The following data are monthly sales of jeans at a local department store. The b
ID: 333133 • Letter: T
Question
The following data are monthly sales of jeans at a local department store. The buyer would like to forecast sales of jeans for the next month, July.
(a) Forecast sales of jeans for March through June using the naïve method, a two-period moving average, and exponential smoothing with an ? = 0.2. (Hint: Use naïve to start the exponential smoothing process.)
(b) Compare the forecasts using MAD and decide which is best.
(c) Using your method of choice, make a forecast for the month of July.
Explanation / Answer
Please refer below table highlighting relevant calculations :
Month
Actual sales
Forecast ( Naïve method)
Absolute deviation
Forecast ( 2 period moving average)
Absolute deviation
Forecast ( Exponential smoothing)
Absolute deviation
January
45
February
30
45
15
45
March
40
30
10
37.5
2.5
42
2.00
April
50
40
10
35
15
41.6
8.40
May
55
50
5
45
10
43.28
11.72
June
47
55
8
52.5
5.5
45.62
1.38
July
47
51
45.90
SUM =
48
33
23.50
Following to be noted :
Forecasted value as per Naïve method :
Ft = At-1 , Ft = Forecast for period t and At-1 = Actual sales for period t-1
Forecasted value as per 2 period moving average :
Ft = ( At-1 + At-2 ) /2 , Ft = forecast for period t , At-1 , At-2 = actual sales for period t-1 and t-2 respectively
Forecasted value as per exponential smoothing method :
First we determine forecasted value for February = 45 as per Naïve method
Subsequently :
Ft = alpha x At-1 + ( 1 – alpha) x Ft-1
= 0.2 x At-1 + 0.8 x Ft-1
Where, alpha = exponential smoothing forecast = 0.2
Also to be noted:
Absolute deviation = Absolute difference between actual sales value and forecasted value
Mean absolute deviation ( MAD) = Sum of absolute deviation / Corresponding number of observations
Based on above definition of MAD ,
MAD for forecast as per Naïve method = 48/5 = 9.6
MAD for forecast as per 2 period moving average = 33/ 4 = 8.25
MAD for forecast as per exponential smoothing method = 23.5 / 4 = 5.875
Since MAD for exponential smoothing forecast is the LOWEST , Exponential smoothing forecast is the best
FORECAST FOR JULY AS PER NAÏVE METHOD = 47
FORECAST FOR JULY AS PER 2 PERIOD MOVING AVERAGE = 51
FORECAST FOR JULY AS PER EXPONENTIAL SMOOTHING METHOD = 45.90
Month
Actual sales
Forecast ( Naïve method)
Absolute deviation
Forecast ( 2 period moving average)
Absolute deviation
Forecast ( Exponential smoothing)
Absolute deviation
January
45
February
30
45
15
45
March
40
30
10
37.5
2.5
42
2.00
April
50
40
10
35
15
41.6
8.40
May
55
50
5
45
10
43.28
11.72
June
47
55
8
52.5
5.5
45.62
1.38
July
47
51
45.90
SUM =
48
33
23.50
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