A comprehensive, up-to-date text on linear programming. Covers all practical modeling, mathematical, geometrical, algorithmic, and computational aspects. Surveys recent developments in the field, including the Ellipsoid method. Includes extensive examples and exercises. Designed for advanced undergraduates or graduates majoring in engineering, mathematics, or business administration.
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Formulation of Linear Programs
The Simplex Method
Geometry of the Simplex Method
14 other sections not shown
affine function artificial variables basic cell basic set basic solution basic variable BFSs canonical tableau column vector computational Consider the LP convex convex combination criterion denote dropping variable dual feasible dual problem dual simplex algorithm ellipsoid method entering variable entries equality constraints Example extreme point feasible basic vector feasible basis Hence inequality constraints infeasible integer inverse tableau lexico linear programming linearly independent matrix of order Minimize z(x minimum ratio nonbasic variable nondegenerate nonzero objective function obtained optimal optimum basis optimum feasible solution optimum objective value optimum solution original problem original tableau parameter Phase I problem pivot column pivot element pivot matrix pivot row pivot step primal feasible relative cost coefficients right-hand-side constants row vector satisfying set of feasible simplex method slack variables solving Subject to Ax subset Suppose system of linear termination theorem tion transportation problem unbounded unit matrix variable choice rules zero