Exercise: Decision Analysis

PART I: Decision Making under Ignorance

General Motors is planning their production strategy for their next model year. Three alternatives are being considered for their model Malibu: 30,000, 20,000, and 12,000. GM decides to categorize the demand for Malibu for the next year as either High (H) or Low (L). The payoffs measured in millions of dollars for different states of nature are presented in the table below.

	States of nature
Decision Alternatives	High Demand (H)	Low Demand (L)
Produce 30K	29	-12
Produce 20K	18	8
Produce 12K	3	11

Find the best alternative based on these criteria (use table below):

1. Maximax

2. Maximin

3. LaPlace

Alternatives	(H)	(L)	Maximax	Maximin	LaPlace
Produce 30K	29	-12
Produce 20K	18	8
Produce 12K	3	11

Create an opportunity loss table and find the best alternative using the Minimax Regret criterion:

Opportunity Loss Table

Alternatives	(H)	(L)	Minimax
Produce 30K
Produce 20K
Produce 12K

PART II: Decision Making under Risk (Uncertainty)

Now consider that the probabilities of the states of nature are known to be 0.62 for High Demand and 0.38 for Low Demand. Compute EVs for each alternative

Alternatives	(H)	(L)	EV
Produce 30K	29	-12
Produce 20K	18	8
Produce 12K	3	11

Fill in the opportunity loss numbers from the previous page and compute the EOL values

Opportunity Loss Table

Alternatives	(H)	(L)	EOL
Produce 30K
Produce 20K
Produce 12K

Compute EVUPI and interpret

Compute EVPI and interpret

Part III – Decision Trees, Sequential Decisions

Draw a decision tree to depict the problem and its solution.

Assume now that new information is available from a source regarding the economy, and the forecast is likely to be either favorable or unfavorable. The reliability of the forecast is given below from past data:

	High Demand	Low Demand
Favorable	0.80	0.30
Unfavorable	0.20	0.70

What is this information worth? Compute EVSI. First draw the decision tree to show the sequential decisions, compute the posterior probabilities, and solve the tree.