In Chapter Four
on Slide Twenty-six,
we're looking at single
exponential smoothing.
There's two formulas
for single exponential smoothing,
and the first one looks at
a smooth forecast (SF) of "time period plus one" (t+1)
is equal to (=)
an alpha
times the actual
time period, and your alpha is a constant here,
plus one minus that constant
times
the smooth forecast for the time period.
And I'm going to go back and we're gonna look at this here a little bit differently in
just a minute, to get at
a better understanding of the formulas,
but the second formula, which is actually a manipulation of the first,
and it is actually found in your book, and of course I didn't write down
the page, is my preferred formula,
and this formula
is
the smooth forecast for a time period plus, one or your next time period,
is equal
to your smooth forecast for the time period
plus that constant, or the alpha,
times
the actual for our time period
minus the smooth forecast for the time period.
This is my preferred
formula
because i find it easier to use,
and I can actually
work through it better.
uh... I like the way it works through things so
I prefer this formula.
So, if we go and take a look
at our single exponential smoothing problem,
which is Slide Twenty-six,
we have a demand for a certain model of snowboard
during the past five months as shown below,
November through March,
and it's reflective of actual demands.
Compute the forecasted demand for each month from November through March using
a single exponential smoothing with an alpha of point zero two (0.02).
Assume that the forecast for November was two hundred and twelve (212).
You need to have a starting forecast here,
so we're going to assume
that our November forecast
was
two hundred
and twelve (212).
What we're going to look at is how do we get
a forecasted, a smooth forecast
for December, if we know what November's actual was,
or how can we do this for next year,
assuming looking at next year's December, etcetera.
So, what I want to take a look at here
is using this formula, I'm going to rewrite it on the next page,
and
go through what we're going to be taking a look at.
So, while it says that the smooth
forecast for a time period plus one
is equal to the smooth forecast for the time period
plus our constant
multiplied by the actual for a time period
minus the smooth forecast for a time period.
What does this mean?
Well, we have a forecast for November,
and we want to find, to begin with, a smooth forecast
for December, which is our next time period.
So, we're going to take a look at the smooth
forecast
for November
plus
our constant, which is point zero two (0.02),
times the actual
forecast
for November,
minus the smooth forecast
for November.
That's what we're looking at, and what we're going to do,
is use the numbers that we have here in this problem.
So,
we want to find our
smooth forecast
for December.
What was our smooth forecast
for November?
It was given at two hundred and twelve (212).
We wanna add to that
our alpha, our constant,
which is two
times what was November's actual forecast,
one hundred and ninety six (196)
minus
the smooth forecast
for November.
So, our formula for this problem ends up being two hundred and twelve (212)
plus point zero two (0.02) times the quantity one ninety six (196)
minus two hundred and twelve (212)
Now, why do I like this so much? Cause it's easy to do on the calculator!
I'm going to work it step-by-step first and then I'm going to tell you how you're gonna
punch it into your calculator,
that this makes it easy,
especially if you don't have a calculator with all the little parentheses and everything on it.
I buy the cheap calculators folks!
They don't have parentheses, as long as they have a square root I'm good!
So, we look
at two hundred and twelve (212) plus 0.02
times a hundred and ninety-six minus
two hundred and twelve is a negative
sixteen.
I'm going to take my two hundred and twelve (212)
my point oh two (0.02) times a negative sixteen (-16)
is a negative point three two (-0.32).
My 212 minus
a point three two (0.32)
is two hundred eleven point six
eight (211.68).
If i wanted to do this quickly on my calculator,
I can take
one ninety six minus two hundred and twelve
multiply that by point zero (0.02) two and add
two twelve (212).
So, I literally am working piecemeal backwards
in order
to do this problem
easily on the calculator, and I think that's really why
I like
this formula better.
Now, I have
my smooth
forecast
for December being two hundred and eleven
point six eight (211.68).
So, I can go back
to my forecasting chart here, and on December say that it was
two eleven point six eight (211.68),
and I'm taking this out to two decimal points
for the simple reason that my exponential smoothing was at two
decimals... my alpha
was at two decimal points.
Depending on
what you produce
will depend on
how many decimal points you go out. If you are producing
uh...
planks of wood
you probably... you know you can't make... a percentage of a plank...
so you might just round up or round down
depending if it's point five
above or below
to get the number of planks of wood forecast that you're gonna be selling
needing whatever.
If you're working with
uh... medication and it's something for neonatal,
you might go out ten, fifteen decimal places, so depending on what you're
producing will depend on how many decimal places you have to go out.
uh...
So, we're looking here
for exponential...
with the exponential smoothing and we found December,
so we now can go back
and look at
January.
What we're looking at, we have now
our smooth forecast for December. We want to find our smoothed
forecast
for January.
How are we gonna do that?
January is our next time period. We're gonna take the smooth forecast
from December
plus our alpha times the actual
forecast from December minus the smooth forecast
from December,
and we're just gonna plug-and-play, is what I call it, just plug in the numbers
that we have.
Well, if we go back one sheet
which, oh good, it's back up regular size again,
we go back one sheet, we found that our smooth forecast for December was two
hundred eleven
point six eight (211.68).
So, I know
that I'm going to have two hundred eleven point six eight (211.68). There! I'm just plugging that
into the number
plus point oh two (0.02).
My actual for December now, cause everything on this formula is from the
same time period,
was two hundred
and sixty-eight minus that forecasted
two hundred eleven point six eight (211.68).
I can now plug into my calculator,
two hundred and sixty-eight (268) minus two hundred eleven point six eight (211.68)
times point zero two (0.02)
plus two hundred eleven
point six eight (211.68)
and I should get two hundred and twelve point eight
one (212.81).
So, that's my smooth forecast
for January.
I'm going to take that
and plug it into my smoothed forecast
for February.
My smooth forecast for February
is the smooth forecast from January two hundred and twelve point eight one (212.81)
plus my alpha
times the actual forecast for January
which, if you go back to your powerpoint slide, was three hundred
and fifteen (315)
subtracting from that the smooth forecast from January,
two hundred and twelve point eight one (212.81).
So, if I take this and I plug it into my calculator,
three hundred and fifteen (315)
minus two hundred and twelve point eight one (212.81)
times point zero two (0.02)
plus
two hundred and twelve point eight one (212.81), I get my smooth forecast for February,
which should be
two one four point eight five (214.85).
So, I now have my smooth forecast for february.
I can go on and find the smooth forecast for March by plugging in the numbers for
February, so I'm just going to move to the space on the next page,
and find
my smooth forecast
for March,
and that's going to be my smooth forecast from February,
two one four point eight five (214.85),
plus
my alpha,
point zero two (0.02),
times the actual from February.
That, back on our slide, was two hundred
and ninety nine (299)
subtract
from that
our smooth forecast from February,
which was two hundred and fourteen point eight five (214.85).
Again, if I take this and work it backwards on my calculator, two hundred
and ninety nine minus two hundred and fourteen point eight five
multiplied by point zero two (0.02)
plus two one four point eight five (214.85),
I end up with my smooth forecast for March,
which is two one six point five three (216.53).
Now, it doesn't ask you to do this on here,
but you can actually find the smooth forecast
for April,
because we have the information we need to find that out.
Where do we get it from? We start with our smooth forecast
from March,
two hundred and sixteen point five three (216.53)
add to that
our alpha
times the quantity "the actual forecast"
from March,
which if you go back onto the slide was a hundred and one (101)
subtract from that the forecasted, the smooth uh...
forecast
for March, which was two hundred
and sixteen
point five three (216.53).
Again, if you work this backwards on your calculator,
a hundred and one (101) minus two hundred and sixteen point five three (101-216.53)
multiplied
by point zero two (0.02), our alpha
plus
the smooth forecast for March, two hundred and sixteen point five three (216.53),
we end up
with
two one four point
two
eight (214.28), I believe,
as
our smooth forecast for April.
Now, because we don't have
the actual demand
in April,
I can't go any further at this point. I need to stop here.
But this is how
you do single exponential smoothing.