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Mgmt Sci

Mgmt Sci. 472.21 4 Fall 2011. Sensitivity Analysis. But what if… How “sensitive” is the answer? Outcomes if parameters change. x 2. 8. x 1 = 5 DeSallaberry x 2 = 2 Carmen Z = $33 60. 6. 4. 2. x 1. 2. 4. 6. 8. 0. Sensitivity Analysis. x 1 = 0 bags of DeSallaberry

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Mgmt Sci

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  1. Mgmt Sci 472.21 4 Fall 2011

  2. Sensitivity Analysis • But what if… • How “sensitive” is the answer? • Outcomes if parameters change

  3. x2 8 x1 = 5 DeSallaberry x2 = 2 Carmen Z = $3360 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis x1 = 0 bags of DeSallaberry x2 = 8 bags of Carmen Z = $2400 Friesen Farms Min Z = $6x1 + 3x2 s.t.2x1 + 4x2≥ 16 4x1 + 3x2≥ 24 x1, x2 0 x1 = 8 DeSallaberry x2 = 0 Carmen Z = $4800

  4. x2 8 x1 = 5 DeSallaberry x2 = 2 Carmen Z = $3360 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis x1 = 0 bags of DeSallaberry x2 = 8 bags of Carmen Z = $2400 Friesen Farms Min Z = $6x1 + 3x2 s.t.2x1 + 4x2≥ 16 4x1 + 3x2≥ 24 x1, x2 0 x1 = 8 DeSallaberry x2 = 0 Carmen Z = $ $4800

  5. x2 8 x1 = 4.8 DeSallaberry x2 = 1.6 Carmen Z = $3360 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis x1 = 0 bags of DeSallaberry x2 = 8 bags of Carmen Z = $2400 Friesen Farms Min Z = $6x1 + 3x2 s.t.2x1 + 4x2≥ 16 4x1 + 3x2≥ 24 x1, x2 0 x1 = 8 DeSallaberry x2 = 0 Carmen Z = $4800

  6. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis Friesen Farms Min Z = $6x1 + 3x2 24 = 6x1 + 3x2

  7. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis Friesen Farms Min Z = $6x1 + 3x2 24 = $12x1 + 3x2 If x1 costs more

  8. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis Friesen Farms Min Z = $6x1 + 3x2 24 = $24x1 + 3x2 If x1 costs more

  9. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis Friesen Farms Min Z = $6x1 + 3x2 24 = $6x1 + 3x2 …start again

  10. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis Friesen Farms Min Z = $6x1 + 3x2 24 = $6x1 + 4x2 If x2 costs more

  11. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis • Friesen Farms • Min Z = $6x1 + 3x2 • 24 = $6x1 + 4x2 • in words: • - You can increase the x1 price as much as you want, it makes no difference, but…

  12. x2 8 6 4 2 x1 2 4 6 8 0 Sensitivity Analysis • Friesen Farms • Min Z = $6x1 + 3x2 • 24 = $6x1 + 4x2 • in words: • - …if you increase the x2 price by only $1, things change

  13. Sensitivity Analysis • remember • in graphs • what matters is: • the slope of the lines • in numbers • the line slope is the same as • the ratio between x1 and x2 • in “real life” • what you focus on is: • prices & costs

  14. Sensitivity Analysis a.k.a. “Post-Optimality Analysis” • so far: • assumed fixed values • real world • changing • probable “What happens if…”

  15. Sensitivity Analysis a.k.a. “dual cost” or “Lagrange multipliers” • Constraints • Shadow Prices •  unit of constraint  Z • within current constraints Hey, have I got a deal for you!

  16. Sensitivity Analysis • Constraints • Shadow Prices • on the computer • much easier than graph or formula • either • run scenarios • read reports

  17. Sensitivity Analysis • Constraints • Shadow Prices • if constraint non-binding • if constraint binding

  18. Sensitivity Analysis • Constraints • Shadow Prices without fundamental change

  19. Where are we now? • working on • Possibility Restaurant • pg 70 • Irwin Textile Mills • ch 3 prob 11-13 pg 98 • United Aluminium Company • ch 3 prob 14-16 pg 98-99 • Julia’s Food Booth • ch 3 case 3 pg 108 • Exeter Mines • ch 3 prob 48-49 pg 105-106

  20. What other uses? • ch 3 • mixes • manufacturing products • factory use • displaying products • advertising • store layout • Mega-Mart • ch 3 prob 38 pg 103 • try

  21. ch 3 worked a lot on maximization some on ratios need to check OK on minimization Rucklehouse Public Relations Excel ch 3 prob 23-25 9th edition, pg 100 ch 4 today complete Julia’s Food Booth Exeter Mines Grafton Metal Works prob 14 Summer Sports Camp case 1 Where are we now?

  22. ch 3 worked a lot on maximization some on ratios minimization reivew Rucklehouse Public Relations Excel ch 3 prob 23-25 9th edition, pg 100 complete Julia’s Food Booth Exeter Mines ch 4 today Lakeside Boatworks prob 10 Grafton Metal Works prob 14 Summer Sports Camp case 1 Where are we now?

  23. Rucklehouse Public Relations Minimization question on the quiz chapter 3 problem 23-25 9th edition: pg 100

  24. for Tue more product mix Quick-Screen read for Tue diet Breathtakers transportation Zephyr Television marketing Biggs ignore Now what? applications – ch 4

  25. for Fri not marked investment Kathleen Allen for Fri marked Ch 4 prob 2: 1st paragraph options Excel sheet prob 3 all Excel sheet ½ page memo prob 5 all ½ page memo Now what? applications – ch 4

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