4. We discovered that there is a need to
forecast demand over the protection
period.
For inventory management purposes,
demand is often forecasted on a daily or
weekly basis and combined with the lead
time and/or the review interval to come up
with the forecast of demand over the
protection period.
4
5. We also learned that Inventory
process performance is impacted
in part by forecasting performance,
because
the optimal timing or quantity of
when inventory should be ordered
and how much should be ordered
depends upon the magnitude
and uncertainty of demand,
both of which are contingent upon the
forecasting method and accuracy.
5
7. To calculate or predict (some future event or condition)
usually as a result of study and analysis of available
pertinent data
To indicate as likely to occur
7
https://www.merriam-webster.com/dictionary/forecast
8. Forecasting is a vast field ranging from
macroeconomic forecasting of GDP, interest
rates, and inflation, to forecasting of long-
term demographic trends, the weather, and
the outcomes of political elections.
However, in this chapter we focus primarily
on short-term forecasting, because this is the
crux of most inventory management
performance challenges, especially for
replenished items.
8
9. For nonreplenished items, such as fashion apparel,
forecasts must be made many months into the future for a
selling season that might last a few weeks.
In that case, the crux of inventory management is a longer
term forecast.
In this book we do not address long-term forecasting.
9
10. Forecasting seems scientific because of the mathematics,
probability theory, statistics, and so on, involved in it.
However, successful forecasting requires knowledge and
understanding of the methods, which ones perform well
under various conditions, which ones do not, and why they
do not perform well.
Technology, databases, data, and software can improve
forecasting and are necessary, but they are not sufficient for
accurate forecasts.
10
12. 1
3
Technology in the hands of a
skilled forecasting analyst
who is knowledgeable of the
domain for which the forecast
is being used can make
progress toward improved
forecasts.
Understanding the domain
requires experience in the
business, knowledge of the
industry, and understanding
of the variables in the
company and the competitors
that drive sales.
15. One challenge in forecasting is finding these rare
individuals who understand forecasting technology,
forecasting methods, databases, and the data per se, and
also have sufficient business domain knowledge.
In reality, it takes a team of individuals, each of which has at
least one of these skills, collaborating to develop the
forecasting method and resolve forecasting problems.
15
16. Imagine that one and only one person, Julie, shops at a particular retail store for a
certain type of candy,a peppermint blueberry fizz hard candy,called Pepfiz.
Every day before Julie goes to this store, she rolls a six-sided die with numbers 1
through 6 on each of the six sides.
The number that comes up on the die is the number of pieces of candy she buys
when she goes to the store, but of course the store replenishment manager does
not know what is going on.
If the store replenishment manager knew how demand was being generated, he
would know that the best forecast is 3.5—the expected value of the roll of a die.
Let X be a random variable representing the demand
16
17. A forecast of 3.5 units is the best forecast.
In the long run, no other forecast would be
better.
Unfortunately, the replenishment manager
doesn’t know how demand is being
generated.
17
18. The solid lines in Figure 4-1 are the
actual purchases (POS), and the
dashed lines represent the average.
In this case, a simple average is the
best forecast.
A simple average is just the average
of all POS, starting from the
beginning, and ending with the most
recent observation.
18
19. Let xi be the ith
observation of a total of n
observations; then the
simple average is
19
20. By about ten days, in this case, the
simple average is close to the mean of the
probability distribution.
However, if you look at the first nine days,
you might think there is a positive trend even
though there is not.
In fact, a number of forecasting methods
would actually suggest a trend using the
first nine days of this data.
20
21. The first few days
look like there is a
negative trend.
However, it
doesn’t take long
for the simple
average to get
close to the mean
of the distribution.
21
22. The cumulative
probability up to a
demand during lead time
of three units is 1/6
+ 1/6 + 1/6 = 0.5.
So, if the manager
stocked up to three
pieces of candy each
day, the manager would
be in stock half the time;
that is, the PPIS = 0.5.
22
23. This is really a (T,OUL)
replenishment process
where T = 1 day and L =
0.
That is, before the store
opens, the manager
review and replenish from
the backroom.
Let’s suppose he
chooses a PPIS = 0.83;
then he sets the OUL =
5.
23
24. Safety stock is the expected
number of units on hand when the
replenishment arrives and is
available for use.
Expected demand is 3.5, so if we
have 5 units at the beginning of the
replenishment interval,
The expected number of units on
hand at the beginning of the next
day, when the replenishment
arrives and is available for use, is
5 − 3.5 = 1.5 units
24
27. If we go to a one-day
moving average, it really
isn’t a moving average, it is
just taking what happened
the previous day as the
forecast.
This is referred to as a
naïve forecast
2
7
29. Figure 4-7 is an example of
where there is a spike in
demand on the first day
This could simply be a data
error.
This is also included in the
five-day moving average but
is out of the calculation for
the five-day moving average
by day 7.
29
30. You can see that the
simple average is
above the five-day
moving average and
the sales from day 7
through day 16.
This illustrates a
problem with the simple
average— outliers have
a lasting impact that can
bias the forecast for
many periods into the
future.
30
35. HOLD OUT
DATA
How well performance on
future sales data is referred to
as hold out data
Forecasting models should be
judged based on how well they
forecast hold out data, not on
how well they do on the data
they were fit to.
There is always a trade-off
with hold out data.
3
5
38. There are many measures of forecast error,
but we are going to look at bias,
mean absolute deviation (MAD),
mean absolute percent error (MAPE), and
standard deviation of the forecast error
(σFE).
Before talking about measuring forecast
error (FE), we need to define forecast error
for one forecast.
3
8
40. On average, if bias is positive, it means that we are under
forecasting, whereas, if it is negative, we are over forecasting.
If bias is positive, it is possible that there is a positive trend that is
not being accounted for in the forecasting model,
Whereas if bias is negative, it is possible that there is negative
trend.
It is not a good measure of the overall accuracy because
positive forecast errors are cancelled by negative forecast
errors.
40
41. MAD overcomes this
because the absolute
value is taken of each
forecast error.
is the average magnitude
of the error, regardless of
the direction of the error.
41
42. This fraction is referred to as that smoothing
constant, usually designated by the Greek
lowercase letter alpha, α, which varies
between zero and one, α (0, 1).
So, if α is small, the adjustment is small, but
if α is large, the adjustment is large.
If ft is the forecast for period t, and at is the
actual sales for period t, then the
exponentially smoothed forecast for period
t+1 is
42
43. If there is a lot of randomness in the
data, alpha should be low.
If the level of demand is
changing, alpha should be
higher, at least for a time.
43
45. One challenge associated with using first order exponential smoothing is
that you have to start with a previous forecast.
So, for the first forecast you need a previous forecast.
If you have data, you could use an average.
If you don’t have data, you could make an estimate with your judgment or
you could get a panel of experts and use an average of their estimates.
45
47. A high bias, meaning you are under
forecasting, may result in an expected
demand during the protection period being
too low, resulting in more stockouts.
47
alpha that is too high
An will cause the
standard deviation of forecast error to be
high, resulting in more safety stock.
The point here is that your initial estimate
and your selection of alpha both have a
lasting impact on the performance of your
inventory management.
48. First order exponential smoothing assumes there is no trend or seasonality in
the demand.
If there is upward trend and first order exponential smoothing is used, there will
be a negative bias.
Increasing alpha will reduce the bias because the forecast will adjust up
more quickly, but there will still be a bias.
Similarly, if there is a downward trend, there will always be a positive bias,
since you will on average be forecasting too high.
48
