Homework Sourse2 The data table below presents a popular brand of sweater s
2. The data table below presents a popular brand of sweater sale (by quarters) over the past three years:
2013
Sale
2014
Sale
2015
Sale
(t)
(Yt)
(t)
(Yt)
(t)
(Yt)
Spring
12
Spring
16
Spring
18
Summer
25
Summer
32
Summer
45
Fall
76
Fall
80
Fall
84
Winter
52
Winter
62
Winter
60
(a) Calculate the \"seasonal indexes\" for each season.
(b) Forecast the sale of each season in 2016, if we expect the annual sales for the product to be 200 (Yearly Demand) units for the year 2016.
| 2013 | Sale | 2014 | Sale | 2015 | Sale |
| (t) | (Yt) | (t) | (Yt) | (t) | (Yt) |
| Spring | 12 | Spring | 16 | Spring | 18 |
| Summer | 25 | Summer | 32 | Summer | 45 |
| Fall | 76 | Fall | 80 | Fall | 84 |
| Winter | 52 | Winter | 62 | Winter | 60 |
Solution
Seasonal Index = period average demand / average demand for all periods
The period can be daily, weekly, monthly, or quarterly depending on the basis
for the seasonality of demand.
The average demand for all periods is a value that averages out seasonality.
This is called the deseasonalized demand. The previous equation can be rewritten as:
Season index = period average demand / deseasonalized demand.
Data Given :
Solution (a)
Above data can be rearranged as below :
Deseasonalized Demand = 187/4 = 47
The seasonal indices can now be calculated as follows:
Seasonal index = 15 / 47 = 0.33 (Spring)
Seasonal index = 34 / 47 = 0.73 (Summer)
Seasonal index = 80 / 47 = 1.71 (Fall)
Seasonal index = 58 / 47 = 1.24 (Winter)
Total of seasonal indices = 4.00
(b)
Forecast for year 2016 = 200
Forecast average quarterly demand = 200 /4 = 50
Expected quarter demand = (seasonal index)(forecast quarterly demand)
Expected Spring demand = 0.33 x 50 = 16.37
Expected Summer demand = 0.73 x 50 = 36.30
Expected Fall demand = 1.71 x 50 = 85.41
Expected Spring demand = 1.24 x 50 = 61.92
Total forecast demand = 200
| 2013 | Sale | 2014 | Sale | 2015 | Sale |
| (t) | (Yt) | (t) | (Yt) | (t) | (Yt) |
| Spring | 12 | Spring | 16 | Spring | 18 |
| Summer | 25 | Summer | 32 | Summer | 45 |
| Fall | 76 | Fall | 80 | Fall | 84 |
| Winter | 52 | Winter | 62 | Winter | 60 |
