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Overview • Understanding of Decision Trees • Theoretical framework • Example • Pros and Cons
Decision Analysis Is the method for structuring and analyzing managerial decision problems in the face of uncertainty in a systematic and rational manner.
Decision Tree Is a systematic way of organizing and representing the various decisions and uncertainties that the decision-maker faces.
It represents a decision. It is when the decision makers is called to make a decision.
Α
Decision Node
Represents the possible choices that a decision-maker has
Α No
Yes
Branch
In represents an uncertain event. The decision-maker cannot make a decision at this point.
Α
Yes
No
Β Bad Offer
Event Node
The following conditions must apply • Outcome branches that emanate from event
nodes must be: – Mutually excluded – Collectively exhaustive
Expected Monetary Value … is the weighted average of all possible numerical outcomes with the probabilities of each of the possible outcomes used as the weights.
EMV = 0.3* $10.000 + 0.5* $5.000 + 0.2* $1.000 = $3.000 + $2.500 + $200 = $5.700
Α
Yes
No
Β
$ 10.000
$ 5.000
$ 1.000
0.3
0.5
0.2
$ 5.700
EMV Example
JOB SEARCH EXAMPLE I. Formulating the Problem
• Ο Bill is looking for a job for next summer • He has a Job offer from John (October)
Α
Accept offe
r from
John
Step 1
n Vanessa and University offers
Α
Accept offe
r from
John
Β
C
Accept offe
r from
Vanessa
No offer from Vanessa D
E
Step 2
• John’s offer $12.000 • Vanessa’s offer $14.000 • University:
Average Weekly Salary
12 Month Salary Probability
$1.800 $21.600 5% $1.400 $16.800 25% $1.000 $12.000 40%
$500 $6.000 25% $0 $0 5%
Data
Α
Accept offe
r from
John
Β
C
No offer from Vanessa
D
E
€12.000
$14.000
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
0,6
0,4
Data Entry
Key Characteristics of a Decision Tree 1. Time in a decision tree flows from the left to right, and the placement
of the decision nodes and the event nodes is logically consistent with the way events will play out in reality. Any event or decision that must logically precede certain other events and decisions is appropriately placed in the tree to reflect the logical dependence.
2. The branches emanating from each decision node represent all of the possible decisions under consideration at that point in time under the appropriate circumstances.
3. The branches emanating from each event node represent a set of mutually exclusive and collectively outcomes at the event nodes.
4. The sum of the probabilities of each outcome branch emanating from a given event must sum to one.
5. Each and every “final” branch of the decision tree has a numerical value associated with it. This numerical value usually represents some measure of monetary value, such as salary, revenue, cost, etc.
JOB SEARCH EXAMPLE II. Solving the Problem
• EMV = 0,05*$21.600 + 0,25*$16.800 + 0,40*$12.000 + 0,25*$6.000 + 0,05*$0 = $11.850
E
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
$11.850
Calculating EMV at (E)
Decision at Point (C)
Α
Accept offe
r from
John
Β
C
No offer from Vanessa
D
E
€12.000
$14.000
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
0,6
0,4
€14.000
€11.850
Calculating EMV at (D)
• EMV = 0,05*$21.600 + 0,25*$16.800 + 0,40*$12.000 + 0,25*$6.000 + 0,05*$0 = $11.850
E
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
$11.850
n EMV = 0,6*$14.000 + 0,4*$11.850 = $13.032
Β
C
D
0,6
0,4
$14.000
$11.850
$13.032
Calculating EMV at (B)
Decision at Point (A)
Α
Accept offe
r from
John
Β
C
No offer from Vanessa
D
E
€12.000
$14.000
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
$21.600
$16.800
$12.000
$6.000
$0
0,05
0,25
0,40
0,25
0,05
0,6
0,4
€14.000
€11.850 €13.032
Procedure of Solving a Decision Tree 1. Start with the final branches of the decision tree, and evaluate
each event node and each decision node as follows: – For an event node, compute the EMV of the node by computing the
weighted average of the EMV of each branch weighted by its probability. Write the EMV number above the event node.
– For each decision node, compute the EMV of the node by choosing that branch emanating from the node with the best EMV value. Write the EMV number above the decision node, and cross off those branches emanating from the node with inferior EMV values by drawing a double line through them.
2. The decision tree is solved when all nodes have been evaluated. 3. The EMV of the optimal decision strategy is the EMV computed for
the starting branch of the tree.
JOB SEARCH EXAMPLE III. Sensitivity Analysis
Initial Solution DataValue of John's Offer € 12,000Value of Vanessa's Offer € 14,000Probabiity of offer from Vanessa's Firm 0.6Cost of participating in Recruiting € 0
Weekly Salary
12 week Salary
Percentage of Stuents who Received this Salary
€ 1,800 € 21,600 5%€ 1,400 € 16,800 25%€ 1,000 € 12,000 40%€ 500 € 6,000 25%€ 0 € 0 5%
Nodes EMVA € 13,032B € 13,032C € 14,000D € 11,580E € 11,580
Distribution of Salaries from Recruiting
EMV of Nodes
BILL SAMPRAS' JOB DECISION PROBLEM
1. Probability that Vanessa’s firm would offer Bill a summer job
2. The cost of Bill’s time and effort in participating in the school’s corporate summer recruiting.
3. The distribution of summer salaries that Bill could expect to receive.
Data under investigation
When p≥0.174 then John’s offer is rejected.
DataValue of John's Offer € 12,000Value of Vanessa's Offer € 14,000Probabiity of offer from Vanessa's Firm 0.174Cost of participating in Recruiting € 0
Weekly Salary
12 week Salary
Percentage of Stuents who Received this Salary
€ 1,800 € 21,600 5%€ 1,400 € 16,800 25%€ 1,000 € 12,000 40%€ 500 € 6,000 25%€ 0 € 0 5%
Nodes EMVA € 12,001B € 12,001C € 14,000D € 11,580E € 11,580
BILL SAMPRAS' JOB DECISION PROBLEM
Distribution of Salaries from Recruiting
EMV of Nodes
Probability that Vanessa’s firm would offer Bill a summer job
When c<€2.578 John’s offer is rejected.
DataValue of John's Offer € 12,000Value of Vanessa's Offer € 14,000Probabiity of offer from Vanessa's Firm 0.6Cost of participating in Recruiting € 2,578
Weekly Salary
12 week Salary
Percentage of Stuents who Received this Salary
€ 1,800 € 21,600 5%€ 1,400 € 16,800 25%€ 1,000 € 12,000 40%€ 500 € 6,000 25%€ 0 € 0 5%
Nodes EMVA € 12,001B € 12,001C € 14,000D € 9,002E € 9,002
BILL SAMPRAS' JOB DECISION PROBLEM
Distribution of Salaries from Recruiting
EMV of Nodes
The cost of Bill’s time and effort in participating in the school’s corporate summer recruiting
When salaries increase more than €2.420 then Vanessa’s offer is rejected and the University is preferred.
DataValue of John's Offer € 12,000Value of Vanessa's Offer € 14,000Probabiity of offer from Vanessa's Firm 0.6Cost of participating in Recruiting € 0
Weekly Salary
12 week Salary
Percentage of Stuents who Received this Salary
€ 1,800 € 24,019 5%€ 1,400 € 19,219 25%€ 1,000 € 14,419 40%€ 500 € 8,419 25%€ 0 € 2,419 5%
Nodes EMVA € 14,000B € 14,000C € 14,000D € 13,999E € 13,999
BILL SAMPRAS' JOB DECISION PROBLEM
Distribution of Salaries from Recruiting
EMV of Nodes
The distribution of summer salaries that Bill could expect to receive
Summary 1. Structure the decision problem. List all of the decisions that have to be made. List all the
uncertain events in the problem and all of their possible outcomes. 2. Construct the basic decision tree by placing the decision nodes and the event nodes in their
chronological and logically consistent order. 3. Determine the probability of each of the possible outcomes of each of the uncertain events.
Write these probabilities on the decision tree. 4. Determine the numerical values of each of the final branched of the decision tree. Write
these numerical values on the decision tree. 5. Solve the decision tree using the folding-back procedure:
– Start with the final branches of the decision tree, and evaluate each event node and each decision node, as follows:
• For an event node, compute the EMV of the node by computing the weighted average of the EMV of each branch weighted by its probability. Write the EMV number above the event node.
• For each decision node, compute the EMV of the node by choosing that branch emanating from the node with the best EMV value. Write this EMV number above the decision node and cross off those branches emanating from the node with inferior EMV values by drawing a double line through them.
– The decision tree is solved when all nodes have been evaluated. – The EMV of the optimal decision strategy is the EMV computed for the starting
branch of the tree. 6. Perform sensitivity analysis on all key data values.
Pros & Cons • Pros
– Clarity of decision problem – Insight into the decision process – Process of key data – Alternative way of thinking
• Cons – Risk assessment – Assessment of variables that are not easily quantifiable
Thank you!
