Question

Quantitative Methods (STAT-201)

Q3 . A manager is deciding whether or not to build a small facility. Demand is uncertain and can be either at a high or low level. If the manager chooses a small facility and demand is low, the payoff is $30. If the manager chooses a small facility and demand is high, the payoff is $10. On the other hand, if the manager chooses a large facility and demand is low, the payoff is -$20, but if demand is high, the payoff is $80.

a. Develop the decision table.

b. What would be the best decision based on the maximax criterion?

c. What would be the best decision based on Hurwicz's criterion of realism using α = 0.6?

Q4 The following payoff table provides profits based on various possible decision alternatives and various levels of demand with probabilities of different demands:

	States of Nature Demand
Alternatives	Low	Medium	High
Alternative A	80	120	140
Alternative B	70	90	100
Alternative C	30	60	120
Probability	0.4	0.3	0.3

What will be the expected value of perfect information (EVPI) for this situation?

Q5 Given the following gasoline data:

Quarter	Year 1	Year 2
1	95	105
2	85	95
3	105	115
4	100	120

a. Compute the seasonal index for each quarter.

b. Suppose we expect year 3 to have annual demand of 400. What is the forecast value for each quarter in year 3?

Q6 Number of students present in a class of STAT201 on different days of the week is given in the following table:

Day	Number of students present in the class
Sunday	20
Monday	30
Tuesday	20
Wednesday	50

a. Develop a three-day moving average for Thursday.

b. Develop a forecast of presents for Thursday using exponential smoothing with an alpha = 0.2. Assume that an initial forecast for Wednesday was 40.

Answer 1

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