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

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

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

Sensitivity analysis on Values

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

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 52500 as interest = $4200 per year Obviously plane option is profitable only if you can make more than $4200 per year.

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.

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 52500 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

Tornado Diagram Used to compare one-way sensitivity analyses for all relevant variables Free software available at http://www.tushar-mehta.com/excel/software/tornado/

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

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

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

Sensitivity analysis on Weights

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

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

Eagle Airlines - Three Variable Tree

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