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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