OPIM 101 - Spring 2012 - Session 9

OPIM 101 - Spring 2012 - Session 9 - Introduction to the...

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Introduction to the Computer as an Analysis Tool Session 9 1 Session 9: Sensitivity Analysis m Sensitivity Analysis for Toy Industries Problem m Sensitivity Analysis for HFL Problem
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Introduction to the Computer as an Analysis Tool Session 9 2 Toy Industries: Model Parameters max 3.50 M + 7.90 J subject to: (Cutting) 0.25 M + 0.25 J <= 700 (Sewing) 0.4 M + 0.6 J <= 700 ( M assembly) M <= 1300 ( J assembly) J <= 900 (Non-negativity) M , J >= 0 Constraint Right hand sides Objective Function Coefficients Constraint Coefficients
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Introduction to the Computer as an Analysis Tool Session 9 3 Approaches to Sensitivity Analysis m If anything in your model changes, re-solve the model, if you have time! 4 Sometimes this is the only approach available… m Whenever you run Solver on a linear model, it also produces a Sensitivity Report which can tell what happens if: 4 Objective function coefficients change from their current values 4 Constraint right-hand-sides change from their current values
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Introduction to the Computer as an Analysis Tool Session 9 4 Solver Sensitivity Report m After clicking “Solve”, the “Solver Results” dialog box appears: m Select “Sensitivity” and click “OK”
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Introduction to the Computer as an Analysis Tool Session 9 5 Sensitivity Report for Toy Industries Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$4 Production per month Model M 400 0 3.5 1.766666667 3.5 $D$4 Production per month Model J 900 0 7.9 1E+30 2.65 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$9 Cutting (hours) Used 325 0 700 1E+30 375 $E$10 Sewing (hours) Used 700 8.75 700 360 160 $E$11 Model M assembly Used 400 0 1300 1E+30 900 $E$12 Model J assembly Used 900 2.65 900 266.6666667 600
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Introduction to the Computer as an Analysis Tool Session 9 6 Objective Coefficient Changes: How robust is your optimal solution? m Optimal production plan will not change unless the profit contribution of model J falls below $5.25 (a $2.65 decrease from its current value of $7.90) m Optimal production plan will not change if the profit contribution of model M stays between $0 and $5.27 (a $3.50 decrease or a $1.77 increase from its current value of $3.50) m We can only consider changes one-at-a-time ! If both objective function coefficients change at the same time, we have to re- solve the model coefficient for any variable stays within limits outlined by “Allowable Increase” and “Allowable Decrease” Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$4 Production per month Model M 400 0 3.5 1.766666667 3.5 $D$4 Production per month Model J 900 0 7.9 1E+30 2.65
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Introduction to the Computer as an Analysis Tool Session 9 7 Right-Hand-Side Changes: Attaching Values to Your Resources m assembly is $2.65. If the J assembly capacity is increased to 904 from 900:
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This note was uploaded on 04/04/2012 for the course OPIM 101 taught by Professor Lee during the Spring '08 term at UPenn.

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OPIM 101 - Spring 2012 - Session 9 - Introduction to the...

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