The document discusses decision trees and their applications, including: 1) Decision trees can help decision makers choose optimal courses of action when there are multiple alternatives and uncertainty about outcomes. 2) An example is provided of a fruit vendor who must decide how many cases of strawberries to order given uncertain daily demand and selling prices. 3) Analyzing the decision tree shows the optimal order is 12 cases, maximizing expected profit.

1. Decision trees

2. Decision trees : applications
• When the user has an objective he is trying to
achieve: max. profit, optimise cost
• When there are several courses of action
• There is a calculable measure of benefit of the
various alternatives
• When there are events beyond the control of
the decision maker: environmental factors
• Uncertainty concerning which outcome will
actually happen

3. • A fruit vendor sells strawberries. One case of
strawberries costs him $20 which he sells for
$50 per case. If not sold on the same day, it is
worthless. Analysis of past data shows that
the demand for cases is as per the table
attached.
• What is the optimal stock he should order?

5. Daily sales No of days sold Probability
10 15 0.15
11 20 0.20
12 45 0.45
13 25 0.25
Total 100 1.00

6. Demand Stock action
10 cases 11 12 13
10 300 280 260 240
11 300 330 310 290
12 300 330 360 340
13 300 330 360 390

7. Expected profit
• Expected profit if he stocks 10 cases is:
300x0.15+ 300x0.20+300x0.40+300x0.25=300
If he stocks 11 cases: exp profit=322.50
12 cases: exp profit =335
13 cases: exp profit =327.50
Optimal course of action is to stock 12 cases

8. • If he had perfect information, then he would stock the
exact number of cases required each day. The actual
demand still varies, but he knows it in advance.
• In this case the conditional profit will be the maximum
profit for each level of demand.
• Expected profit with perfect information will be:
• 300x0.15+330x0.20+360x0.40+390x0.25= 352.50
• So with perfect information he makes an additional
profit of 352.50-335=17.50
• This is the maximum price he will be willing to pay for
‘perfect information’

9. Decision tree analysis
• A graphic model of the decision process
• Useful in making decisions concerning
investments, project management
• Squares symbolize decision points
• Circles represent chance events

10. • When analyzing decision trees:
i) Start from the right (top of the tree) and work back to the left (root)
ii) When analyzing a chance node (circle) calculate the expected value at
that node by multiplying the probability on each branch emanating
from that node by the profit at the end of that branch and then
summing up for all the branches that emanate from that node
iii) When analyzing a decision node (square), let the expected value at
that node be the maximum of the expected values for all the branches
emanating from that node.
iv) In this way, we choose the action with the largest expected value
while pruning the branches corresponding to the less profitable
actions

11. • Christie has recently received an offer from a large hotel chain to
operate the resort for the winter , guaranteeing her a $ 45000 for
the season. She is also considering leasing snow making equipment
for the season.If the equipment is leased, the resort will be able to
operate full-time , regardless of the amount of natural snowfall. If
she decides to use snowmakers to supplement the natural snowfall,
her profit for the season will be$1,20,000 minus the cost of leasing
and operating the equipment. The leasing cost will be $ 12,000 per
season irrespective of how much it is used. The operating cost will
be $10,000 if the snowfall is more than 40 inches, $ 50000 if the
snowfall is between 20 and 40 inches and $ 90,000 if it is less than
20 inches.
• The probability distribution of the snowfall and the resulting profit
is summarized in the attached table
• What should Christie do?

12. Amount of snow Profit Probability
More than 40 1,20,000 0.4
inches
Between 20 and 40 40,000 0.2
inches
Less than 20 inches -40,000 0.4