Should you carry an umbrella today? Part of the answer for you
most likely depends on how much you care about getting wet!
Assuming you care, then you have to look to the future and think
about what you think might happen. You would be making a
forecast, even if you have listened to the weather report.
In a business setting we often can use a forecast as well. We
might like to forecast sales, profit, the consumer price index, or
units sold by a competitor.
In a statistics class you may have seen how regression analysis
can be used to forecast. I would like to start with an example and
then go over some methods of forecasting.
Table 11.3 has some demand data. Let’s start slowly with
the example. Say demand in the first three periods was:
The average of the demand in the 3 periods is
(10 + 18 + 29)/3 = 57/3 = 19. This average can now be
used as a forecast for the demand in period 4. This
forecast will then help use decide how to schedule
The idea behind the moving average method of forecasting
is that next period will not be much different than the past
few periods. In the example so far, I have waited three
periods before I calculated an average. This would be
called a three – period moving average method.
On the next slide I continue with the example.
End of period 3
Moving Average Forecast error=D-F
So, at the end of period 3 there is enough information to
calculate a three-period moving average. At that point a
forecast can be made for period 4. The forecast is that
demand will be 19 and plans can be made accordingly.
On the next slide let’s add the actual demand that happens
in period 4 and show some other ideas.
Period Demand Moving Average Forecast error=D-F
With the passage of time and period 4 arriving we see
demand actually is only 15. We planned on 19. This
means we had an error of -4 when we take the actual
minus the forecast. (I find this a bit weird because the -4
means we made too much!)
Now, as we look to period 5 we can use the most recent 3
periods of actual data to calculate an average: (18 + 29 +
15) / 3 = 62/3 = 20.7. So at the end of period 4 we have
the basis for the period 5 forecast. Let’s see that next.
Period Demand Moving Average Forecast error=D-F
So, at the end of period 4 we can
1) See how our forecast for period 4, called F4, was really
the three-period moving average at period 3, called A3 (and
thus F4 = A3),
2) See how good the forecast worked out by looking at the
error D4 – F4,
3) Make a forecast for period 5 by using the three-period
moving average up to period 4, F5 = A4.
Table row 13
As we look at the table on page 231 lets’ look at row 13 to
make sure we understand what is happening.
The forecast for period 13 is really the average of periods
10, 11, and 12. We do this at the end of period 12 and get
When actual demand comes in in period 13 we see the
value 30 and we see the error = 30 – 18.7 = 11.3
The forecast for period 14 will be the average of periods 11,
12, and 13, for a value of 24.
Other moving averages
In our example so far we have used a three-period moving
average. We could have used a two-period, 4-period, or
10-period moving average.
The advantage of using a longer time frame is that the new
data point will have less influence and thus the forecasts
from period to period will not change much, what is called
The disadvantage of using a longer time frame is that the
forecasts are slow to respond to demand changes. Thus
we could have persistent errors.
Later we will go over ways to evaluate and choose
methods of forecasting.
Weighted moving average
In our example at the end of period 3 I calculated the
average as (10 + 18 + 29)/3 = 57/3 = 19. By basic math
rules I could have done the following
(10 + 18 + 29)/3 = (1/3)10 + (1/3)18 + (1/3)29. The
average you and I always calculate is really a weighted
average where each data point is weighted the same, here
Some folks may want to give more weight to the most
recent data point, and thus give less weight to less recent
data points. This overcomes the problem of the forecast
being slow to respond to demand changes. The
requirement to use a weighted average is that each weight
has to be between 0 and 1 and the sum of the weights has
to add to 1.
Exponential smoothing is another forecasting method. After
some algebra, the method makes the forecast for next
period = the forecast you had for this period plus a fraction
of the error this period. In the book this is on page 233.
The fraction is given the name of the small greek letter
So, once you have the initial forecast and alpha, you are all
set. Page 234 has a table with alpha = .1 and alpha = .3
and in both cases the initial forecast is 15 (an arbitrary
number – though based on judgment). Note for period 2 the
forecast when alpha = .1 is 14.5 = 15 + .1(-5), while for
alpha = .3 the forecast is 13.5.
In general, the forecast error or deviation is defined as the actual
value minus the forecast value.
Say ei is the deviation for the ith unit, where units are time periods,
and say di is the actual value and fi is the forecast value. Then ei =
di – fi.
In a data set when we have values for the actual data and forecasts,
AD = Σ׀ei ׀, or in words you take the absolute value of all the
deviations, then add up the absolute values.
A method of forecasting is called better if the method has a lower
AD. This way the one with less error is chosen as better. If we
divide the sum by n we get the mean absolute deviation of forecast
Bias is another way to judge a forecasting method. Bias
would just be to add up all the errors without taking the
absolute value. This is also called CFE, or the cumulative
sum of forecast errors.
You would think that over time a method would have a bias
of zero meaning some years you get positive errors and
some years you get negative errors and the two cancel
each other out. But, often we do not have the luxury of
looking over a long period of time so we would say a
method of forecasting is better if it has smaller bias.
If a method has both smaller bias and smaller AD then it is
preferred. But if one method has smaller bias but more
error, then you have to decide which is the more desirable
factor for you.
Tracking signal TS
TS = CFE/MAD. If TS gets bigger than 6 or less than
minus six, then the forecasting method should be stopped
and reworked because we are too far off.
Note the worked problems on pages 246, 247 and 248.