTER 17 NETWORKS AND THE TRANSSHIPMENT PROBLEM
  24. CHAPTER 18 VARIABLES WITH UPPER BOUNDS
  25. CHAPTER 19 MAXIMAL FLOWS IN NETWORKS
  26. CHAPTER 20 THE PRIMAL-DUAL METHOD FOR TRANSPORTATION PROBLEMS
  27. CHAPTER 21 THE WEIGHTED DISTRIBUTION PROBLEM
  28. CHAPTER 22 PROGRAMS WITH VARIABLE COEFFICIENTS
  29. CHAPTER 23 A DECOMPOSITION PRINCIPLE FOR LINEAR PROGRAMS
  30. CHAPTER 24 CONVEX PROGRAMMING
  31. CHAPTER 25 UNCERTAINTY
  32. CHAPTER 26 DISCRETE VARIABLE EXTREMUM PROBLEMS
  33. CHAPTER 27 STIGLER’S NUTRITION MODEL: AN EXAMPLE OF FORMULATION AND SOLUTION
  34. CHAPTER 28 THE ALLOCATION OF AIRCRAFT TO ROUTES UNDER UNCERTAIN DEMAND
  35. BIBLIOGRAPHY
  36. INDEX

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Yes, you can access Linear Programming and Extensions by George B. Dantzig in PDF and/or ePUB format, as well as other popular books in Mathematics & Linear & Nonlinear Programming. We have over one million books available in our catalogue for you to explore.