For upper-division/graduate courses in operations research/management science, mathematics, and computer science, this text covers basic theory, selected applications, network flow problems, and advanced techniques.
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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