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

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