"This comprehensive treatment of the fundamental ideas and principles of linear programming covers basic theory, selected applications, network flow problems, and advanced techniques. Using specific examples to illuminate practical and theoretical aspects of the subject, the author clearly reveals the structures of fully detailed proofs. The presentation is geared toward modern efficient implementations of the simplex method and appropriate data structures for network flow problems. Completely self-contained, it develops even elementary facts on linear equations and matrices from the beginning."--Back cover.
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How the Simplex Method Works
Pitfalls and How to Avoid Them
How Fast Is the Simplex Method?
The Duality Theorem
Gaussian Elimination and Matrices
The Revised Simplex Method
Solutions by the Simplex Method
Approximating Data by Linear Functions
Systems of Linear Inequalities
Finding All Vertices of a Polyhedron
The Network Simplex Method
Applications of the Network Simplex Method
UpperBounded Transshipment Problems
Maximum Flows Through Networks
Theorems on Duality and Infeasibility
Efficient Allocation of Scarce Resources
Scheduling Production and Inventory
The CuttingStock Problem
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algorithm arcs ij augmenting path auxiliary problem basic feasible solution basic solution basic variables bipartite graph Chapter coefficients column vector components computing constraints convex convex hull convex sets corresponding defined entering arc entering column entering the basis entering variable eta column example feasible tree solution finals of width finite Gaussian elimination Hence identity matrix integer leaving the basis leaving variable linear inequalities linear programming linear programming problem LP problems maximize cx subject maximum-flow problem mixed strategy network simplex method node nonbasic variables nonzero number of iterations objective function obtain optimal solution original problem path payoff matrix permutation permutation matrices pivot polyhedron problem maximize cx procedure proof Prove pure strategies replace resulting revised simplex method right-hand side satisfies slack variables solvable Solving the system Step subject to Ax system Ax systems of linear Theorem transshipment problem triangular factorization update upper bound zero