Page 93 - DMGT523_LOGISTICS_AND_SUPPLY_CHAIN_MANAGEMENT

Logistics and Supply Chain Management

Notes The last item would be the average
F = [(A + A + A + A + A /5]
12 8 9 10 11 12
The stability of the series often determines how many periods to include in the moving average.
Large values of ‘n’ should be used when the series is relatively stable, including more historical
data in the average results in a forecast that is less susceptible to random variations. However,
where the individual values are prone to change, small values of ‘n’ are recommended.
Simple Moving Averages (MA) is an effective and efficient approach to forecasting the future
provided the time series is stationary in both mean and variance. This is important and needs to
be ascertained. Also, if there is a trend in the data, the moving average has the adverse characteristic
of lagging the trend.

Weighted Moving Averages

In a simple moving average, each period has the same weight. However, very often, it may be
desirable to emphasize specific elements more than others. For example, you may decide that
recent demand needs more emphasis over earlier demand. In such a case, weights can be placed
on each element as desired, subject to the condition that the total of the weights should add up
to ‘1’.

The general formula for the weighted moving average then changes to:
F = [(w A + w A + w A + w A + ……+ w A )/n]
t + 1 t t t – 1 t – 1 t – 2 t – 2 t – 3 t – 3 t – n + 1 t – n + 1
Where: F is the weighted moving average for the period t+1,
t + 1
And, w is the weighing factor, and w = 1
t t
For example, if ‘n’ is 5, we could weight the moving average as follows:
w = 5/(1 + 2 + 3 + 4 + 5) = 5/15 = 1/3;
1
w = 4/15;
2
w = 3/15 = 1/5;
3
w = 2/15 and
4
w = 1/15.
5
w = 1/3 + 4/15 + 1/5 + 2/15 + 1/15 = 1
In this example, the most recent period has the highest weight compared to the earlier periods.
The weight progressively reduces as the period increases.
An advantage of this model is that it allows one to compensate for seasonality or any unusual
event by carefully fitting the coefficients, wA . However, it must be remembered that the choice
t
of the coefficient has to be made by management and this choice is critical to the applicability of
the model.

Exponential Smoothing

A forecast based on an exponential-weighted moving average is based on a belief that the most
recent demand observations can best predict future demand. Therefore, exponential smoothing
models are very popularly used in Supply Chain Management. It produces a smoothed time
series when the forecasting horizon is relatively short and when there is little information
about cause and effect relationship between the demand of an item and the independent factors
that influence it.

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