A forecast is never completely
accurate; forecasts will always deviate from the actual demand. The objective
of forecasting is that it be as slight as possible. There are many measures
of forecast error, the more popular ones are; mean absolute deviation (MAD),
mean absolute percent deviation (MAPD), cumulative error, and average error
or bias (E).
MEAN
ABSOLUTE DEVIATION (MAD)
· Most popular and simplest to use measure of forecasting
· MAD is and average of the difference between the forecast and the actual
demand
· Formula: MAD= (Sum D_{t}  F_{t})
n
Where: t = the period number
D_{t}
= the demand in period t
F_{t}
= the forecast for period t
n = the
total number of periods
  = the
absolute value
· The smaller/lower value of MAD, the more accurate the forecast
· One benefit of MAD is to compare the accuracy of several different forecasting
techiniques.
MEAN
ABSOLUTE PERCENT DEVIATION (MAPD)
· Measures the absolute error as a percentage of demand rather than per period.
· Resulting in elimination of the problem fo interpreting the measure of accuracy
relative to the magnitude of the demand and forecast values, as MAD does.
· Formula: MAPD= (Sum D_{t}  F_{t})
Sum(D_{t})
CUMULATIVE
ERROR
· Formula: E= Sum(e_{t})
· A large postive value indicates the forecast is probably consistently lower
than the actual demand, or is biased low.
· A large negative value implies the forecast is consistently higher than
actual demand or is biased high.
· The cumulative error for exponential smoothing forecast is simply the sum
of the values in the error column.
AVERAGE
ERROR
· A measure closely related to cumulative error is the average error or bias.
It is computed by averaging the cumulative error over the number of time periods.
· Formula: E= Sum (e_{t})
n
· A positive value indicates low bias and a negative value indicates a high
bias. A value close to zero implies a lack of bias.
FORECAST
CONTROL
· There are several ways to monitor forecast error over time to make sure
the forecast is performed correctly.
· Can provide inaccurate forecasts for several reasons;
· Change in trend
· Unanticipated appearance of a cycle
· Irregular variation
· Promotional campaign
· New competition
· Politcial event that distracts consumers
· A tracking signal
monitors the forecast to see if it is high or low. It is recomputed each period
and each movement is compared to control limits.
· It is computed
as simply the error divided by MAD.
· Forecast errors are typically normally distributed which results in the
following relationship between MAD and the standard deviation of the distribution
of error: 1MAD is about 0.8 stadard deviations. This enables us to establish
statistical control limits for the tracking signal that corresponds to the
more familiar normal distribution.
· Statistical control charts are another method
for monitoring forecast error.
· For example, ±3 stadard deviation, control
limits would reflect 99.7 percent of the forecast errors (assuming they are
normally distributed).
· Formula: Divide the Sum (D_{t}
 F_{t})^2
n1
· This formula without the square root is the
mean squared error (MSE).
· MSE is the average
of the squared forecast errors and is sometimes used as a measure of forecast
error.
