Given the following gasoline data: Quarter Year 1 Year 2 1 160 156 2 150 148 3 1

Question

Given the following gasoline data:

Quarter

Year 1

Year 2

1

160

156

2

150

148

3

195

201

4

170

174

(a) Compute the seasonal index for each quarter. FOR THE SEASONAL INDEX, GIVE YOUR ANSWER TO TWO DECIMAL PLACES. (EG: 0.55)

Quarter 1 Answer=

Quarter 2 Answer=

Quarter 3 Answer=

Quarter 4 Answer=

(b) Suppose we expect year 3 to have annual demand of 800. What is the forecast value for each quarter in year 3?

FOR THE FORECAST VALUE, GIVE YOUR ANSWER TO THE NEAREST WHOLE NUMBER. (EG: 120)

Quarter 1 Answer=

Quarter 2 Answer=

Quarter 3 Answer=

Quarter 4 Answer=

Quarter

Year 1

Year 2

1

160

156

2

150

148

3

195

201

4

170

174

Explanation / Answer

a> the steps required to find the seasonal index are as follows :

1. calculate the average for each cycle :

we are given the quaterly data for two years

for year 1 the average or the mean for the gasoline data is = [160+150+195+170]/4 = 143.75

for year 2 the average or the mean for the gasoline data is = [156+148+201+174]/4 = 169.75

2.Calculate the proportion or average percentage for each piece of original data :

to get the proportion we'll divide the data for each quater for each year by the mean for that year, that is

for year 1 :

quarter 1 proportion = 160/143.75 = 1.11

quarter 2 proportion = 150/143.75 = 1.04

quarter 3 proportion = 195/143.75 = 1.36

quarter 4 proportion = 170/143.75 = 1.18

for year 2 :

quarter 1 proportion = 156/169.75 = . 92

quarter 2 proportion = 148/169.75 = .87

quarter 3 proportion = 201/169.75 = 1.18

quarter 4 proportion = 174/169.75 = = 1.02

3. Calculate the seasonal index or seasonal component for each season

To calculate the seasonal index for each quarter we'll calculate the average of the proportions for each quarter.

seasonal inder for quarter 1 = (1.11+.92)/2 = 1.015 = 1.02

seasonal inder for quarter 2 = (1.04+.87)/2 = .95

seasonal inder for quarter 3 = (1.36+ 1.18)/2 = 1.27

seasonal inder for quarter 4 = (1.18+ 1.02)/2 = 1.10

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