Question

1. 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?

2. Given the following gasoline data:

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

1. Compute the seasonal index for each quarter.
2. Suppose we expect year 3 to have annual demand of 400. What is the forecast value for each quarter in year 3?

3. 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

1. Develop a three-day moving average for Thursday.
2. 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 these questions

*write it in MS format not Pic

course name is Quantitative Methods

Answer 1

1.

Alternatives	Low	Medium	High	Expected Value
Alternative A(xi)	80	120	140	110
Alternative B(xi)	70	90	100	85
Alternative C(xi)	30	60	120	66
Probability(pi)	0.4	0.3	0.3
	Expected value = ∑pixi

Expected value of perfect information (EVPI) for this situation : Alternative A will be chosen having highest expected value of 110

2.

Quarter	Year 1	Year 2
1	95	105
2	85	95
3	105	115
4	100	120
Average	96.25	108.75
Quarter	Year 1(Ratio)	Year 2(Ratio)	SI
1	0.987	0.966	0.9762651142
2	0.883	0.874	0.8783400508
3	1.091	1.057	1.0741901776
4	1.039	1.103	1.0712046574
			4

Steps:-

1. Calculate mean of quarterly data for each year

2. Create new table and divide each data of a year by respective mean

    e.i. for quarter-1 year-1 : 95/96.26 = 0.987

3. To Calculate SI value for each quarter , add ratio value of each year and divide by number of year

   e.i SI for Quarter 1 = Ratio(year1)+Ratio(year1) / 2

                                = (0.987 + 0.966)/2

                                        = 0.9762651142