Question

Calculations 10. The manager of an industrial pump manufacturing facility must forecast future demand. She has generated 2 series of forecasts already, and wishes to compare them to a 2-period moving average forecast. a. (7 points) Compute the 2-period moving average forecast. Time Demand Forecast l Forecast 2 Moving Average 492 470 3 485 480 493 490 498 497 2 478 488 492 493 6 492493 b. (10 points) Compute the ME and MAD for all three methods. c. (5 points) Which forecasting method would you recommend for these data? Why?

Answer 1

a. 2 period moving average forecast for a particular period is the average of actual demand for the previous 2 period. Hence we get the forecast for 2 period moving average as below

Forecast for week 3 = (Actual Demand for week 2 + Actual Demand for week 1)/2 = (470+492)/2 = 481

Forecast for week 4 = (Actual Demand for week 3 + Actual Demand for week 2)/2 = (485+470)/2 = 477.5

Forecast for week 5 = (Actual Demand for week 4 + Actual Demand for week 3)/2 = (493+485)/2 = 489

Forecast for week 6 = (Actual Demand for week 5 + Actual Demand for week 5)/2 = (498+493)/2 = 495.5

b. ME is the mean error and is calculated as the average of the difference between the actual demand and the forecasted demand.

For forecast 1,

For Week 3, error = 485-480=5
For Week 4, error = 493-490=3
For Week 5, error = 498-497=1
For Week 6, error = 492-493=-1

Hence ME for forecast 1 = (5+3+1-1)/4 = 2

For forecast 2,

For Week 3, error = 485-478=7
For Week 4, error = 493-488=5
For Week 5, error = 498-492=6
For Week 6, error = 492-493=-1

Hence ME for forecast 2 = (7+5+6-1)/4 = 4.25

For forecast 3,

For Week 3, error = 485-481=4
For Week 4, error = 493-477.5=15.5
For Week 5, error = 498-489=9
For Week 6, error = 492-495.5=-3.5

Hence ME for forecast 3 = (4+15.5+9-3.5)/4 = 6.25

MAD is the mean absolute deviation and is calculated as the average of the absolute difference between the actual demand and the forecasted demand. In absolute deviation the negative sign is ignored.

For forecast 1,

For Week 3, absolute error = |485-480|=5
For Week 4, absolute error = |493-490|=3
For Week 5, absolute error = |498-497|=1
For Week 6, absolute error = |492-493|=1

Hence MAD for forecast 1 = (5+3+1+1)/4 = 2.5

For forecast 2,

For Week 3, absolute error = |485-478|=7
For Week 4, absolute error = |493-488|=5
For Week 5, absolute error = |498-492|=6
For Week 6, absolute error = |492-493|=1

Hence MAD for forecast 2 = (7+5+6+1)/4 = 4.75

For forecast 3,

For Week 3, absolute error = |485-481|=4
For Week 4, absolute error = |493-477.5|=15.5
For Week 5, absolute error = |498-489|=9
For Week 6, absolute error = |492-495.5|=3.5

Hence MAD for forecast 3 = (4+15.5+9+3.5)/4 = 8

c. I would recommend forecasting method 1 for these data. This is due to the fact that the ME and MAD for method 1 is lesser compared to method 2 and 3. This means that the forecast as per method 1 is much more closer to the actual demand compared to forecast as per method 2 and 3. Hence I would recommend forecast method 1 for this data.