Operations and Supply Chain Management The Core

FORECASTING chapter 3 67
where
RSFE = The running sum of forecast errors, considering the nature of the error.
(For example, negative errors cancel positive errors and vice versa.)
MAD = The average of all the forecast errors (disregarding whether the deviations are
positive or negative). It is the average of the absolute deviations.
Exhibit 3.12 illustrates the procedure for computing MAD and the tracking signal for a
six-month period where the forecast had been set at a constant 1,000 and the actual
demands that occurred are as shown. In this example, the forecast, on average, was off by
66.7 units and the tracking signal was equal to 3.3 mean absolute deviations.
We can get a better feel for what the MAD and tracking signal mean by plotting the
points on a graph. Though this is not completely legitimate from a sample-size standpoint,
we plotted each month in Exhibit 3.12 to show the drift of the tracking signal. Note that it
drifted from minus 1 MAD to plus 3.3 MADs. This happened because actual demand was
greater than the forecast in four of the six periods. If the actual demand does not fall below
the forecast to offset the continual positive RSFE, the tracking signal would continue to
rise and we would conclude that assuming a demand of 1,000 is a bad forecast.
Computing the Mean Absolute Deviation (MAD), the Running Sum of Forecast Errors
(RSFE), and the Tracking Signal (TS) from Forecast and Actual Data
exhibit 3.12
​ ​ MONTH
DEMAND
SUM OF MAD
FORECAST ACTUAL DEVIATION RSFE ABS. DEV. ABS. DEV. (% ERROR)*
RSFE†
​TS = _____
MAD
1 1,000 950 −50 −50 50 50 50 (5.26%) −1
†Overall, ​TS = _____ RSFE
MAD = ____ 220
66.7 = 3.3 MADs​.
2 1,000 1,070 +70 +20 70 120 60 (5.61%) 0.33
Excel:
Forecasting
3 1,000 1,100 +100 +120 100 220 73.3 (6.67%) 1.64
4 1,000 960 −40 180 40 260 65 (6.77%) 1.2
5 1,000 1,090 +90 +170 90 350 70 (6.42%) 2.4
6 1,000 1,050 +50 +220 50 400 66.7 (6.35%) 3.3
*Overall, MAD = 400 ÷ 6 = 66.7. MAPE = (5.26 + 6.54 + 9.09 + 4.17 + 8.26 + 4.76)/6 = 6.35%.
4
Tracking
signal
3
2
1
0
Actual
exceeds
forecast
–1
–2
–3
1 2 3 4
Month
5 6
Actual is
less than
forecast