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# 6417c06 - SIMPLEX ALGORITHM IN GENERAL FORM CONTENTS...

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1 SIMPLEX ALGORITHM IN GENERAL FORM CONTENTS Sensitivity and Parametric Analysis (Section 7.1) Primal Simplex Method in General Form (Section 9.1)

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2 Parametric and Sensitivity Analysis Sensitivity Analysis : Having found an optimal solution of a LP, how much can we change the data so that the current basis remains optimal. Change some c j or b i or a ij . Minimize cx, subject to Ax = b, x 0 Parametric Analysis : Solve a family of linear programming problems parametrized by a single variable λ Minimize (c 0 + λ c*)x, subject to Ax = b, x 0 Minimize cx, subject to Ax = b 0 + λ b* , x 0
3 Sensitivity Analysis Minimize cx, subject to Ax = b, x 0 x B = B -1 b {Primal feasibility: x B 0} y = c B B -1 = c j - yA j {Dual feasibility: 0 for all j nonbasic} ξ * = yb What if the cost of a nonbasic variable changes? What if the cost of a basic variable changes? What if one element in the right-hand side vector changes?

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6417c06 - SIMPLEX ALGORITHM IN GENERAL FORM CONTENTS...

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