Question

Sales of tablet computers at Ted​ Glickman's electronics store in​ Washington, D.C., over the past 10 weeks are shown in the table​ below:                                      

Week	1	2	3	4	5	6	7	8	9	10
Demand	20	21	28	37	25	29	36	22	25	28

​a) The forecast for weeks 2 through 10 using exponential smoothing with alphaα ​= 0.50 and a week 1 initial forecast of 20.0 are ​(round your responses to two decimal ​places)​:

Week	1	2	3	4	5	6	7	8	9	10
Demand	20	21	28	37	25	29	36	22	25	28
Forecast	20.0

​b) For the forecast developed using exponential smoothing ​(alphaα ​= 0.50 and initial forecast 20.0), the MAD​ = ______sales ​(round your response to two decimal​ places).

Answer 1

Solution:

(a) Exponential smoothing:

In exponential smoothing,

F(t+1) = A(t) + (1-) F(t)

where,

F(t+1) = Forecast for the next period

A(t) = Actual demand for the current period

F(t) = Forecast for the current period

= Smoothing constant

= 0.50

(1-) = 0.50

Using exponential smoothing, forecasts for weeks 2 through 10 are calculated in the table below:

The calculated values are summarized in the table below:

(b) Mean Absolute Deviation (MAD):

MAD = Sum of absolute values of (Actual demand - Forecast demand) / Number of periods

MAD = Absolute values of [(20 - 20) + (21 - 20) + (28 - 20.5) + (37 - 24.25) + (25 - 30.63) + (29 - 27.82) + (36 - 28.41) + (22 - 32.21) + (25 - 27.11) + (28 - 26.06)] / 10

MAD = (0 + 1 + 7.5 + 12.75 + 5.63 + 1.18 + 7.59 + 10.21 + 2.11 + 1.94) / 10

MAD = 4.99 sales