Question

Given the following data, use exponential smoothing with a = 0.3 and α =.5 to develop a demand forecasts for period 7.  Assume that the forecast for week 1= 19. Use the Mean Absolute Percent Error to determine which forecasts are more accurate.

Period	1	2	3	4	5	6
Demand	17	19	15	19	13	18

Answer 1

Given , data may be tabulated as ,

PERIOD	ACTUAL DEMAND (At)	FORECAST DEMAND (Ft)
1	17	19 (given)
2	19
3	15
4	19
5	13
6	18
7

Now , since we have been given with

Therefore , we have ,

According to exponential smoothening method , the formula for calculating the forecast for period F_t+1 is given by -

Thus, we have ,

Now since we have , for period 1,

Therefore , for period 2 , we have ,

i.e., F₂ = 18

Similarly , for period 3 , we have ,

For period 4 , we have ,

For period 5 , we have ,

For period 6 , we have ,

And , finally for period 7 , we have ,

THUS , THE ABOVE TABLE BECOMES -

PERIOD	ACTUAL DEMAND (At)	FORECAST DEMAND (Ft)
1	17	19 (given)
2	19	18
3	15	18.5
4	19	16.75
5	13	17.875
6	18	15.4375
7		16.71875

thus , the forecast demand for period 7 = 16.71875

Now , we calculate Mean Absolute Percent Error , which is the mean of the percent of the error with respect to actual demand and is calculated as ,

where , |error| = | actual demand - forecast demand|

So , we have the following table,

PERIOD	ACTUAL DEMAND (At)	FORECAST DEMAND (Ft)	ERROR		Absolute percent error
1	17	19 (given)	-2	2	11.76%
2	19	18	1	1	5.26%
3	15	18.5	-3.5	3.5	23.33%
4	19	16.75	-3.75	3.75	19.73%
5	13	17.875	-4.875	4.875	37.5%
6	18	15.4375	-3.4375	3.4375	19.09%
7		16.71875

Therefore , Mean Absolute Percent Error =

= 19.445 %

i.e., MAPE = 19.445 %