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FORMULATION OF LINEAR PROGRAMS
THE SIMPLEX METHOD
THE GEOMETRY OF THE SIMPLEX METHOD
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admissible cells algorithm terminates artificial variables assignment problem associated basic set basic variable branch and bound candidate problem canonical tableau Cholesky factor column vector complementary feasible computed convex cutting plane dual feasible dual simplex dual solution edge entering variable entries equal equations Example extreme point feasible basic vector feasible basis feasible flow vector Figure Hence infeasible integer program inverse tableau Lagrange multiplier linear programming linearly independent LU decomposition matrix of order maximum flow problem Minimize z(x minimum cost minimum objective value node nonbasic variable nonnegative nonzero objective function obtained optimal optimum feasible solution optimum solution original problem P-matrix pair Phase I problem pivot column pivot row pivot step primal feasible relative cost coefficients satisfies set of feasible shortest chains simplex algorithm simplex method slack variables solving stage Subject to Ax subset Suppose theorem transportation array transportation problem zero