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QingPeng (QP) Zhang qpzhang@email.arizona.edu

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Sensitivity analysis is concerned with how changes in an linear programming’s parameters affect the optimal solution.

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Profit generated by each soldier $3 Profit generated by each train $2

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Constraint/ObjectiveSlope Finishing constraint-2 Carpentry constraint-1.5 Objective function Basic variable Basic solution

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CChange objective function coefficient CChange right-hand side of constraint OOther change options SShadow price TThe Importance of sensitivity analysis

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How would changes in the problem’s objective function coefficients or the constraint’s right-hand sides change this optimal solution?

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? ?

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Change objective function coefficient Change right-hand side of constraint Other change options Shadow price The Importance of sensitivity analysis

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As long as the binding point (B) of finishing and carpentry constraints is feasible, optimal solution will occur at the binding point.

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Change objective function coefficient Change right-hand side of constraint Other change options Shadow price The Importance of sensitivity analysis

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Change objective function coefficient Change right-hand side of constraint Other change options Shadow price The Importance of sensitivity analysis

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To determine how a constraint’s rhs changes the optimal z-value. The shadow price for the ith constraint of an LP is the amount by which the optimal z-value is improved (increased in a max problem or decreased in a min problem).

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Change objective function coefficient Change right-hand side of constraint Other change options Shadow price The Importance of sensitivity analysis

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Deal with the uncertainty about LP parameters

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Chapter 6 Simplex-Based Sensitivity Analysis and Duality

Chapter 6 Simplex-Based Sensitivity Analysis and Duality

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