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MIE376 Lec 4 - PostOpt

# MIE376 Lec 4 - PostOpt - Post-Optimality Analysis...

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MIE376 - Mathematical Programming 1 Post-Optimality Analysis Sensitivity Analysis Revisiting Excel Solver Reduced Costs & Changes in Obj. coefficients Shadow Prices & Changes in RHS For Slack Variables: Reduced Costs = Shadow Prices Duality

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MIE376 - Mathematical Programming 2 Post-Optimality Analysis Sensitivity Analysis Revisiting Excel Solver Reduced Costs & Changes in Obj. coefficients Shadow Prices & Changes in RHS For Slack Variables: Reduced Costs = Shadow Prices Duality
MIE376 - Mathematical Programming 3 Post-Optimality Analysis Clearly the LP solution yields Optimal decision variables Optimal value of the objective In addition it yields Valuable information on Impact of prices – reduced costs Value of resources – shadow prices How the solution changes with marginal changes Objective function coefficients Right-hand side constraint coefficients Duality A powerful concept Closely coupled to shadow prices and reduced costs Later leads to NLP Kuresh-Kuhn-Tucker (KKT) conditions

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MIE376 - Mathematical Programming 4 Post-Optimality Analysis Sensitivity Analysis Revisiting Excel Solver Reduced Costs & Changes in Obj. coefficients Shadow Prices & Changes in RHS For Slack Variables: Reduced Costs = Shadow Prices Duality
MIE376 - Mathematical Programming 5 Revisiting Excel

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MIE376 - Mathematical Programming 6 LP sensitivity analysis Changes in objective function coefficients Changes in right-hand side coefficients
MIE376 - Mathematical Programming 7 Post-Optimality Analysis Sensitivity Analysis Revisiting Excel Solver Reduced Costs & Changes in Obj. coefficients Shadow Prices & Changes in RHS For Slack Variables: Reduced Costs = Shadow Prices Duality

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Reduced Costs By how much does the cost coefficient of a decision variable have to change before the variable becomes basic? (Zero if already basic!) If we are minimizing costs, by how much would a product cost have to be reduced before it is used in the optimal solution How much less must it’s obj. coefficient be before it enters the basis If we are maximizing revenues – as in our case – then by how much would the per unit revenue have to be raised before it is used in the optimal solution How much more must it’s obj. coefficient be before it enters the basis Since reduced costs are more important for the original decision variables (versus the slack variables) and in our example they are both basic, let’s introduce a new product MIE376 - Mathematical Programming 8