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Lecture4web - MBAC6080 Decision Modeling and Applications Thomas Vossen Assistant professor of Operations Management Leeds School of Business

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1 MBAC6080 Thomas Vossen Assistant professor of Operations Management Leeds School of Business University of Colorado Boulder, CO 80309-0419 Decision Modeling and Applications
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Lecture 4, 2-6-2008 2 MBAC6080 Today’s Agenda Sensitivity Analysis LP Applications DEA Multi-Objective/Goal Programming Intro Network Models and Integer Programming
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Lecture 4, 2-6-2008 3 MBAC6080 Sensitivity Analysis
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Lecture 4, 2-6-2008 4 MBAC6080 General Form of a LP Problem MAX (or MIN): c 1 X 1 + c 2 X 2 + … + c n X n Subject to: a 11 X 1 + a 12 X 2 + … + a 1 n X n <= b 1 : a k 1 X 1 + a k 2 X 2 + … + a kn X n <= b k : a m 1 X 1 + a m 2 X 2 + … + a mn X n = b m How sensitive is a solution to changes in the c i , a ij , and b i ?
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Lecture 4, 2-6-2008 5 MBAC6080 Approaches to Sensitivity Analysis Change the data and re-solve the model! Sometimes this is the only practical approach. Solver also produces sensitivity reports that can answer various questions…
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Lecture 4, 2-6-2008 6 MBAC6080 Solver’s Sensitivity Report Answers questions about: Amounts by which objective function coefficients can change without changing the optimal solution. The impact on the optimal objective function value of changes in constrained resources. The impact on the optimal objective function value of forced changes in decision variables. The impact changes in constraint coefficients will have on the optimal solution.
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Lecture 4, 2-6-2008 7 MBAC6080 Product Mix Example Product Mix LP .  A potter produces two products, a pitcher  and a bowl. It takes about 1 hour to produce a bowl and  requires 4 pounds of clay.  A pitcher takes about 2 hours and  consumes 3 pounds of clay.  The profit on a bowl is $40 and  $50 on a pitcher. She works 40 hours weekly, has 120  pounds of clay available each week, and wants more profits. Max Z = 40 + 50 y profits s.t. 1 + 2 y    40hours 4 x  + 3 y    120 clay x y    0 non-negativity
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Lecture 4, 2-6-2008 8 MBAC6080 The Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$13 Number to produce Pots 24 0 40 26.66666667 15 $C$13 Number to produce Pitchers 8 0 50 30 20 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$23 Clay consumed 120 6 120 40 60 $E$20 Hours consumed 40 16 40 40 10
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Lecture 4, 2-6-2008 9 MBAC6080 Changes in Objective Function
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Lecture 4, 2-6-2008 10 MBAC6080 Product Mix Example Max Z = 40 + 50 y profits s.t. 1 + 2 y    40hours 4 x  + 3 y    120 clay x y    0 non-negativity How/When do changes in the  profit contribution impact the optimal solution?
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Lecture 4, 2-6-2008 11 MBAC6080 30 20 x Geometric Representation
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Lecture 4, 2-6-2008 12 MBAC6080 Geometric Representation 30 20 x
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Lecture 4, 2-6-2008 13 MBAC6080 Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$13 Number to produce Pots 24 0 40 26.66666667 15 $C$13 Number to produce Pitchers 8 0 50 30 20 Constraints Final
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This note was uploaded on 06/01/2008 for the course MBAC 6080 taught by Professor Vossen during the Spring '08 term at Colorado.

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Lecture4web - MBAC6080 Decision Modeling and Applications Thomas Vossen Assistant professor of Operations Management Leeds School of Business

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