Decision making using decision tree analysis

Decision Tree
And
Analysis

PREPARED BY

Young Kim

IE417 Section 1 Spring 2013

REVISION PAGE:

REVISION        DATE                           DESCRIPTION

      N/C                        06-05-2013                  Initial Release

1.0  Introduction:

The following report demonstrates decision making analysis using decision tree.

2.0  PROBLEM

CEO of Cerebrosoft, Charlotte Rothstein, is faced with a situation where her company needs to make decision whether to launch the product or abandon it. When decided to launch it, they can go with a price of 3 categories, $50, $40, or $30. Once again, with $50 pricing range, they can choose either to hire researcher or not.

3.0  OBJECTIVE

To use technique of decision tree and probabilities to choose optimal scenario for Cerebrosoft with maximum expected revenue.

4.0  REFERENCE DOCUMENTS:

A. Operational Research Applications and Algorithms 4^th Edition, Wayne Winston
B. Lecture slide

5.0  REFERENCE SOFTWARE:

A.      Microsoft Excel

B.      Microsoft Word

6.0  ASSUMPTIONS & RATIONALE:

-          When abandoned, their initial investment of $800000 is lost

-          No marketing, including advertising, or annual support cost of $50000 is encountered in calculation of revenue.

7.0  Decision Tree and Probabilities

Below is embedded file of Decision Tree Diagram and Probabilities Calculation

(I actually have files 4 files embedded in this documents, but its not visible here, hence i will just post it here :))

Without Researcher

-

                         With Researcher

d

EVWPI(expected value with perfect information tree diagram)

Above is the probabilities




 Note: The expected value of node that contains multiple scenarios with probabilities in each tree diagram was calculated by multiplying previous expected value with the corresponding probability.

8.0  Findings

As you can see with the decision tree diagram without researcher, setting product price at $50 will give maximum expected revenue of $715,000 for the first year. If we take in account of support fee of $50,000, then our expected revenue of first year will be $665,000. From the following years, under the assumption that our probabilities stay same, we will have expected revenue of $1,465,000 since our initial investment of $800,000 is made up from first years revenue. The expected revenue from the following year will be

When it comes to decision of whether to hire researcher or not, our expected revenue from hiring researcher is determined to be $705,000.

EVSI is calculated by using equation EVSI = EVWSI – EVWOI which is ($705000+$10,000) - $715,000

EVSI is determined to be = $0.

EVPI is calculated by using equation EVPI = EVWPI – EVWOI

EVWPI is calculated by calculating expected maximum value for each state.
EVWPI = 0.2*$625,000 + 0.7*$725,000 + 0.1*$825,000
EVWPI is determined to be $715,000

EVWOI is calculated from calculation in EVSI which is determined to be $715,000
EVPI = $715,000 - $715,000 = $0

9.0  Conclusion

From the analysis, we can conclude that company should not hire a researcher and set the price of the product at $50 to have maximum expected revenue for first year of $715,000 before support investment of $50,000. This conclusion is drawn from the value of EVSI and EVPI. The minimum desired EVSI value is $10,000 which is the amount that company is willing to pay for the research. The EVSI calculated tells that the amount of research price that company is should pay to have extra expected value is $0, which means that as soon as price of research goes up, the expected profit of company drops by same amount. In other words, unless it is free to conduct the research, it is not worth doing it. The EVPI tells that the amount of money that company is willing to pay to know the trends is $0. Hence, in summary of this analysis, the company should not invest any money on extra information and set the price of product at $50 to maximize their expected profit.