Linear and integer programming: theory and practice, 第 1 巻
This unique reference/text details the theoretical and practical aspects of linear and integer programming - covering a wide range of subjects, including duality, optimality criteria, sensitivity analysis, and numerous solution techniques for linear programming problems.
Requiring only an elementary knowledge of set theory, trigonometry, and calculus, Linear and Integer Programming reflects both the problem-analyzing and problem-solving abilities of linear and integer programming...presents the more rigorous mathematical material in such a way that it can be easily skipped without disturbing the readability of the text...contains important pedagogical features such as a user-friendly, IBM-compatible computer software package for solving linear-programming problems, numerous case studies, fully worked examples, helpful end-of-chapter exercises, the answers to selected problems, key literature citations, and over 1375 equations, drawings, and tables...and more.
Linear and Integer programming is a fundamental reference for applied mathematicians, operations researchers, computer scientists, economists, and industrial engineers, as well as an ideal text for upper-level undergraduate and graduate students in this disciplines.
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LINEAR PROGRAMMING DANTZIGS SIMPLEX METHOD
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basic feasible solution basic variables calculated column Computer exercise Consider constraints convex convex set corresponding crew exchanges cycle decision variables defined degenerate demand denoted determine digraph dual model dual optimal solution dual variables easily check entries equivalent feasible region formulated Gaussian elimination graph Hence hyperplanes incidence matrix infeasible Interior Path interior point Iteration Knapsack Problem Linear Programming LP-model LP-relaxation minimal Model Dovetail napkins node nonbasic variables nondegenerate nonnegativities nonsingular nonzero Note objective coefficient objective function optimal objective value optimal Simplex Tableau optimal value parameter perturbation function planning period platform primal model procedure production Proof of Theorem right-hand side satisfies schedule Section shadow cost shadow price shortage Simplex Algorithm Simplex Method slack variables solution of model solved spanning tree Step subperiod Table technology matrix Theorem tolerance interval totally unimodular Traveling Salesman Problem vector vertex vertices x e Rn zero