Linear Programming 1: IntroductionSpringer Science & Business Media, 6 квіт. 2006 р. - 435 стор. By George B. Dantzig LINEAR PROGRAMMING The Story About How It Began: Some legends, a little about its historical sign- cance, and comments about where its many mathematical programming extensions may be headed. Industrial production, the ?ow of resources in the economy, the exertion of military e?ort in a war, the management of ?nances—all require the coordination of interrelated activities. What these complex undertakings share in common is the task of constructing a statement of actions to be performed, their timing and quantity(calledaprogramorschedule), that, ifimplemented, wouldmovethesystem from a given initial status as much as possible towards some de?ned goal. While di?erences may exist in the goals to be achieved, the particular processes, and the magnitudes of e?ort involved, when modeled in mathematical terms these seemingly disparate systems often have a remarkably similar mathematical str- ture. The computational task is then to devise for these systems an algorithm for choosing the best schedule of actions from among the possible alternatives. The observation, in particular, that a number of economic, industrial, ?nancial, and military systems can be modeled (or reasonably approximated) by mathem- ical systems of linear inequalities and equations has given rise to the development of the linear programming ?eld. |
Зміст
THE LINEAR PROGRAMMING PROBLEM | 1 |
List of Tables | 2 |
SOLVING SIMPLE LINEAR PROGRAMS | 35 |
THE SIMPLEX METHOD | 63 |
INTERIORPOINT METHODS | 113 |
DUALITY | 129 |
EQUIVALENT FORMULATIONS | 145 |
PRICE MECHANISM AND SENSITIVITY ANALYSIS | 171 |
A1 Six Points in 2dimensional Space | 340 |
B LINEAR EQUATIONS | 341 |
SYSTEMS OF EQUATIONS WITH THE SAME SOLUTION SETS | 343 |
HOW SYSTEMS ARE SOLVED | 345 |
ELEMENTARY OPERATIONS | 346 |
CANONICAL FORMS PIVOTING AND SOLUTIONS | 349 |
PIVOT THEORY | 354 |
NOTES SELECTED BIBLIOGRAPHY | 357 |
TRANSPORTATION AND ASSIGNMENT PROBLEM | 205 |
NETWORK FLOW THEORY | 253 |
A LINEAR ALGEBRA | 315 |
Інші видання - Показати все
Linear Programming 1: Introduction George B. Dantzig,Mukund N. Thapa Обмежений попередній перегляд - 1997 |
Linear Programming 1: Introduction George B. Dantzig,Mukund N. Thapa Попередній перегляд недоступний - 2013 |
Linear Programming 1: Introduction George B. Dantzig,Mukund N. Thapa Попередній перегляд недоступний - 1997 |
Загальні терміни та фрази
activity arc capacities artificial variables assignment problem Assume augmenting path basic feasible solution basic solution basic variables basis canonical form coefficients column compute constraints convex function corresponding Dantzig defined Definition desk determine DTZG Simplex Primal dual Exercise feasible region formulation Fourier-Motzkin Elimination goal programming Illustration infeasible integer interior-point methods inverse Lemma linear combination lower bound matrix maximal flow minimal spanning tree Minimize cTx minimum cost-flow problem node nonbasic variables objective function objective value obtained optimal solution original system Phase pivot primal affine Primal software option program in standard reduced costs right-hand side satisfy Show shown in Figure Simplex Algorithm Simplex Method simplex multipliers Simplex Primal software slack slack variables Solve the problem standard form subject to Ax system of equations tableau triangular unit upper bound vector zero