Linear Programming and Extensions

Voorkant
Princeton University Press, 10 aug 2016 - 656 pagina's

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.

 

Geselecteerde pagina's

Inhoudsopgave

CHAPTER 1 THE LINEAR PROGRAMMING CONCEPT
1
CHAPTER 2 ORIGINS AND INFLUENCES
12
CHAPTER 3 FORMULATING A LINEAR PROGRAMMING MODEL
32
CHAPTER 4 LINEAR EQUATION AND INEQUALITY SYSTEMS
69
CHAPTER 5 THE SIMPLEX METHOD
94
CHAPTER 6 PROOF OF THE SIMPLEX ALGORITHM AND THE DUALITY THEOREM
120
CHAPTER 7 THE GEOMETRY OF LINEAR PROGRAMS
147
CHAPTER 8 PIVOTING VECTOR SPACES MATRICES AND INVERSES
173
CHAPTER 17 NETWORKS AND THE TRANSSHIPMENT PROBLEM
352
CHAPTER 18 VARIABLES WITH UPPER BOUNDS
368
CHAPTER 19 MAXIMAL FLOWS IN NETWORKS
385
CHAPTER 20 THE PRIMALDUAL METHOD FOR TRANSPORTATION PROBLEMS
404
CHAPTER 21 THE WEIGHTED DISTRIBUTION PROBLEM
413
CHAPTER 22 PROGRAMS WITH VARIABLE COEFFICIENTS
433
CHAPTER 23 A DECOMPOSITION PRINCIPLE FOR LINEAR PROGRAMS
448
CHAPTER 24 CONVEX PROGRAMMING
471

CHAPTER 9 THE SIMPLEX METHOD USING MULTIPLIERS
210
CHAPTER 10 FINITENESS OF THE SIMPLEX METHOD UNDER PERTURBATION
228
CHAPTER 11 VARIANTS OF THE SIMPLEX ALGORITHM
240
CHAPTER 12 THE PRICE CONCEPT IN LINEAR PROGRAMMING
254
CHAPTER 13 GAMES AND LINEAR PROGRAMS
277
CHAPTER 14 THE CLASSICAL TRANSPORTATION PROBLEM
299
CHAPTER 15 OPTIMAL ASSIGNMENT AND OTHER DISTRIBUTION PROBLEMS
316
CHAPTER 16 THE TRANSSHIPMENT PROBLEM
335
CHAPTER 25 UNCERTAINTY
499
CHAPTER 26 DISCRETE VARIABLE EXTREMUM PROBLEMS
514
AN EXAMPLE OF FORMULATION AND SOLUTION
551
CHAPTER 28 THE ALLOCATION OF AIRCRAFT TO ROUTES UNDER UNCERTAIN DEMAND
568
BIBLIOGRAPHY
592
INDEX
617
Copyright

Overige edities - Alles bekijken

Linear Programming and Extensions
George Bernard Dantzig
Gedeeltelijke weergave - 1998
Linear Programming and Extensions: A Report Prepared for U.S. Air Force ...
George Bernard Dantzig
Fragmentweergave - 1963
Linear Programming and Extensions
George Bernard Dantzig
Fragmentweergave - 1963

Veelvoorkomende woorden en zinsdelen

activity algorithm amount application arcs artificial assigned associated assumed basic basic variables basis bound called canonical capacity Chapter choose coefficients column combination computational consider constant convex corresponding cost cycle demand determine developed dropped dual equal equations equivalent example Exercise exists expression feasible Figure flow function given Hence increase inequality initial integer iteration least linear programming mathematical matrix method minimize multipliers negative nodes non-basic nonnegative Note objective obtained operations optimal original Phase pivot positive possible primal problem procedure production proof Prove reduced REFERENCES relation remaining replaced restricted route satisfying selected Show shown simplex simplex method slack solution solving standard Step Suppose Table Theorem transportation unit values variables vector yields zero

Over de auteur (2016)

George B. Dantzig (1914–2005) is widely acclaimed as the father of linear programming and was a leading figure in the development of mathematical optimization, making important contributions to fields such as industrial engineering, economics, and statistics. He was professor emeritus of operations research and computer science at Stanford University.

Bibliografische gegevens

TitelLinear Programming and Extensions
Volume 25 van Princeton Landmarks in Mathematics and Physics
AuteurGeorge B. Dantzig
Editiegeïllustreerd
UitgeverPrinceton University Press, 2016
ISBN1400884179, 9781400884179
Lengte656 pagina's
  
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