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 67 65 2 75 67 66 3 70 73 70 4 74 69 69 5 69 72 72 6 72 66 73 7 80 70 75 8 78 77 81 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 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 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 are used, MSE would be natural; if 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 appears to be more accurate.

Answer 1

ANSWER:

Given that,

a)

Period	Demand	F1	E	|e|	e2	(|e|/actual)x100
1	68	67	1	1	1	1.5
2	75	67	8	8	64	10.7
3	70	73	-3	3	9	4.3
4	74	69	5	5	25	6.8
5	69	72	-3	3	9	4.3
6	72	66	6	6	36	8.3
7	80	70	10	10	100	12.5
8	78	77	1	1	1	1.3
	586			37	245	49.6

Period	Demand	F2	E	|e|	e2	(|e|/actual)x100
1	68	65	3	3	9	4.4
2	75	66	9	9	81	12.0
3	70	70	0	0	0	0.0
4	74	69	5	5	25	6.8
5	69	72	-3	3	9	4.3
6	72	73	-1	1	1	1.4
7	80	75	5	5	25	6.3
8	78	81	-3	3	9	3.8
	586			29	159	39.0

MAD = |Actual - Forecast| / n

MAD_F1 = 37/8 = 4.625

MAD_F2 = 29/8 = 3.625

F2 forecast results appears to be more accurate because MAD model gives less error than F1.

b)

MSE = |Actual - Forecast|² / (n-1)

MSE_F1 = 245 / 7 = 35.00

MSE_F2 = 159 / 7 = 22.71

F2 forecast results appears to be more accurate because MSE model gives less error than F1.

c)

MSE, as it squares the error term , mathematically "punishes" the forecast with larger errors (hence more incorrect). MSE is more sensitive measure of accuracy when considering the size of the deviation from actual demand. Both MAD and MSE are good and valid measures of forecast accuracy.

d)

MAPE =( (|Actual - Forecast| / actual) x 100) / n

MAPE_F1 = 49.6 / 8 = 6.21

MAPE_F2 = 39 / 8 = 4.87

F2 forecast results appears to be more accurate because MAPE model gives less error than F1.