Question

In: Operations Management

Use the data below to answer the question parts (a) and (b). This data is for...

Use the data below to answer the question parts (a) and (b). This data is for forecasting fure sale consdiering additive seasonality approach and answer related questions.

SHOW EACH CALCULATION STEP AND DESCRIBE IT

ROUND answers to 2 decimal points.

Time	Year	Season	Sale
1	2018	Q1	1
2		Q2	7
3		Q3	3
4		Q4	2
5	2019	Q1	6
6		Q2	8
7		Q3	1
8		Q4	9

PART a) What is the seasonality index for second season (Q2) ?

Part b)

Assume that we run the regression for the deseasonalized data after calculating seasonality index . We find that regression line slope is 0.4 , and intercept is 2.8. By considering the slope and intercept, what is your final forecast for second season of 2020 by considering both trend and seasonality?

Solutions

Expert Solution

We know that seasonality for a particular quarter is equal to (average of that particular quarter over all the provided years divided by the average sales per quarter for all the provided year).

Here the table is:

Time	Year	Season	Sale
1	2018	Q1	1
2		Q2	7
3		Q3	3
4		Q4	2
5	2019	Q1	6
6		Q2	8
7		Q3	1
8		Q4	9

We have to find the seasonality for Q2.

For Q2 for both the years, the sales = 7 and 8

Average sales in Q2 over both the years = (7 + 8)/2 = 15/2 = 7.5

Average sales per quarter over all the 8 quarters = (1 + 7 + 3 + 2 + 6 + 8 + 1 + 9)/8 = 37/8 = 4.625

Hence seasonality = average for Q2 / average per quarter = 7.5/4.625 = 1.622

Seasonality for Q2 = 1.622

For the deseasonalized data, the regression line has been found.

Slope = 0.4

Intercept = 2.8

Hence, the trend line is: y = 2.8 + 0.4*x (where y is sales and x is time)

For second season of year 2020, time = 10

Hence, the deseasonalized forecast is:

y = 2.8 + 0.4*10 = 2.8 + 4 = 6.8

We know that forecast including seasonality = deseasonalized sales * seasonality

Seasonality for Q2 = 1.622

Deseasonalized forecast = 6.8

So Forecast with trend and seasonality = 6.8 * 1.622 = 11.03

Forecast for Q2 of 2020 considering trend and seasonality = 11.03 units (can be rounded to 11 if required as whole number)

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keosha answered 2 hours ago

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