Question

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:

Month	Sales	Forecast 1	Forecast 2
1	771	769	769
2	790	788	791
3	794	795	796
4	776	780	778
5	772	772	771
6	770	774	773
7	761	760	762
8	774	771	772
9	792	792	791
10	794	798	796

a. Compute a tracking signal for the 10th month for each forecast using the cumulative error for months 1 to 10. Use action limits of ± 4. Is there bias present? (Do not round your intermediate calculations. Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Forecast	Tracking Signal	Bias
Method 1		(Click to select)  Not present  Present
Method 2		(Click to select)  Not present  Present

b. Compute 2s control limits for each forecast. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

Forecast	Control Limits
Method 1
Method 2

Answer 1

a) Tracking signal is given by fromula,

Tracking signal=Sum of errors/MAD

The errors and absolute errors have been tabulated for both the methods below:-

Month	Sales	Forecast 1	Forecast 2	Error 1	Error 2	Abs Error 1	Abs Error 2
1	771	769	769	2	2	2	2
2	790	788	791	2	-1	1	1
3	794	795	796	-1	-2	2	2
4	776	780	778	-4	-2	2	2
5	772	772	771	0	1	1	1
6	770	774	773	-4	-3	3	3
7	761	760	762	1	-1	1	1
8	774	771	772	3	2	2	2
9	792	792	791	0	1	1	1
10	794	798	796	-4	-2	2	2

For method 1,

Sum of errors=-5, MAD=1.7, so, tracking signal=-5/1.7=-2.94

Similarly, for method 2,

Sum of errors=-5, MAD=1.7, so, tracking signal=-5/1.7=-2.94

As the tracking errors are within the action limits, so, there is no bias in any of the forecast methods.

b) 2s control limits

For the forecast methods, 2s control limits are given by

UCL=Mean(of forecast)+2*(1.25*MAD)=Mean+2.5*MAD, and

LCL=Mean-2*(1.25*MAD)=Mean-2.5*MAD

For Method 1,

UCL=779.9+2.5*(1.7)=784.15, LCL=779.9-2.5*(1.7)=775.65

For Method 2,

UCL=779.9+2.5*(1.7)=784.15, LCL=779.9-2.5*(1.7)=775.65