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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

Mgmt Sci

472.21

4

Fall 2011


Sensitivity analysis

Sensitivity Analysis

  • But what if…

    • How “sensitive” is the answer?

    • Outcomes if parameters change


Sensitivity analysis1

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


Sensitivity analysis2

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


Sensitivity analysis3

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


Sensitivity analysis4

x2

8

6

4

2

x1

2

4

6

8

0

Sensitivity Analysis

Friesen Farms

Min Z = $6x1 + 3x2

24 = 6x1 + 3x2


Sensitivity analysis5

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


Sensitivity analysis6

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


Sensitivity analysis7

x2

8

6

4

2

x1

2

4

6

8

0

Sensitivity Analysis

Friesen Farms

Min Z = $6x1 + 3x2

24 = $6x1 + 3x2

…start again


Sensitivity analysis8

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


Sensitivity analysis9

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…


Sensitivity analysis10

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


Sensitivity analysis11

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


Sensitivity analysis12

Sensitivity Analysis

a.k.a. “Post-Optimality Analysis”

  • so far:

    • assumed fixed values

  • real world

    • changing

    • probable

“What happens if…”


Sensitivity analysis13

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!


Sensitivity analysis14

Sensitivity Analysis

  • Constraints

    • Shadow Prices

      • on the computer

        • much easier than graph or formula

        • either

          • run scenarios

          • read reports


Sensitivity analysis15

Sensitivity Analysis

  • Constraints

    • Shadow Prices

      • if constraint non-binding

      • if constraint binding


Sensitivity analysis16

Sensitivity Analysis

  • Constraints

    • Shadow Prices

without fundamental change


Where are we now

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


  • What other uses

    What other uses?

    • ch 3

      • mixes

        • manufacturing products

        • factory use

        • displaying products

        • advertising

      • store layout

        • Mega-Mart

          • ch 3 prob 38 pg 103

            • try


    Where are we now1

    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?


    Where are we now2

    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?


    Rucklehouse public relations

    Rucklehouse Public Relations

    Minimization

    question on the quiz

    chapter 3

    problem 23-25

    9th edition: pg 100


    Now what

    for Tue

    more product mix

    Quick-Screen

    read for Tue

    diet

    Breathtakers

    transportation

    Zephyr Television

    marketing

    Biggs

    ignore

    Now what?

    applications – ch 4


    Now what1

    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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