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Unformatted text preview: 1 Sensitivity Analysis II 73220 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 Nonbasic variable Binding constraint Nonbinding 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 resolved 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. Nonbasic Variable ● Nonbasic variables assume zero in the optimal soln. ● If the objective function coefficient of a nonbasic variable changes within allowable limits, – Optimal solution is unchanged – Objective function value is unchanged ● Reduced cost is usually nonzero – 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 resolve 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. Nonbinding constraints ● If the RHS of a nonbinding constraint changes within allowable limits – Optimal solution is unchanged – OFV is unchanged ● The shadow price for a nonbinding 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.
 Spring '11
 chan
 Finance

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