Mathematical background; Theory of the simplex method; Detailed development and computational aspects of the simplex method; Further discussion of the simplex method; Resolution of the degeneracy problem; The revised simplex method; Duality theory and its ramifications; Transportation problems; Network flows; Special topics; Applications of linear programming to industrial problems; Applications of linear programming to economic theory.
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Theory of the Simplex Method
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activity vector artificial variables artificial vectors assume basic feasible solution basis matrix basis vectors branch capacity cells Chapter column components compute Consider contains convex combination convex set corresponding cost degeneracy denoted destination discussed dual problem dual variables enter the basis equations example extreme point finite number given Hence hyperplane identity matrix industry inequalities initial basic feasible inverse iteration labeled linear programming problem linearly independent loop maximal flow minimum nodes non-negative Note objective function obtain optimal basic solution optimal solution path Phase player positive primal problem primal-dual algorithm procedure refinery removed restricted primal revised simplex method satisfied set of constraints set of feasible simplex algorithm slack variable surplus variables Table tableau tion transhipment transportation problem unbounded solution unique unit upper bound vector to enter yield zero level