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38	Sensitivity Analysis • How does the value of the optimum solution change when coefficients in the obj. fcn. or constraints change? • Why is sensitivity analysis important? Coefficients and/or limits in constraints may be poorly known Effect of expanding capacity, changes in costs of raw materials or selling prices of products. • Market demand of products vary • Crude oil prices fluctuate Sensitivity information is readily available in the final Simplex solution. Optimum does not have to be recomputed.
39	Sensitivity Analysis (Constraints) Shadow price: The change in optimum value of obj. fcn. per unit change in the constraint limit. Final Set of Equations of Refinery Blending Problem x₃ = 0 x₄ = 0 x₅ + 0.14 x₃ – 4.21 x₄ = 896.5 x₁ + 1.72 x₃ – 7.59 x₄ = 26,207 x₂ – 0.86 x₃ + 13.79 x₄ = 6,897 f – 4.66 x₃ – 87.52 x₄ = -286,765
40	Sensitivity Analysis
41	Sensitivity Analysis gasoline capacity is worth $4.66/bbl kerosene capacity is worth $87.52/bbl fuel oil capacity is worth $0/bbl←No effect Capacity limit in original constraints * shadow prices 4.66 (24,000) + 87.52 (2,000) = 286,880 Same as $286,740 Duality (roundoff)
42	Sensitivity Analysis (Obj. Fcn.)
43	Duality One dual variable exists for each primal constraint One dual constraint exists for each primal variable • The optimal solution of the decision variables (i.e., the Dual Problem) will correspond to the Shadow Prices obtained from solution of the Primal Problem. • Commercial Software will solve the Primal and Dual Problems. i.e., it provides sensitivity information.
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