73-220-Lecture10 - 73-220 Lecture 10 1 Agenda...

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1 Sensitivity Analysis II 73-220 Lecture 10
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2 Agenda Sensitivity Analysis for LP problems in more  than two variables Next Class
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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
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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).
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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
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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
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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
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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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