Decision Analysis Lecture 8

1
Decision Analysis - Lecture 8

• Fatigue Management simulation
• Decision Analysis Refresher
• Decision trees
• Decision rules
• EMV

2
Fatigue Management
3
What is decision analysis?

• Structured way of looking at decisions
• Doesnt explicitly consider intangibles
• Can choose decision rule based on intangibles
• Fundamental idea is that it pays to look at all
  the options before making a decision
• Way of taking uncertainty into account

4
Four Steps

• Structure Problem
• Make Assessments
• Decision
• Sensitivity Analysis

5
Structure

• Two elements
• 1) decision options (square)
• 2) states of nature or uncertain events
  (circle)
• Use a tree to represent the decision
• Events must be in proper sequence in a tree
• States of nature must be exhaustive and mutually
  exclusive

6
Stocking Decision Example

• Decision is how many of a product to stock.
• The three states of nature are the possible
  customer demand levels 10 units, 11 units or 12
  units.
• Find out about customer demand after decide how
  many to stock.

7
Stocking Decision

• The cost of each unit is 60.
• The profit from each unit sold is 50 (i.e.
  revenue from each unit is 110).
• Units not sold this period are worthless.

8
Decision tree
9
Assessments

• Two types of assessments must be made
• 1) payoffs
• 2) probabilities

10
Payoffs

• Payoffs are monetary outcomes.
• Usually the particular payoff you get depends not
  only on your decision but also on some uncertain
  event or events.
• Payoffs can be shown in a table or put onto a
  decision tree.

11
Payoff table

• For straightforward decisions, can use a payoff
  table
• Your decision choices go along the top of the
  table or down the side
• All possible outcomes from an uncertain event go
  down the side or along the top
• Payoffs go into the table

12
Stocking Example

• Payoffs are profits/losses both revenues and
  costs have been considered and combined.

13
Probabilities

• Need estimates of the probability of each state
  of nature. (Note Probabilities should always add
  to 1.)
• Put probabilities into tree diagram.
• Customer demand probabilities are
• Demand 10 with probability 0.4
• Demand 11 with probability 0.3
• Demand 12 with probability 0.3

14
Tree with probabilities
15
Decision Rules (for a profit maximising example)

• Make a decision that gives you the greatest
  potential up side. MAXIMAX
• Make a decision that gives you the lowest
  potential down side. MAXIMIN
• Make a decision that gives you the least
  potential for regret. MINIMAX REGRET
• Make a decision that gives you the greatest
  expected value. EMV (Expected Monetary Value)

16
MAXIMAX

• What is the highest payoff?
• Make the decision that gives you the possibility
  of getting this payoff.

17
MAXIMIN

• What is the worst possible payoff for each
  decision?
• Choose the largest of these (i.e. do the best you
  can in the worst case scenario) and make the
  decision giving you that payoff.

18
MINIMAX Regret

• Find the regret (opportunity loss) you would
  feel for each decision and state of nature at not
  having made a different decision.

19
MINIMAX Regret (cont.)

• For each decision what is the largest amount of
  regret? (another type of worst case scenario)
• Choose decision where this number is smallest.
  (Do best you can in worst case scenario.)

20
EMV

• An expected value takes into account the
  probability of uncertain events.
• Expected payoff is
• P(A) ? Payoff if A occurs P(B) ? Payoff if B
  occurs etc for all outcomes of an uncertain
  event
• Write expected payoffs into decision tree at
  every circle (state of nature node).

21
(No Transcript)
22
EMV (cont.)

• At decision node (square) find highest EMV and
  make that decision.

23
Folding back a decision tree

• Draw tree
• Put in probabilities and payoffs
• Working backwards from payoffs, calculate EMVs at
  each state of nature node (circle) and choose
  highest EMV from the branches coming out of each
  decision node (square).
• Mark off which branch is chosen for each decision
  node.

24
Folding back (cont.)

• Stop when reach the left hand side of tree.
• Marked branches tell you which decisions to make.

25
Decision Rules

• When might you use each rule?
• Is EMV always the best rule to use?
• Are there other decision rules you could use?

26
Sensitivity Analysis

• Asks questions like
• Would decision change if the probabilities were
  different?
• Would decision change if the payoffs were
  different?
• Robust decisions remain the same even if
  probabilities and payoffs are changed slightly.

27
Building decision trees in Excel
28
Next lecture

• Read texts
• Read and prepare Gilbert Gilbert