Question

Assume that you are planning to have a party at your house. You really would like to have the party outside in the sun, but there is a chance that it might rain. You have two decisions to make – whether or not you will watch the forecast and then whether to have the party inside or outside. If you choose to watch the forecast, it will either tell you that the weather will be sunny or that it will be rainy. If you choose to watch the forecast, you will not have to make the location decision until after you see the forecast. If you do not watch the forecast, you do not get to know what the forecast would have said had you watched it – you need to make the location decision without the knowledge of the forecast. However, the forecast is imperfect (probabilities are below). It also costs you some time, and you are already cutting it close in terms of getting ready.

Your task is to draw the decision tree for this situation, answer some questions about the decision tree, and recommend a course of action on the basis if your analysis.

The information you will need:

Probabilities (note that p(A|B) signifies the probability of event A given that event B has occurred – it is a conditional probability).

p(forecast says it will be sunny) = 0.95

p(it is sunny|forecast said it would be sunny) = 0.99

p(it is sunny|forecast said it would be rainy) = 0.15

p(sunny) = 0.948 [hint: this is to use on the branch of the tree where you decide not to watch the forecast]

Utilities (note that U(case X) represents the utility of case X)

U(watch forecast, party indoors, sunny weather) = 0.3

U(watch forecast, party indoors, rainy weather) = 0.4

U(watch forecast, outdoors, sunny weather) = 0.9

U(watch forecast, outdoors, rainy weather) = 0.0

U(do not watch forecast, indoors, sunny weather) = 0.4

U(do not watch forecast, indoors, rainy weather) = 0.5

U(do not watch forecast, outdoors, sunny weather) = 1.0

U(do not watch forecast, outdoors, rainy weather) = 0.1

(a) (10 points): Draw the decision tree for this problem. Include clear labels for all branches. Include all probabilities and utilities.

(b) (10 points): If you choose to watch the forecast and it says that the weather will be sunny, should you have the party indoors or outdoors? What is your expected utility for this choice?

(c) (5 points): What should your sequence of decisions be? In other words, should you watch the forecast? If you do watch the forecast, what is the optimal location decision for each of the two possible forecast reports? What is your expected utility for the overall decision situation?

d) (10 points): Analyzing a simple party problem might seem silly. However, the structure of this tree has many important applications in engineering. Think of a project management situation that could be described by this structure of decision tree. Write a one-paragraph description of the decision situation you think of (like the description at the beginning of this question), and re-draw the tree with new labels on the branches. You do not need to include any probabilities or utilities on your new tree.

Answer 1