APMGNZ632 Operations Management
Maths & Excel skills
Quantitative Forecasting using Excel.
The tension between demand and capacity is one of the driving
ideas in operations management and the need to predict demand so
that investments into capacity are made at the right time, and of
the right size, is extremely important to the marketing and
operations departments.
Quantitative methods are widely used and excel is the usual tool.
We are going to set up SS for
 moving averages
 weighted moving averages
 seasonal index
 exponential smoothing
 finding errors
If you can’t make a prediction after that, you are on your own (!)
(Chapter 4 from the text is where most of the formulas can be
found, and pp 168-170 are useful.)
The data below are from question 4.6, pp172.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Sales
20
21
15
14
13
16
17
18
20
20
21
23
The data can be cut and pasted from the table into Excel. (You may
need to format font size or type (calibri is good) to make SS rows
look better).
Assuming a three month manufacture and delivery cycle for the
units being sold, a three month moving average could be useful in
scheduling production.
APMGNZ632 Operations Management
Maths & Excel skills
Three month moving average (3MA) is quite easy.
1.
Open Excel SS / Save as something
2.
Copy and paste data from table into SS / format to get right
3.
In a clear column, choose a cell that centres on the three
month period you want to average (i.e. for Jan, Feb, March,
choose Feb so that answer is in the middle of appropriate time
period).
4.
Enter =average( and then click and drag to select the three
month period you have chosen.
5.
Close the bracket / click enter. (You should see the answer)
6.
Click and drag the result to fill the column (using small square
black handle) / format numbers to have two decimal places.
That is a three month moving average.
One feature about moving averages to be aware of is the need to
centre them against the period they represent. This is easy with an
odd number of data points in the calculation as there is always a
‘midpoint’ (as in the case above using three data points).
Finding a four month moving average will illustrate this point.
1.
Select a cell in a clear column for a four month average. Note
that you cannot centre it exactly on a four month period from
the original data. It does not matter (yet). Put the answer in
either of the possible ‘mid cells’ by repeating steps 4 6 from
above, BUT select four cells not three for the range in the
brackets.
2.
To centre the data on the four month period of choice we can
find the average of the two possible mid point cells and use
this as our final answer.
Choose a cell in a clear column and select the top two cells
from you four month average answer. Average these and the
final answer will be a final four month average, centred on
your data period.
Output should be similar to below
APMGNZ632 Operations Management
Maths & Excel skills
(Compare the centred four month moving average with a five
month moving average over the same range of months for fun(!))
WEIGHTED MA
A weighted moving average is used where we think there is a trend
in the data which we want to find and extrapolate.
This is done by weighting the more recent data points more than
the earlier data points.
1.
Recalculate the three month moving averages for the data set
in a column to the right of the data.
2.
To find a weighted average we will use multiplication as our
weighting factor, as follows;
Jan * 1 / Feb * 2 / Mar * 3 (etc)
By doing it this way the data from March will have a greater
effect on the answer than that of January.
To correct for the fact that we have multiplied the data points,
we also need to divide to bring them back to the correct range
of values. In this case the total multiplication is by six and so
we divide by six also. The formula is therefore:
= ((Jan*1) + (Feb*2) + (Mar*3))/6 for the first month.
3.
Click and drag to fill the cells and compare the weighted
average with the non-weighted average. Note the slight
increase in values from the weighting. This is useful to show a
trend more clearly.
APMGNZ632 Operations Management
Maths & Excel skills
HOUSEHOLD ENERGY USE DATA
January
February
March
April
May
June
July
August
September
October
November
2013
5
6
10
13
18
15
23
26
21
15
12
2014
15
16
20
23
28
25
33
36
31
25
22
2015
23
19
25
28
35
43
49
46
38
28
31
December
14
24
23
This is a difficult set of data. There is almost certainly a seasonal
pattern (power use for heating etc), as well as a trend of increase/
decrease depending on number of consumers, pricing etc.
Looking at the data what questions come to you?
Now we have to make sense of it . . .
Moving Average, Seasonal Index & Trend
1.
In a cell in a clear column find the monthly average of the
three years of data. Do this either by using the AVERAGE
function, or by entering your own formula.
2.
Find the total of the monthly averages by using SUM formula
in a cell near bottom of column of data
3.
Check you have labelled each answer (otherwise you will
forget what it is).
4.
Find the averaged annual monthly demand (total average
demand/12).
Now we divide the average monthly demand for each month by the
averaged annual monthly demand. This will show how each month
average (eg Jan of each year), compares to the overall average of
all thirtysix months in the three year sample.
5.
Choose a clear column and a cell at the top of the data array.
6.
You need to enter a formula that absolutely ($) references the
annual average, and relatively references the monthly
averages. Divide the monthly average by the annual monthly
average.
APMGNZ632 Operations Management
Maths & Excel skills
So we can see the ratio by which each month varies against an
annual average. For example January is 0.597 of the annual
average. With this info we can give more accurate seasonal
forecasts, once we have an annual figure to work from.
If we find the annual totals for each year (SUM each column of
table) and then the monthly average for each year (total /12) we
can see something of the trend of increase.
The TREND formula can be used here once the data are prepared.
In cells under (or over) the monthly average showing the trend we
want to extrapolate enter the numbers 1,2,3 as shown in screen
shot below. (This gives Excel the beginning of the trend and we will
ask for data point number ‘4’).
1.
Choose a cell nearby your data.
2.
From formula choose ‘more / statistical/ scroll down to select
TREND. This open up a data entry dialog box.
3.
(Referring to the dialog box)
Known Y’s are our monthly figures from each year
Known X’s are our 1, 2, 3, ( showing start of a trend)
New X’s enter ‘4’ ( i.e. the next point in the trend)
Click ‘enter’ to close dialog box and show result.
We have now found the seasonal variation and a possible monthly
trend, so we are ready to (finally) make a prediction that we can be
proud of, by combining the two answers to create our prediction by
multiplying the monthly trend figure by the seasonal index for each
month.
1.
Head up a column ‘prediction’ and multiply the trend result
(absolute ref please) by the seasonal index (relative ref
please).
This shows the expected monthly figure from combining the TREND
(into the future) with the annual cycle of variation.