A company has recorded its sales volumes for the last four weeks on a daily basis. It ships products only on weekdays and has recorded the following sales volumes:

Week	Day	Day Number	Sales Volume
Week 1	Monday	1	1130
	Tuesday	2	851
Wednesday		3	859
	Thursday	4	828
	Friday	5	726
Week 2	Monday	6	1085
	Tuesday	7	1042
Wednesday		8	892
	Thursday	9	840
	Friday	10	799
Week 3	Monday	11	1303
	Tuesday	12	1121
Wednesday		13	1003
	Thursday	14	1113
	Friday	15	1005
Week 4	Monday	16	1849
	Tuesday	17	1607
	Wednesday	18	1489
	Thursday	19	1490
	Friday	20	1384

QB4, contd

1. Calculate a (multiplicative) Winters forecast for Friday of Week 5, given that the smoothed

levels and trends for Thursday of Week 4 were as follows:

S19 = 1350

, b19 = 120 , and the

smoothed seasonal factors calculated at the end of Thursday Week 4 were:

F15 = 0.78

F16 = 1.28 , F17 = 1.14 , F18 = 0.90 , F19 = 0.90 . Use the following smoothing constants:

smoothing constant for level (A) =0.2, smoothing constant for trend (B) =0.2, smoothing constant for seasonality (C) =0.1. It is not required to adjust seasonal factors to average 1.00.

2. It is found that increasing the smoothing constant for trend from 0.2 to 0.4 improves forecasting accuracy. Explain why this might be. (No calculations required).

3. An alternative method produced the following forecasts for Week 4: 1250 (Monday), 1350 (Tuesday), 1450 (Wednesday), 1550 (Thursday), 1650 (Friday). Calculate the Mean Error and the Mean Absolute Error for these forecasts .

4. Look again at the data and the forecasts produced by the alternative method. Explain why

these forecasts are not as accurate as they should be. (No further calculations required).

5. How many initial (multiplicative) seasonal values need to be estimated? Describe one method

of initialization of seasonal indices and briefly mention its advantages and disadvantages.