Decision Analysis
Decision Theory / Systems Analysis
Summer 2003
IS 601
Ö. S. Benli
Key Characteristics of a
Decision Tree
• Time flows from left to right & placement
of decision and event nodes are
consistent with the way events will play
out in reality.
• The branches emanating from each
decision node represent all possible
decisions under consideration.
Summer 2003
IS 601
Ö. S. Benli
Key Characteristics of a
Decision Tree, cont.
• The branches emanating from each
event node represent a set of mutually
exclusive and collectively exhaustive
outcomes of the event node.
• The sum of probabilities of each
outcome branch emanating from a
given event node must sum to one.
Summer 2003
IS 601
Ö. S. Benli
Key Characteristics of a
Decision Tree, cont.
• Each and every “final” branch of the
decision tree has a numerical value
associated with it. The numerical value
represents usually (but not necessarily)
some measure of monetary value, such
as salary, revenue, cost, etc.
Summer 2003
IS 601
Ö. S. Benli
Expected Monetary Value
(EMV)
of an uncertain event is the weighted
average of all possible numerical
outcomes, with probabilities of each of
the possible outcomes used as weights.
Summer 2003
IS 601
Ö. S. Benli
Bill’s Optimal Decision
Strategy
• Reject John’s offer
• If Vanessa offers a job, accept it. Else,
participate in corporate summer
recruiting.
• The EMV of this strategy is $13,032.
Summer 2003
IS 601
Ö. S. Benli
The output from constructing
and solving a decision tree
is a very concrete plan of action, which
states what decisions should be made
under each possible uncertain outcome
that might prevail.
Summer 2003
IS 601
Ö. S. Benli
Procedure for Solving a
Decision Tree
1. Start with the final branches of the tree
•
•
For an event node, compute the EMV of
the node by weighted average of the
EMV of each branch weighted by its
probability
For a decision node, compute the EMV of
the node by choosing that branch
emanating from the node with the best
EMV value
Summer 2003
IS 601
Ö. S. Benli
Procedure for Solving a
Decision Tree, cont.
2. The decision tree is solved when all
nodes have been evaluated
3. The EMV of the optimal strategy is the
EMV computed for the “root” node of
the tree.
Summer 2003
IS 601
Ö. S. Benli
Sensitivity analysis of the
optimal decision
9Issue 1: The probability that Vanessa
would offer Bill a summer job.
9Issue 2: The cost of Bill’s time and effort
in participating in the corporate summer
recruiting
9Issue 3: The distribution of summer
salaries that Bill could expect to receive.
Summer 2003
IS 601
Ö. S. Benli
9Issue 1: as long as the probability of
Vanessa’s offering a job is 18% or
larger, then optimal strategy will still be
reject John’s offer and to accept the
offer from Vanessa if it realized.
Summer 2003
IS 601
Ö. S. Benli
9Issue 2: as long as the implicit cost to
Bill of participating in summer recruiting
is less than $2,578, then the optimal
strategy will still be to reject John’s offer
and to accept Vanessa’s offer if it is
realized.
Summer 2003
IS 601
Ö. S. Benli
• Issue 3: in order for Bill’s optimal
strategy to change, all of the possible
summer corporate recruiting salaries
would have to increase by more than
$2,419.
Summer 2003
IS 601
Ö. S. Benli
Principal Steps of Decision
Analysis
1. Structure the decision problem
– List all decisions that have to be made.
– List all uncertain events, and their
possible outcomes, in the problem.
2. Construct the basic decision tree by
placing the decision nodes and the
event nodes in their chronological and
consistent
Summer logically
2003
Ö. S. Benliorder.
IS 601
Steps of Decision Analysis,
cont.
3. Determine the probability of each of
the possible outcomes of each of the
uncertain events.
4. Determine the numerical value of each
of the final branches of the decision
tree.
Summer 2003
IS 601
Ö. S. Benli
Steps of Decision Analysis,
cont.
5. Solve the decision tree using the
folding back procedure:
a) Starting with the final branches “evaluate”
each event and decision node of the tree
b) The decision tree is solved when all
nodes have been evaluated.
c) The EMV of the optimal decision strategy
is the EMV computed for the root node of
the tree.
Summer 2003
IS 601
Ö. S. Benli
Steps of Decision Analysis,
cont.
6. Perform sensitivity analysis on all key
data values.
•
For each data value for which decision
maker lacks confidence, test how the
optimal strategy will change relative to a
change in the data value, one data value
at a time.
Summer 2003
IS 601
Ö. S. Benli
Two additional aspects of
Decision Analysis
Methodology
• The EMV Criterion and the Consideration of
Risk
– Expected Utility Theory
• Non-quantifiable Consequences
Summer 2003
IS 601
Ö. S. Benli
Benefits of Using Decision
Analysis
• Clarifying the decision problem
• Providing insight into the decision
process
• Ascertaining the importance of key data
• Providing new ways to think about the
decision problem
Summer 2003
IS 601
Ö. S. Benli
The need for a systematic
theory of probability
• §1.4 “Development of a new consumer
product”
– Pr{result positive | market weak} = 10%
– Pr{result negative | market strong} = 20%
• Conditional probabilities; Bayes’
Theorem ---- Chapter 2.
Summer 2003
IS 601
Ö. S. Benli