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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

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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

### 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