Decision Analysis Problems

Decision Analysis Problems
5 Decision Analysis questions. The answer could be in graphs or table or few words and short scentences or calculations. Please refer to Decision Analysis for the Professional (DAP), Third or Fourth Edition, by McNamee and Celona (2005), to finish the work.

 

Partial credit will be given so please show all your work and circle your answer. When drawing a decision tree, please clearly label alternatives, outcomes, probabilities, and values on the tree. When drawing an influence diagram, please clearly label decision, chance, and value nodes.
Learning Objectives
By the end of the course students will be able to:
1) Identify and frame key issues of decisions
2) Create doable alternatives
3) Obtain decision-relevant information in an unbiased manner
4) Define values and tradeoffs
5) Analyze, evaluate, and compare each alternative
6) Present a cogent case to gain commitment to action

This course will improve your decision making, modeling, analytical and excel skills.
PROBLEM 1 (20 points): A communication-electronics firm is deciding whether to manufacture a new communications device. The decision to produce the device means an investment of $3M, and the demand for such a device is uncertain. Estimates of probability for the continuous random variable, Demand, are shown below:

P(Demand < $6 million) = 0.9 (High Demand)
P(Demand < $4 million) = 0.5 (Moderate Demand)
P(Demand < $1 million) = 0.1 (Low Demand)

a) Draw a decision tree of your problem. Compute the expected value of each alternative. Should the firm make the investment?
b) Determine the values of perfect information and control for Demand.
PROBLEM 2 (20 points): A to Z Marketing is deciding whether to purchase the rights to a new algorithm that would optimize online advertising across various retail business categories. The following decision tree illustrates A to Z Marketing’s decision.

Suppose a survey is available from Company Z that indicates whether the new algorithm will be favorable or unfavorable in the market. The following table provides the probability of a “favorable” or “unfavorable” result from the survey given the actual demand.

Actual Demand “Favorable” “Unfavorable”
High 0.9 0.1
Moderate 0.6 0.4
Low 0.2 0.8

Determine how much this survey is worth.

Problem 3 (20 points): Thomas Bayes had long been promised a graduation present of $10,000 by his father, to be received on graduation day, 3 months hence. His father had recently offered an alternative gift, and Bayes was trying to decide between the two gifts, since his father had asked for a decision by the following day. The alternative gift would be 1,000 shares of stock in Satisficing Systems, Inc., a strategic consulting firm. On the day he was deciding the stock was selling for $12 per share. Thus, it looked to Bayes as if he would be wise to take the stock, since its value was $12,000. He would not receive the stock until graduation day, however, and he recognized that the stock price 3 months in the future was uncertain. With these facts in mind, Bayes reached the following conclusions (probability assessments):

He thought that the stock price was more likely to rise than fall in the intervening 3 months, and that it was likely to be above $14 per share as below that figure when he would receive the stock. He thought that there was only 1 chance in 100 that the stock price would drop to $6 per share, and a 1 chance in 100 that the price would be more than twice its current price on graduation day He thought that there was only 1 chance in 5 that the price would be below $10, and there was 1 chance in 5 that it would be above $16 when he received it.

Draw a decision tree of Bayes’ decision. Use the extended Swanson-Megill to model the stock price. Compute the expected value for each alternative. What is the preferred course of action?

Problem 4 (20 points): Ward Edwards recognized that his utility for money was not linear, and that his risk aversion would therefore influence his decision. Use the following risk assessments to plot Ward’s utility function. Assume U($0) = 0 and U($25) = 1.

His certain equivalent was $9 for a gamble consisting of a 0.5 chance of $0 and 0.5 chance of $25. His certain equivalent was $3 for a gamble consisting of a 0.2 chance of $25 and 0.8 chance of $0. His certain equivalent was $12 for a gamble consisting of a 0.5 chance of $3 and 0.5 chance of $25. His certain equivalent was $17 for a gamble consisting of a 0.5 chance of $12 and 0.5 chance of $25.

Using the above utility function, determine Ward’s preferred course of action by computing the certain equivalent for each alternative shown below:

Problem 5 (20 points): Draw an influence diagram of the following decision problem. You have been called upon to pick up the XYZ project where the previous decision analyst has left it. As the analyst is hurrying off, she hands you her notes and says “This is all I have on the XYZ project; you will have to draw the influence diagram yourself.” Here are the notes she hands you:

If color is red, then profit = revenues – fee.

If color is blue, then profit = revenues.

The only color alternatives are red and blue.

revenues = domestic + foreign

Fee is either $25K or $50K (equally likely) and will be known before choosing color.

Foreign revenues are equally likely to occur between $0 and $200K, inclusive.

If color is blue, then domestic revenues are p($400K) = 0.3 and p($50K) = 0.7.

If color is red, then domestic revenues are uncertain, and normally distributed with a mean of $200K and a standard deviation of $25K.

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