73-220-Lecture10 - 1 Sensitivity Analysis II 73-220 Lecture...

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Unformatted text preview: 1 Sensitivity Analysis II 73-220 Lecture 10 2 Agenda ● Sensitivity Analysis for LP problems in more than two variables ● Next Class 3 Sensitivity Tree Objective function coefficient changes RHS of constraint changes Add or delete constraint Basic variable Non-basic variable Binding constraint Non-binding Constraint Add constraint Delete constraint 5 2 3 4 1 6 4 Change of Objective coefficient or RHS of constraint ● If the change in objective function coefficient or RHS of a constraint is outside allowable increase/decrease, the problem needs to be re-solved on the computer and we cannot say anything about the objective function value (OFV) or the optimal solution(OS). 5 1. Basic Variable ● Basic variables assume positive in the optimal solution. ● If the objective function coefficient of a basic variable changes within allowable limits, – Optimal solution is unchanged – Objective function value changes » The new OFV can be determined by substituting the OS into the new objective function. ● Reduced cost is always zero for a basic variable 6 2. Non-basic Variable ● Non-basic variables assume zero in the optimal soln. ● If the objective function coefficient of a non-basic variable changes within allowable limits, – Optimal solution is unchanged – Objective function value is unchanged ● Reduced cost is usually non-zero – If reduced cost is zero, it indicates the existence of an alternate optimal solution. ● For a maximization problem – Reduced cost is negative or zero – Allowable increase = -reduced cost – Allowable decrease = infinite ● For a minimization problem – Reduced cost = positive or zero – Allowable increase = infinite – Allowable decrease = reduced cost 7 3. Binding Constraints ● If the RHS of a binding constraint changes within allowable limits – Optimal solution changes (must re-solve to get the optimal solution) – OFV changes and its impact can be assessed as follow: » New OFV = old OFV + change in RHS*(shadow price) ● Shadow price for a binding constraint is usually nonzero. ● For nonzero shadow price for a maximization problem – Positive for <= type constraint – Negative for >= type constraint ● For nonzero shadow price for a minimization problem – Positive for >= type constraint – Negative for <= type constraint 8 4. Non-binding constraints ● If the RHS of a non-binding constraint changes within allowable limits – Optimal solution is unchanged – OFV is unchanged ● The shadow price for a non-binding constraint is always zero....
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This note was uploaded on 11/28/2011 for the course FINANCE 101 taught by Professor Chan during the Spring '11 term at Aarhus Universitet.

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73-220-Lecture10 - 1 Sensitivity Analysis II 73-220 Lecture...

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