Question

Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water. Actual demand and the two sets of forecasts are as follows:

		PREDICTED DEMAND
Period	Demand	F1	F2
1	68	63	62
2	75	66	61
3	70	73	70
4	74	65	71
5	69	71	73
6	72	69	73
7	80	70	76
8	78	72	80

a. Compute MAD for each set of forecasts. Given your results, which forecast appears to be more accurate? (Round your answers to 2 decimal place.)

MAD F1
MAD F2

(Click to select)  F1  F2  None  appears to be more accurate.

b. Compute the MSE for each set of forecasts. Given your results, which forecast appears to be more accurate? (Round your answers to 2 decimal places.)

MSE F1
MSE F2

(Click to select)  F1  F2  None  appears to be more accurate.

c. In practice, either MAD or MSE would be employed to compute forecast errors. What factors might lead a manager to choose one rather than the other?

Either one might already be in use, familiar to users, and have past values for comparison. If    (Click to select)  control charts  tracking signals  are used, MSE would be natural; if  (Click to select)  control charts  tracking signals  are used, MAD would be more natural.

d. Compute MAPE for each data set. Which forecast appears to be more accurate? (Round your intermediate calculations to 2 decimal places and and final answers to 2 decimal places.)

MAPE F1
MAPE F2

(Click to select)  F1  F2  None  appears to be more accurate.

Answer 1

a. Mean Absolute Deviation (MAD) calculation:

		PREDICTED DEMAND
Period	Demand (D)	F1	F2	Absolute Error |(D-F1)|	Absolute Error |(D-F2)|
1	68	63	62	5	6
2	75	66	61	9	14
3	70	73	70	3	0
4	74	65	71	9	3
5	69	71	73	2	4
6	72	69	73	3	1
7	80	70	76	10	4
8	78	72	80	6	2
Mean Absolute Deviation (MAD) (Average)				5.88	4.25
MAD F1	5.88
MAD F2	4.25

F2 is more accurate as value of MAD F2 is lower.

b. Mean Squared Error (MSE) Calculation:

		PREDICTED DEMAND
Period	Demand (D)	F1	F2	Absolute Error (D-F1)	Absolute Error (D-F2)	squared error = (D-F1)^2	squared error = (D-F2)^2
1	68	63	62	5	6	25	36
2	75	66	61	9	14	81	196
3	70	73	70	3	0	9	0
4	74	65	71	9	3	81	9
5	69	71	73	2	4	4	16
6	72	69	73	3	1	9	1
7	80	70	76	10	4	100	16
8	78	72	80	6	2	36	4
Mean Squared Error (MSE)= {Sum of squared error/(n-1)}				5.88	4.25	49.29	39.71
MSE F1	49.29
MSE F2	39.71

Where n is number of errors = 8

F2 is more accurate as value of MSE F2 is lower.

c. Either one might already be in use, familiar to users, and have past values for comparison. If control charts are used, MSE would be natural; if tracking signals are used, MAD would be more natural

d. Mean Absolute Percentage Error (MAPE) Calculation:

		PREDICTED DEMAND
Period	Demand (D)	F1	F2	Absolute Error (D-F1)	Absolute Error (D-F2)	Absolute Percentage Error {(D-F1)/D} *100	Absolute Percentage Error {(D-F2)/D} *100
1	68	63	62	5	6	7.35%	8.82%
2	75	66	61	9	14	12.00%	18.67%
3	70	73	70	3	0	4.29%	0.00%
4	74	65	71	9	3	12.16%	4.05%
5	69	71	73	2	4	2.90%	5.80%
6	72	69	73	3	1	4.17%	1.39%
7	80	70	76	10	4	12.50%	5.00%
8	78	72	80	6	2	7.69%	2.56%
Mean Absolute Percentage Error (MAPE) (Avearge)				5.88	4.25	7.88%	5.79%
MAPE F1	7.88%
MAPE F2	5.79%

  F2 is more accurate as value of MAPE F2 is lower.