Transcript Decision Making Under Uncertainty

Decision Making Under
Uncertainty
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Two Basic Questions
• What are the possible actions (alternatives)
for this problem?
• What is it about the future that affects the
desirability of each action?
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Terms
• Descriptions of the future: states of nature
• The state of nature items are outcomes.
– The key distinction between an action and a
state of nature is that the action is taken is under
your control, whereas the state of nature that
occurs is strictly a matter of chance.
• The payoff is the result of an action (A) an
a state of nature (S)
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Payoff Table
Action
A1
A2
A3

Ak
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
11
21
31
State of Nature
S1
S2 S3 ……. Sn
12 13 …… 1n
22 23 …… 2n
32 33 …… 3n
k1
k2
k3 …… kn
Conservative (Minimax) Strategy
• The action chosen is that action that under
the worst conditions produces the lowest
“loss.”
• The opportunity loss, Lij, is the difference
between the payoff for action I and the
payoff for the action that would have the
largest payoff under the state of nature j.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Minimax Strategy
• Construct an opportunity loss table by using
the maximum payoff for each state of nature.
• Determine the maximum opportunity loss for
each action.
• Find the minimum value of the opportunity
losses found in step 2; the corresponding
action is the one selected.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
The Gambler (Maximax)
Strategy
The Maximax strategy is to choose that
action having the largest possible payoff.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
The Strategist
(Maximizing the Expected Payoff)
• This strategy assigns a probability to each
state of nature.
• The expected payoff of each action is
determined.
• The action chosen is that action that
produces the largest expected payoff
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Utility
• Utility combines the decision maker’s
attitude toward the payoff and the
corresponding risk of each alternative.
• The utility value of a particular outcome is
used to measure both the attractiveness and
the risk associated with this dollar amount.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Utility Value
• Step1: Assign a utility value of 0 to the
smallest payoff amount (min ) and a value
of 100 to the largest (max ).
• Step 2: The utility value for any payoff
under consideration is found by using:
U(ij) = P * 100
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Utility
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Decision Trees and Bayes’ Rule
• A decision tree graphically represents the
entire decision problem, including:
– The possible actions facing the decision maker.
– The outcomes that can occur.
– The relationships between the actions and
outcomes.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Decision Trees
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Decision Trees and Bayes’ Rule
• Bayes’ rule allows you to revise a
probability in light of certain information
that is provided.
P(Ei and B)
ith path
P(Ei B) 

P( B)
sum of paths
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Use of Bayes’ Rule
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Deriving the Posterior
Probabilities
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Resulting Decision Tree
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing
Deriving the Posterior
Probabilities
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College
Publishing