Customers, Products, and OM: Forecasting
1
Introduction
Forecasting is vital to every business organization. Forecasts drive a wide variety of business
decisions, from short-term personnel scheduling to long term facility design. Forecasts are the basis
for budget allocations, funding of equipment, and long term strategy. Forecasts will determine a
large number of operational decisions as for example the technologies used, the capacity of the
facilities, the mix of services or products to make, and what are some areas of business
opportunities.
Forecasting is both a science and an art. There are no perfect forecasts given the many factors that
affect a business organization. Based on this premise, the objective of forecasting is to determine
what forecasting method is the most appropriate for what is being forecasted, and to maintain a
strict discipline of reviewing forecasts.
Forecasts are typically of two types, qualitative and quantitative. Qualitative methods are based on
perception and knowledge and are typically used for long term planning and strategy. Quantitative
forecasts are based on past data, mathematical models, and are typically used for medium to short
term planning. In many cases a combination of both methods are used, where knowledge is used to
modify quantitative forecasts and some data and mathematical models are used in the processes of
qualitative forecasting.
2
Product Demand
The demand over time for a specific product can be broken down into three main components:
trend, season, and random. Figure 1 shows these three components. A trend is a linear relationship
between demand and time. Trends often change, where a firm entering a market may experience
rapid growth during the first year, and then taper off after that, with a slow growth trend. In some
cases, recognizing changes in trends is one of the qualitative aspects of quantitative forecasting.
The seasonal factor relates to periodic changes in demand that reoccur at a steady cycle. We all
know about seasons here in SW Florida. The random component relates to variation that cannot be
explained by the trend or seasonal effect.
There are models for product demand that are not time based. For example a product demand
model can be based on product characteristics, size of the customer base, and other economic
factors. For example, product price can have a significant effect on demand. Figure 2 shows the
effect of price (competitor price/selling price) on product demand. This helps companies strategically
price products to help manage demand. In seasons when demand is typically low, prices are
reduced to increase demand (for example coupons are offered with special discount, i.e. 2 for 1
dinners), and on the period where demand is high, prices may be increased to both maximize sales
and keep requirements within the organizations capacity.
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1
Figure 1
55
Season
Effect
50
45
40
Trend
35
Sales
30
Season
Effect
25
May
Mar
Jan
Nov
Sep
July
May
Mar
Jan
Nov
Sep
July
May
Mar
Jan
Nov
Sep
July
20
Figure 2
Demand (000)
1000
800
600
400
200
32
31
30
29
28
27
26
25
0
Price ($)
3
Forecasting and Small Businesses
Forecasting demand for a new business is typically a difficult task, as patterns have not been
established. Given this, new businesses should establish procedures to track customer
demand/needs and the characteristics of these customers. Establishing an understanding of the
type of customers and the pattern of customer demand will help manage the operational processes.
Marketing/ advertising and demand management (price structure) will play a significant role in
demand. Qualitative forecasts will be more useful for small businesses until data can be obtained
and analyzed.
4
Qualitative Forecasts
There are two main types of qualitative forecasts, those driven by customer perceptions and those
driven by field experts. Combining the results from both is a common and good practice.
2
Chapter 3
Customer based forecasts
Customer perceptions of actual and future requirements are determined though interviews,
focus groups, and/or surveys. These types of forecasts are driven in many cases by marketing
organizations, and involve the use of market research techniques to find what customers want.
Developing market surveys is not a simple task as the design of the questions may lead to
wrong conclusions. Some of the most important characteristics of a good survey instrument are
(Alreck and Settle, 1985):
Focus:
Brevity:
Clarity:
Questions in a survey should only focus on a single specific subject.
Brief questions are typically easier to understand, and therefore to answer.
Questions should have little left to interpretation.
Expert based forecast
While many varieties exist of expert based forecasts, two good examples are the panel
consensus method and the Delphi method. In the panel consensus method a group of
individuals that could include customers, employees, and consultants meets in brainstorming
sessions to develop a forecast. While in principle this method could be very effective, typically a
few individuals dominate the meeting (consultants) and the voice of low level employees may be
ignored. The Delphi method a group of individuals (could include all those mentioned above) are
surveyed by mail (or some other method) about the future (forecasts). Once the responses have
been received, they are summarized and based on the results, a new survey may be sent. In
this method, the opinions of all surveyed is given an equal weight.
5
Quantitative Forecasts: Time-Based Relationships
Quantitative forecasts are those where functions replace opinions. Quantitative forecasts are
normally used for short term planning, although quantitative forecasts are used to calculate
population figures 20-50 years into the future. Time based relationships reflect the connection
between the passage of time and the “item” in question. The example shown in Figure 1 is such a
case. This section will describe four time-based forecasting methods: Simple Moving Average,
Weighted Moving Average, Exponential Smoothing, and Linear Regression.
Simple Moving Average
This method is appropriate when there is not a significant trend (fast up or down trend) or
seasonal characteristics. It is useful only to smooth out randomness of the data. This method is
very simple to compute and requires one decision: the number of time periods to consider n. The
larger the number of time periods considered, the smoother the forecast.
w = 1/n
Ft = w (At-1 + At-2 + ….. + At-n)
Where
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3
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
Example
A small retail store owner wants to know how many T-shirts will be sold per month. The owner
has tracked T-shirt sales for the last 7 months and needs a forecast for August. The data is
shown in Figure 2 and the forecasts are shown in the table below.
Figure 2. T-shirt Sales per Month
Sales
750
700
Sales
650
600
jan
Month
January
February
March
April
May
June
July
August
Period
1
2
3
4
5
6
7
8
Sales
712
733
689
738
688
654
709
feb mar apr may jun
jul
n=2
n=3
n=4
1/2(709) +
1/2(654) = 681.33
1/3(709) +
1/3(654) +
1/3(688) = 683.55
1/4(709) +
1/4(654) +
1/4(688) +
1/4(738) = 697/16
Weighted Moving Average
This forecasting method is similar to the Simple Moving Average, but it allows the decision-maker
to place more emphasis on recent (or past) data. The computations are also simple and require
two decisions: the number of time periods to consider n, and the weight for each period x, wx.
Note that the sum of all weights must be equal to 1. While there are no rules to select weights,
typically a larger weight is given to more recent data.
w = forecaster’s decision (0 to 1)
Ft = w1 At-1 + w2 At-2 + ….. + wn At-n
Where
4
Chapter 3
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
w1 = Weight for the actual demand period t - 1
w2 = Weight for Actual Demand period t - 2
wn = Weight for Actual Demand period t - n
sum all w’s must be equal to 1
Example
Using the data from the above example and investigating three cases; n = 2, and w1 = 0.7, w2 =
0.3, n = 3, and w1 = 0.7, w2 = 0.2, w3 = 0.1, and n = 4, and w1 = 0.7, w2 = 0.1, w3 = 0.1, w4 =
0.1 we get the following forecasts.
Month
January
February
March
April
May
June
July
August
Period
Sales
1
2
3
4
5
6
7
8
712
733
689
738
688
654
709
n = 2, w1 = 0.7, w2 n = 3, w1 = 0.7, w2 n = 4, w1 = 0.7, w2
= 0.3
= 0.2, w3 = 0.1
= 0.1, w3 = 0.1, w4
= 0.1
0.7(709) +
0.3(654) = 692.26
0.7(709) +
0.2(654) +
0.1(688) = 695.66
0.7(709) +
0.1(654) +
0.1(688) +
0.01(738) =
704.06
Exponential Smoothing
Exponential smoothing is another forecasting technique that is also simple to compute. In this
case, past data and forecasts are used in the generation of a forecast for the next period. This
method is widely used in practice, but it has some of the same problems as simple moving
average (not useful when there are significant trends and seasonal effects). The computations are
simple and require one decision and a forecast number for the period before the forecast period in
question: the smoothing constant . Note that the smoothing constant, , has to be greater than 0
and less than 1. The smaller the , the less reactive the forecasts will be.
Ft = Ft-1 + (At-1 - Ft-1)
Where
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
 = Smoothing Constant
Example
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5
Using the data from the above example and investigating three cases; F1 =700,  = 0.8, F1
=700,  = 0.4, and F1 =730,  = 0.8 we get the following forecasts.
Month
January
February
Period
1
2
Sales
712
733
March
3
689
April
May
June
July
August
4
5
6
7
8
738
688
654
709
F1 =700,  = 0.8
700
700 + 0.8(712 700) = 709.6
709.6 + 0.8(733 709.6) = 728.6
697.3
729.9
696.4
662.5
699.4
F1 =700,  = 0.4
700
700 + 0.4(712 700) = 704.8
704.8 + 0.4(733 704.8) = 716.2
705.5
718.5
706.3
685.4
694.7
F1 =730,  = 0.8
730
730 + 0.8(712 730) = 715.6
715.6 + 0.8(733 715.6) = 729.8
697.5
729.9
696.4
662.5
699.4
Linear Regression
This is a mathematical tool used for many purposes and you probably remember it from the
introductory statistics class. This technique is especially good for the forecasting of products with a
clear trend (growing or decreasing).
Linear regression is based on the linear relationship between time (for example days, weeks, or
months) and the variable to be forecasted (T-shirt sales for example). This relationship is
formulated in the familiar Y = mX + b format, where Y is the variable to be predicted, X is the time
factor, m is the slope of the line, and b is the constant. This text will not present the details of how
this equation is formulated/calculated given this is covered in other courses and texts and in
practice, the regression equation can be easily computed using spreadsheet software such as
Excel or statistical software such as SPSS.
To forecast using regression analysis it is necessary to enter the data into the software and obtain
the regression equation. At this time it is important to examine the resulting r value; a high r value
means the regression equation is a good predictor of the data. If the r2 value is low, the data may
be graphed and analyzed to remove outliers, or it may be determined that linear regression is not
the best technique. The equation will then be used to predict the period of interest.
Example
The data from the T-shirt example does not show a trend, does applying the linear regression
method is not a good option. However, sales for New Age CD's seemed to have a trend (sales
are decreasing). The data is shown in Figure 3.
The data was entered in Excel and using the data analysis tool, the following regression
equation was obtained: sales = 134.28 - 11.21 * (period), thus sales for August are forecasted
by
F8 = 134.28 - 11.21 * (8) = 44.6
6
Chapter 3
Figure 3. Graph for New Age CD sales
CD's Sales
150
120
100
118
95
87
80
81
50
45
0
jan
feb
mar
apr
may
jun
jul
It is important to note that the r2 value for this equation was 0.90, which is good. Other examples
and the use of Microsoft ® Excel will be presented during class.
6 Seasonal Effects
In many environments and for many products, there are clear seasonal effects to product demand.
Here in Southwest Florida, a strong seasonal pattern is felt during the months of December through
April given a large influx of tourists. Other regions and products may have other seasonal patterns,
such as the demand for air travel to some destinations; high season during summer and winter, low
season during spring and fall. Forecast accuracy will be greatly enhanced by taking into account
seasonal effects in the forecasting process.
To determine seasonal effects, the decision-maker should first estimate the seasonal breakdown
and the time periods. For example, seasonal effects can be calculated in a monthly basis or in a trimonthly basis. It is rare to encounter seasonal effects smaller than one month. Special occasions
such as Thanksgiving travel are not typically considered seasons.
To determine seasonal effects, we must have data from previous years including all seasons. At
least three years of data are recommended to get reasonable accurate seasonal effects. The
process is as follows:
1) For each year calculate the total average per period.
2) For each value of actual sales, divide the sales by the average per period. This is the
ratio for that period for that year.
3) Add all the ratios for a similar period and divide by the number of ratios. This is the
seasonal effect for that period.
While other options exist, we will use linear regression to determine the average per period forecast
that will allow to develop a forecast for the next year. Even if the regression coefficient is not
acceptable, the regression will provide an estimate for average sales.
Example
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7
The owner of the retail store believes there is a seasonal effect in Souvenir sales. After
spending three hours looking through old papers, data for the last three years was obtained for
actual sales. The owner estimated four seasons, High: January - March, Summer: April-June,
Summer B: July-September, and Fair: October-December. The data and the process to
determine seasonal effects is shown below.
Figure 4
2500
2000
1500
1000
500
0
H-96 SA-96 SB-96 M-96
H-97 SA-97 SB-97 M-97
Season
1996
1997
1998
High
Summer A
Summer B
Medium
AVERAGE (Step 1)
1856
1327
835
1739
1439
1977
1344
815
1672
1452
2133
1450
983
1780
1587
H-98 SA-98 SB-98 M-98
(Step 2)
1996
1997
1998
(ratio) (ratio) (ratio)
1.29
0.92
0.58
1.21
1.36
0.93
0.56
1.15
1.34
0.91
0.62
1.12
Average Ratio
(Step 3) =
Seasonal Index
1.33
0.92
0.59
1.16
Once the ratios for each period are calculated (Step 2), an average ratio per period is
calculated; the seasonal index (Step 3). This effect will be used to modify the forecast for the
period average for 1999. The linear regression equation for the data above is: 1345.3 + 73.6,
thus the average sales for 1999 is 1639.8.
8
Season
(from above - Step 3)
Seasonal Index
High
Summer A
Summer B
Medium
1.33
0.92
0.59
1.16
Chapter 3
(Step 4)
Estimated Average
for 1999
1639.8
1639.8
1639.8
1639.8
(Step 5)
Forecast per
Season
2184.2
1509.7
962.7
1903.3
7
Forecasting Errors
As discussed in the previous sections, there are many methods to develop quantitative forecasts.
For the T-shirt example, we have at least six possible forecasts for the month of August. The
question now is, what method is the best and what are the best parameters? While it will be
impossible for anyone to evaluate all the possible options (for example all the possible set of weights
in a weighted moving average), the evaluation of forecasting methods is based on comparing a few
pre-selected options for a specific data set.
The evaluation process is based on the average error of a method given historical data. Therefore,
we look at multiple data points, determine what the forecasting method would have calculated and
determine the error. IF the forecasting method does not work for past data, we can guess it will not
work in generating forecasts.
For each data point (where there is historical data and a forecast value) and forecasting method we
calculate an absolute deviation.
Dt = Absolute value of (Ft - At )
The mean absolute deviation (MAD) is the average measure of error, and the basis to make a
decision regarding what is the best forecasting method. The MAD is calculated by:
MAD = SUM 1..g (Dt ) / g
Where
g = number of periods where there is a forecast and actual data.
Example
The owner of the store wants to know which is the most accurate forecast for the month of
August, and which method should they use to forecast T-shirt sales every month. To determine
this we calculate the forecasts for all possible periods. Lets evaluate the simple moving average
forecasts under our three parameters.
Month
January
February
March
April
May
June
July
August
(Period)
1
2
3
4
5
6
7
Sales
712
733
689
738
688
654
709
n=2
722.7
711.4
713.7
713.0
671.0
681.3
n=3
711.6
720.3
705.1
693.3
683.6
n=4
718.2
712.2
692.4
697.2
MAD
Dt
Dt
Dt
33.3
26.6
25.7
59.0
37.7
26.4
32.3
51.1
15.3
30.2
58.2
16.3
36.4
31.3
34.9
Using 3 periods (n=3) results in the lowest MAD, thus 683.6 is the so far the best estimate for
August (and the best forecasting method for T-shirt Sales). Let's now look at the weighted
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9
moving average forecasts. Option 1 = (n = 2, w1 = 0.7, w2 = 0.3); Option 2 = (n = 3, w1 = 0.7,
w2 = 0.2, w3 = 0.1) and Option 3 = (n = 4, w1 = 0.7, w2 = 0.1, w3 = 0.1, w4 = 0.1).
Month
January
February
March
April
May
June
July
August
(Period)
1
2
3
4
5
6
7
Sales
712
733
689
738
688
654
709
Option 1 Option 2 Option 3
727.0
702.6
723.4
703.0
664.2
692.3
700.5
727.8
698.1
669.2
695.7
730.1
697.7
669.3
704.1
MAD
Dt
Dt
Dt
37.5
35.4
35.4
49.0
44.5
37.5
39.8
44.1
39.5
42.1
43.7
39.3
40.4
40.2
41.7
The three options of the weighted moving average resulted in MAD's that were higher than 31.3,
thus the simple moving average with 3 periods (n = 3) is best estimate for August. Let's now
look at exponential smoothing.
Month
January
February
March
April
May
June
July
August
(Period)
Sales
1
2
3
4
5
6
7
712
733
689
738
688
654
709
F1 =700, F1 =700, F1 =730,
 = 0.8  = 0.4  = 0.8
700
700
730
709.6
704.8
715.6
728.6
716.2
729.8
697.3
705.5
697.5
729.9
718.5
729.9
696.4
706.3
696.4
662.5
685.4
662.5
699.4
694.7
699.4
MAD
Dt
Dt
Dt
23.8
39.2
40.7
41.9
42.4
46.2
28.6
26.8
32.5
30.5
52.3
23.3
17.8
40.4
40.5
41.9
42.4
46.2
39.0
32.3
38.2
The second option of the exponential smoothing method resulted in a lowest MAD for this
method, but still, the simple moving average with three months results in the lowest MAD (31.3).
Therefore the forecast for August is 683.6 and simple moving average with n = 3 is selected as
the forecasting method. If we had used a linear regression equation, the process would have
included a MAD analysis for the regression forecasts.
7
The Forecasting Process for Time Based Relationships
Just like everything else, a good forecast is based on a good process, experience, good data
(garbage in – garbage out) and luck. The first one will be covered next, the second one will depend
on your job, the third one depends on a good data collection system and in your ability to determine
if the data represents reality, and the fourth is up to? The steps to forecast are below and illustrated
in Figure 5.
Figure 5
10
Chapter 3
Plot the Data
No
All Points Normal?
Yes
No
Is there a Trend
or Season?
Remove Point (s)
Yes
Yes
Use Linear Regression
Only a trend?
No
Determine the
Seasonal Factors
Transform using
seasonal factors
Use SMA, WMA,
and
Exponential
Smoothing
(Paramter Selection
is up to you)
Use MAD to determine
best forecast method
Use Linear Regression
to determine next year
average per period.
1. Plot the data. Look for points that do not fit the pattern. Find out the reason behind those
strange numbers, for example a rare discount due to another store being closed down, and
eliminate those that are "non random".
2. From the data, determine if there is a distinguishable trend or season? If there is no trend or
season, develop forecasts using simple moving average, weighted moving average, and
exponential smoothing. Use the MAD method to determine the best method and parameters
(selecting parameters is up to you). Else go to 3.
3. If there is a trend but no season, use linear regression. Else go to 4.
4. If there is a season (trend or no trend), calculate seasonal factors, then use the yearly averages
to calculate a trend for yearly average using linear regression. Forecast using the linear
equation and the seasonal factors.
Activities
1. Find out about forecasting software on the web. Summarize the major features of the
software.
2. Search the web for forecast data on population growth, internet use, or other general
purpose measure. Describe the data and forecasting process that applies to this data.
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11
3. You have just started a new business in internet sales for used shoes. What factors
would influence demand of products and the number of hits your site will receive per
day?
Exercises
1. A plot of the number of customers at Aceite Lube Center shows the number of weekly
customers is not subject to a trend or season. Using the data below:
a) Develop a forecast using simple moving average with 3 months
b) Develop a forecast using weighted moving average with n = 3, w1 = 0.5, w2 =
0.4, w3 = 0.1
c) Develop an exponential smoothing forecast using F1 = 190 and  = 0.65
Month
September
October
November
December
January 1999
Customers
189
196
192
205
176
Month
February
March
April
May
June 1999
Customers
184
203
218
211
197
2. Using the MAD method, determine which of the three methods in #1 results in a better
forecast (and what forecast should be used for planning).
3. Select one set of parameters for exponential smoothing and one set for weighted moving
average. Are the parameters you selected better than the one given in #1?
4. The number of customers visiting a local restaurant in Fort Myers Beach is highly dependent
on the season. The management of the restaurant has divided the data for the number of
entrees sold in three groups: Jan-April (Winter/Spring), May-Sept (Summer), Oct-December
(Fall).
a) Determine the seasonal effects
b) Calculate an average for 1999 and 2000 using linear regression.
c) Forecast sales by season for 1999 and 2000
Year
Season
Winter/Spring
Summer
Fall
1996
1468
793
987
5. Data set 1 (web page)
12
Chapter 3
1997
1492
845
1124
1998
1593
861
1098
1999
1650
6. Data set 2 (web page)
7. Data set 3 (web page)
For each data set (problem)
Create a plot.
Determine the forecasting method(s) which apply for this data.
 For data sets with a seasonal effect, create a season grouping and
follow the seasonal forecasting process. Generate a forecast for a
complete year. Plot the data grouped into seasons.
 For data sets with only a trend, determine the linear equation. Generate
a forecast for a complete year. Plot the data and the regression line.
 For data sets with no trends and seasons, generate one period
forecasts with weighted moving average (n = 2, w1 = 0.7, w2 = 0.3) and
exponential smoothing (F1 = A1,  = 0.75).
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13