1. Sensitivity Analysis: Chapter 5
What is it? – The answer to the question:
“How would our decision (or recommendation) change if some of the numbers we used changed?”
Why is it important?
Much of what we use in decision analytic models is subjectively derived
Many of the numbers we use are subject to measurement error or other sources of uncertainty
It will help us understand the model better
It will help us understand the decision problem better

2. Sensitivity Analysis (continued)
How do we do it?
Important part of the modeling effort
No structured procedure for doing it
Requires common sense
Requires creativity
Can consider various aspects of the problem:
Problem structure
Data
Probabilities (or distributions)
Simply Put: Vary elements of the problem and see how it changes the output

3. Problem Identification and Structure
Check for correct specification of the problem
Rule: Assume that the first articulation of the problem is wrong
Stay in touch with decision maker to stay on track
Structure of Model
We have seen that different people can structure a problem differently
Different value structure
Different measures
Try the problem in multiple ways

4. Sensitivity analysis on Values

5. One-Way Sensitivity Analysis
Only one factor is varied at a time
All others are held at the nominal (base) values
Need to establish the range over which the variable will vary
Maybe there is a known range
Vary by percentage (e.g. +/- 30%)
Bottom Line: Does a change in the variable affect the output – and therefore, the decision
Also Important: If not, we don’t have to worry about the variable

6. Eagle Airline case study
Decision to be made: Invest in Money market at 8% growth or buy planes and run a business.
To buy planes 40% of $87500 will be financed so 60% of $87500 =$52500 will be paid
As cash down
Or use $52500 in money market to earn 8% of as interest = $4200 per year
Obviously plane option is profitable only if you can make more than $4200 per year.

7. Eagle Airlines - Case Study
NOTE: Diagram created using Netica©, a probability network (“Bayes nets”) tool.
Netica is an alternative tool for solving influence diagrams, among other uses.

8. One-Way Sensitivity Analysis
To buy planes 40% of $87500 will be financed so 60% of $87500 =$52500 will cash down
Or use $52500 in money market to earn 8% of as interest = $4200 per year
Obviously plane option is profitable only if you can make more than $4200 per year.
To draw the purchase Seneca (aircraft) line you must calculate profit=revenue-cost and
vary hours flown to get atleast 2 points on the line (see page 178 for calculation)
From Graph, plane option is profitable only if it flies for 664 hours

9. Tornado Diagram
Used to compare one-way sensitivity analyses for all relevant variables
Free software available at

10. Eagle Airlines - Tornado Diagram
Each bar is the range of profit when that variable is changed from its lower to upper
bound while maintaining other variables at base value
If the intention is to make atleast $4200 profit the most important variables are the
first four on the tornado diagram

11. Eagle Airlines - Two Variable Plot
Base value capacity 0.5
Base value Op cost 245
At base value it’s a
profit situation to buy
planes
Point C is a slight
deviation from base
value and the result
is a loss to buy planes

12. Simulation to Model Uncertainty
If computer models are available, they can be solved repeatedly for different assumptions
Tedious, but better than doing by hand!
All variables can be varied simultaneously through Monte Carlo simulation
Tools provided with textbook:
Top Rank
PrecisionTree
@Risk

13. Sensitivity analysis on Weights

14. Sensitivity Analysis on Weights
The most subjective and controversial part of a decision analysis is the weights
Good idea to check sensitivity of the recommendation to the weights
Method:
Choose one attribute to vary, say attribute i
Rescale others so weights still sum to one

15. Example Payoff Do I take my umbrella or not?
– If I don’t and it is sunny, that is best - value 1.00
– If I do I won’t get wet but it’s inconvenient
- value 0.80
– If I don’t and it rains I ruin my suit - value 0.00
– Probability of sunshine is p
Payoff
sunshine
rain p
1 - p
0.00
1.00
0.80
Payoff Calculation:
– Take umbrella
0.8p + 0.8(1-p) = 0.8
– Don’t take umbrella
1.0p + 0(1-p) = p
Therefore:
Take umbrella if
p < 0.8
Take
Umbrella
Don’t take
Umbrella

16. Eagle Airlines - Three Variable Tree

17. LDW software can do sensitivity on weights
See the separate word file on class website