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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

472.21

4

Fall 2011

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

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

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

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

x2

8

6

4

2

x1

2

4

6

8

0

Sensitivity Analysis

Friesen Farms

Min Z = \$6x1 + 3x2

24 = 6x1 + 3x2

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

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

x2

8

6

4

2

x1

2

4

6

8

0

Sensitivity Analysis

Friesen Farms

Min Z = \$6x1 + 3x2

24 = \$6x1 + 3x2

…start again

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

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…

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 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 Analysis

a.k.a. “Post-Optimality Analysis”

• so far:
• assumed fixed values
• real world
• changing
• probable

“What happens if…”

Sensitivity Analysis

a.k.a. “dual cost” or “Lagrange multipliers”

• Constraints
•  unit of constraint

 Z

• within current constraints

Hey, have I got a deal for you!

Sensitivity Analysis
• Constraints
• on the computer
• much easier than graph or formula
• either
• run scenarios
Sensitivity Analysis
• Constraints
• if constraint non-binding
• if constraint binding
Sensitivity Analysis
• Constraints

without fundamental change

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?
• ch 3
• mixes
• manufacturing products
• factory use
• displaying products
• store layout
• Mega-Mart
• ch 3 prob 38 pg 103
• try
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?
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

Minimization

question on the quiz

chapter 3

problem 23-25

9th edition: pg 100

for Tue

more product mix

Quick-Screen

diet

Breathtakers

transportation

Zephyr Television

marketing

Biggs

ignore

Now what?

applications – ch 4

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