Question 4Forecasting Below is the sales data for Forever Young Boutique in 18 w
ID: 374942 • Letter: Q
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Question 4Forecasting Below is the sales data for Forever Young Boutique in 18 weeks. (You can find the Excel sheet containing this data on Blackboard.) Week Sales Week Sales 246 288 245 204 236 257 174 248 229 254 153 244 252 198 162 199 189 213 2 3 4 13 15 16 18 (a) Develop a forecast for week 19 by using three different forecasting techniques: i. Three-week simple moving average, ii. Weighted moving average with weights wl-0.5, w2-0.3, w3-0.2 111. Exponential smoothing technique with a smoothing constant of -03 (Hint: You may use Excel to calculate the problem.) (b) Which forecasting method you considered in Question (a) is the most accurate according to the Mean Absolute Deviation (MAD) criterion? Please justify your answer.Explanation / Answer
Following formula may be taken note of which have been used to calculate forecasted value :
Simple Moving average :
Ft = ( St-1 + St-2 + St-3 ) / 3
Ft = Forecast for period t
St, St-1, St-2 = Actual sales for period t-1, t-2 and t-3 respectively
Weighted moving average :
Ft = 0.5xSt-1 + 0.3xst-2 + 0.2xSt-3
Ft = Forecast for period t
St, St-1, St-2 = Actual sales for period t-1, t-2 and t-3 respectively
Exponential smoothing technique :
Ft = alpha x St-1 + ( 1- alpha) x Ft-1 = 0.3xSt-1 + 0.7xFt-1 ( where , alpha = exponential smoothing constant = 0.3
Accordingly , please find calculated values of forecast under different methods in below table :
Week
Sales
Forecast ( simple moving average)
Absolute deviation
Forecast (weighted moving average)
Absolute deviation
Forecast ( exponential smoothing )
Absolute deviation
1
254
2
153
3
244
4
252
217.00
35.00
218.7
33.3
244
8
5
198
216.33
18.33
229.8
31.8
236.41
38.41
6
262
231.33
30.67
223.4
38.6
234.43
27.57
7
199
237.33
38.33
240.8
41.8
231.12
32.12
8
189
219.67
30.67
217.7
28.7
234.02
45.02
9
213
216.67
3.67
206.6
6.4
229.13
16.13
10
246
200.33
45.67
203
43
222.37
23.63
11
288
216.00
72.00
224.7
63.3
216.56
71.44
12
245
249.00
4.00
260.4
15.4
219.00
26.00
13
204
259.67
55.67
258.1
54.1
231.42
27.42
14
236
245.67
9.67
233.1
2.9
239.42
3.42
15
257
228.33
28.67
228.2
28.8
237.53
19.47
16
174
232.33
58.33
240.1
66.1
234.73
60.73
17
248
222.33
25.67
211.3
36.7
236.34
11.66
18
229
226.33
2.67
227.6
1.4
228.83
0.17
19
217.00
223.7
228.46
459.00
492.3
411.20
Thus :
FORECASTED VALUE FOR WEEK 19 UNDER SIMPLE MOVING AVERAGE
459
FORECASGTED VALUE FOR WEEK 19 UNDER WEIGHTED MOVING AVERAGE
492.3
FORECASTED VALUE FOR WEEK 19 UNDER EXPONENTAIL SMOOTHING METHOD
411.20
Mean absolute Deviation for any type of forecast = Sum of Values of Absolute deviation / 15 ( number of observations from 14 to 18)
Thus :
MAD FOR SIMPLE MOVING AVERAGE FORECAST = 459/15 =
30.6
MAD FOR WEIGHTED MOVING AVERAGE FORECAST
32.82
MAD FOR EXPONENTIAL SMOOTHING FORECAST
27.41
The forecast with least MAD is most preferable because it represents least deviation between forecasted and actual values and therefore more accuracy.
Accordingly , Exponential smoothing forecast which has the least value is the most accurate forecast
Week
Sales
Forecast ( simple moving average)
Absolute deviation
Forecast (weighted moving average)
Absolute deviation
Forecast ( exponential smoothing )
Absolute deviation
1
254
2
153
3
244
4
252
217.00
35.00
218.7
33.3
244
8
5
198
216.33
18.33
229.8
31.8
236.41
38.41
6
262
231.33
30.67
223.4
38.6
234.43
27.57
7
199
237.33
38.33
240.8
41.8
231.12
32.12
8
189
219.67
30.67
217.7
28.7
234.02
45.02
9
213
216.67
3.67
206.6
6.4
229.13
16.13
10
246
200.33
45.67
203
43
222.37
23.63
11
288
216.00
72.00
224.7
63.3
216.56
71.44
12
245
249.00
4.00
260.4
15.4
219.00
26.00
13
204
259.67
55.67
258.1
54.1
231.42
27.42
14
236
245.67
9.67
233.1
2.9
239.42
3.42
15
257
228.33
28.67
228.2
28.8
237.53
19.47
16
174
232.33
58.33
240.1
66.1
234.73
60.73
17
248
222.33
25.67
211.3
36.7
236.34
11.66
18
229
226.33
2.67
227.6
1.4
228.83
0.17
19
217.00
223.7
228.46
459.00
492.3
411.20
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