MGT713 Production / Operations Management GDB No. 1 Solutions Fall 2014


It is important to include an indication of the extent to which the forecast might deviate from the value of variable that actually occurs. This will provide the forecast user with a better perspective on how far off a forecast might be. This also provides a decision maker a measure of accuracy to use as a basis for comparison, when choosing among different techniques.

2.2.1 Forecast Accuracy

Forecasting error is defined as the difference between actual and forecast, i.e.,

.

Two commonly used measures are

· Mean absolute deviation (MAD)
, and
Mean squared error (MSE)

.

The difference between these two measures is that MAD weights all errors evenly, and MSE weights errors according to their squared values.

For the usage of these measures, either MAD or MSE, a manager could compare the results of exponential smoothing with values of .1, .2, and .3, and select the one that yields the least MAD or MSE for a given set of data.

2.2.2 Forecasting Control

It is necessary to monitor forecast errors to ensure that the forecast is performing adequately over time. This is generally accomplished by comparing forecast errors to predefined values, or action limits, as illustrated below.




Possible sources of forecast errors:

· the omission of an important variable,

· a sudden or unexpected change in the variable (causing by severe weather or other nature phenomena, temporary shortage or breakdown, catastrophe, or similar events),

· appearance of a new variable,

· being used incorrectly,

· data being misinterpreted, and

· random variation.

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Two common methods in forecast control / monitor are tracking signal and control chart.

Tracking Signal

A tracking signal focuses on the ratio of cumulative forecast error to the corresponding MAD:

.
The tracking signal often ranges from to . For the most part, we shall use limits of , which are roughly comparable to three standard deviation limits. Values within the limits suggest --- but do not guarantee --- that the forecast is performing adequately.

MAD can be updated using the following exponential smoothing equation:

.

Control Chart

The control chart sets the limits as multiples of the squared root of MSE. Basic assumptions are

· Forecast errors are randomly distributed around a mean of zero, and

· The distribution of errors is normal.


The square root of MSE is used in practice as an estimate of the standard deviation of the distribution of errors. That is,

.

For a normal distribution, 95% of the errors fall within , and approximately 99.7% of the errors fall within . Errors fall outside these limits should be regarded as evidence that corrective action is needed.

Plotting the errors with the help of a control chart can be very informative. A plot helps you to visualize the process and enables you to check for possible patterns, nonrandom errors, within the limit that suggests an improved forecast is possible