Question

Given the following data, use exponential smoothing with  = 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

Answer: Exponential forecast using alpha= 0.3

Period	Demand	Forecast, Ft	Absolute deviation= |Forecast - Actual|	Percent error= (absolute error/actual sales) * 100
1	17	19	2.00	11.76%
2	19	18.40	0.60	3.16%
3	15	18.58	3.58	23.87%
4	19	17.51	1.49	7.86%
5	13	17.95	4.95	38.11%
6	18	16.47	1.53	8.51%
7		16.93
				15.55%
				MAPE

Answer: Exponential forecast using alpha= 0.5

Period	Demand	Forecast, Ft	Absolute deviation= |Forecast - Actual|	Percent error= (absolute error/actual sales) * 100
1	17	19	2.00	11.76%
2	19	18.00	1.00	5.26%
3	15	18.50	3.50	23.33%
4	19	16.75	2.25	11.84%
5	13	17.88	4.88	37.50%
6	18	15.44	2.56	14.24%
7		16.72
				17.32%
				MAPE

Exponential forecast using alpha= 0.3 is more accurate because it has a lower value

• the formula to be used in Simple Exponential smoothing is

F_t+1= alpha*A_t + (1-alpha) F_t

A_t means Actual demand of t'th period, if you want to find out the Forecast through exponential smoothing= forecast of 3rd period = alpha*actual demand of 2nd period +(1-alpha) *forecast demand of 2nd period

• remember forecast of 1st period is 19, alpha= 0.3 and 0.5

Formula used:

Absolute deviation= |Forecast - Sales|

Percent error= (absolute error/actual sales) * 100

MAPE = mean absolute percent error = sum of percent error / no. of periods

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