Decision Trees

1
Decision Trees

• in 30 minutes
• Anne Ku15 September 2005

2
Diagram

• Decision nodes alternatives
• Chance nodes probabilities
• Outcomes
• Expected values
• Rolling back
• Perfect and imperfect information

3
Examples

• Decisions only - no uncertainty
• Uncertainties only - no decision
• Roll of dice, flip of a coin
• Imperfect information test, sample, rumour, hire
  consultant
• Perfect information perfect foresight,
  clairvoyant

4
Expected Value

• Also known as weighted average (as all the
  probabilities add to one)
• Multiply each outcome of an uncertain alternative
  by its probability, then
• Add the results together
• Expected value criterion choose the alternative
  with the highest or lowest expected value
  (depending on whether more is better, or less is
  better)

5
Simple decision trees

• Surgery or medication example
• Which game to play? Tossing a die
• What to wear weather changes
• Tutorial how to build decision trees

6
Flu Vaccine introduce or not?

• A government committee is considering the
  economic benefits of a program of preventative
  flu vaccinations. If vaccinations are not
  introduced then the estimated cost to the
  government if flu strikes in the next year is 7m
  with probability 0.1, 10m with probability 0.3
  and 15m with probability 0.6. It is estimated
  that such a program will cost 7m and that the
  probability of flu striking in the next year is
  0.75.One alternative is to institute an
  "early-warning" monitoring scheme (costing 3m)
  which will help detect an outbreak of flu early
  and hence institute a rush vaccination program
  (costing 10m because of the need to vaccinate
  quickly before the outbreak spreads).

7
RD Funding

• GM was evaluating two competing technologies in
  their engine development program. One used a new
  type of coating (Project A), while the other
  incorporated a new material (Project B). Project
  A had been going on for some time when Project B
  was identified. While they could be researched
  simultaneously, the two technologies offered the
  same benefits and could not be implemented
  together. The decision alternatives were
  therefore1. Continue with Project A only 2.
  Stop Project A and start Project B 3. Do both
  4. Cease Project A and not do Project B.

8
Applications

• Medical, healthcare, pharmaceutical
• Energy
• Business
• Manufacturing
• Litigation sue, claim, mediation
• RD investment
• Drug research

• Drilling for oil
• Product planning
• Product development
• Capacity planning
• Applying for a job, graduate school, project
  proposal
• EXAMPLES

9
Exercises

• Draw a decision tree at the time when you were
  applying to get into college. Which colleges did
  you apply? What were your chances? Assign values.
• Draw a decision tree for job hunting
• Draw a decision tree for choosing a date
• Draw a decision tree for travelling