Question

Nelson Fabricators sells a portable EKG machine. The sales manager requires a weekly forecast of the portable EKG machine so that he can schedule production. The manager uses exponential smoothing with α = 0.30.

Week Actual Production

1 535

2 689

3 601

4 768

5 433

1. Forecast the number of machines at the end of week 5.

2. Calculate the bias and MAD. Which measure is more accurate?

Need to show formula either hand or in Excel pls

Answer 1

Let Actual value be and forecast value be

We have smoothing constant  α = 0.30.and since we have not been given we assume that , Hence 2nd row

(1)

We know the formula for forecasting

We simplify to

Actual (At)	Forecast (Ft)
535	535
689	535
601	581.2
768	587.14
433	641.398
	578.8786
alpha	0.3
1-alpha	0.7

Using Excel we apply this formula from the second week

We input the values in the forecast column in excel ' =0.3*At+0.7*Ft '

Final Ans: 641.398 = 641

(2)

We don't have forecast for week 1 and no actual for week six. This reduces our no. of obs 'n' = 4

Bias =

Actual (At)	Forecast (Ft)	Error(At-Ft)
535	535	0
689	535	154
601	581.2	19.8
768	587.14	180.86
433	641.398	-208.398
	578.8786
		146.262
alpha	0.3
1-alpha	0.7
Bias	36.5655	=146.262/4

MAD(Mean Absolute Deviation )=

Actual (At)	Forecast (Ft)	Error(At-Ft)	Absolute Error
535	535
689	535	154	154
601	581.2	19.8	19.8
768	587.14	180.86	180.86
433	641.398	-208.398	208.398
	578.8786
		Sum	563.058
alpha	0.3
1-alpha	0.7
MAD	140.7645	=563.058/4

MAD = 140.76

A low Bias and MAD indicate a good forecast. In my opinion MAD is better error calculator since it takes absolute values of the total error,i.e. in terms of magnitude. Whereas bias can be misleading since it reduces the error due to -ve values.