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Chapter 3
The Importance of Forecasting in POM

Assumes causal system
past ==> future
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Forecasts rarely perfect because of
randomness
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Forecasts more accurate for
groups vs. individuals
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Forecast accuracy decreases
as time horizon increases
I see that you will
get an A this semester.
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Prepare the forecast
Step 4 Gather and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
The Importance of Forecasting in P.O.M
Procurement
Plans
Marketing
Plans
Demand
Forecast
Sales
Forecast
Facility Expansion,
Contraction, &
Relocation Plans
Personnel
Plans
Financial
Plans
Production
Plans
Factors Influencing Demand
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Business Cycle
Product Life Cycle
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Testing and Introduction
Rapid Growth
Maturity
Decline
Phase Out
Factors Influencing Demand
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Other Factors
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Competitor’s efforts and prices
Customer’s confidence and attitude
Who makes the sales forecast?
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Sales Personnel
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32%
Marketing Personnel
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29%
Reliance on Forecasting
A Classification of
Forecasting Methods:
Forecasting
Historical Data are available
No Historical Data Available
Statistical
Short
Judgement
--Strategic Forecasting of new Technology
Midrange
Range
Casual or
Regressive
Models
Time
Series
Models
Trend
Projection
Long
Range
Classical
Decomposition
Expert
Opinion
Smoothing
Interm ediate
Short Range
Range --
Exponential
Seasonal
&
Moving Averages
Market
Surveys
Delphi
Judgmental Forecasts
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Executive opinions
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Sales force opinions
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Consumer surveys
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Outside opinion
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Delphi method
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Opinions of managers and staff
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Achieves a consensus forecast
Statistical Forecasting: Time Series Model
In Statistical Forecasting, we assume that the actual value of the time series
we are trying to forecast consists of a pattern plus some random error.
Time Series Value = Pattern ± Random Error
Actual
Observations
2
3
4
5
4
2.5
4
4.5
3
2
4
5
6
9
8
7
9
8
7
Actual
Observations
6
Value
1
2
3
4
3
1.5
3
3.5
2
1
3
4
5
8
7
6
Pattern
10
Random
Error
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
Time
10
11
12
13
14
15
16
Time Series Forecasting -using the Past to Develop Future Estimates
History
Future
Cycle
Pattern
10
9
?
8
Cyclical
7
Long
Term
Trend
Sales
6
5
Seasonal
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Time (years)
11
12
13
14
15
16
Uncertainty
Will it repeat the
past?
Time Series Forecasts
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Trend - long-term movement in data
Seasonality - short-term regular
variations in data
Cycle – wavelike variations of more than
one year’s duration
Irregular variations - caused by unusual
circumstances
Random variations - caused by chance
Forecast Variations
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
Naive Forecasts
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week
we should sell....
The forecast for any period equals
the previous period’s actual value.
Naïve Forecasts
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Simple to use
Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
Can be a standard for accuracy
Uses for Naïve Forecasts
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Stable time series data

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Seasonal variations
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F(t) = A(t-1)
F(t) = A(t-n)
Data with trends

F(t) = A(t-1) + (A(t-1) – A(t-2))
Short Run Forecasts
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Moving Average Method
Exponential Smoothing
Moving Average Method
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This method consists of computing an
average of the most recent n data values
in the time series. This average is then
used as a forecast for the next period.
Moving average =
 (most recent n data values)
n

Moving average usually tends to eliminate
the seasonal and random components.
Moving Average Method

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The larger the averaging period, n, the
smoother the forecast.
The ultimate selection of an averaging
period would depend upon
management needs.
Simple Moving Average
Actual
MA5
47
45
43
41
39
37
MA3
35
1
2
3
4
5
6
7
8
9
10 11 12
High AP forecast has a low impulse response
and a high noise dampening ability.
Weighted Moving Average Method
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Weighted moving average – More recent
values in a series are given more weight in
computing the forecast.
Exponential Smoothing
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It is a forecasting technique that uses a
smoothed value of time series in one period to
forecast the value of time series in the next
period. The basic model is as follows:
Ft+1 = aYt + (1-a)Ft
Where:
Ft+1= the forecast of time series for period t+1
Yt = the actual value of the time series in period
t
Ft = the forecast of time series for period t
a = the smoothing constant 0£a£1
Example 3 - Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
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Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
F2 = F1+.1(A1-F1)
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= 42+.1(42-42) = 42
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
Alpha = 0.4 Error
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92

42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
F3 = F2+.1(A2-F2)
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= 42+.1(40-42) = 41.8
Week
8
a = .1
Forecast
Error
a = .2
Forecast
Error
85.0 17.0
85.0 17.0
a = .3
Forecast
Error
85.0 17.0
9
110
86.7 23.3
88.4 21.6
90.1 19.9
10
90
89.0
1.0
92.7 2.7
96.1 6.1
11
105
89.1 15.9
92.2 12.8
94.3 10.7
12
95
90.7
94.8
.2
97.5 2.5
13
115
91.1 23.9
94.8 20.2
96.8 18.2
14
120
93.5 26.5
98.8 21.2
102.3 17.7
15
80
96.2 16.2
103. 23.
107.6 27.6
16
95
94.6
.4
98.4 3.4
99.3 4.3
17
100
94.6 5.4
97.7 2.3
98.0
Total Errors
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Actual
Demand
102
Forecasts
4.3
2.0
133.9
124.4
126
MAD=13.39
MAD=12.44
MAD=12.60
The smoothing constant a = .2 gives slightly better accuracy when compared to a = .1, and a = .3.
Picking a Smoothing Constant
Actual
Demand
50
a  .4
45
a  .1
40
35
1
2
3
4
5
6
7
Period
8
9 10 11 12
Forecast Accuracy
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Error - difference between actual value and
predicted value
Mean Absolute Deviation (MAD)
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Mean Squared Error (MSE)
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Average absolute error
Average of squared error
Mean Absolute Percent Error (MAPE)
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Average absolute percent error
MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
( Actual
 forecas
t
n
/ Actual*100)
Example 10
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Actual
217
213
216
210
213
219
216
212
2.75
10.86
1.28
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2
4
9
1
16
4
25
1
16
76
(|A-F|/Actual)*100
0.92
1.41
0.46
1.90
0.94
2.28
0.46
1.89
10.26
Controlling the Forecast
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Control chart
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A visual tool for monitoring forecast errors
Used to detect non-randomness in errors
Forecasting errors are in control if
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All errors are within the control limits
No patterns, such as trends or cycles, are
present
Sources of Forecast errors
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Model may be inadequate
Irregular variations
Incorrect use of forecasting technique
Tracking Signal
•Tracking signal
–Ratio of cumulative error to MAD
(Actual-forecast)

Tracking signal =
MAD
Bias – Persistent tendency for forecasts to be
Greater or less than actual values.
Common Nonlinear Trends
Parabolic
Exponential
Growth
Trend Projection
History
Future
10
9
?
8
7
Long
Term
Trend
Sales
6
5
Forecast
Assuming it repeat
the past?
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Time (years)
11
12
13
14
15
16
Trend Projection

The approach used to determine the linear function
that best approximates the trend is the least –
squared method. The objective is to determine the
value of a and b that minimize:
n
 (t – Ft)2
t=r
Where:
t = actual value of time series in period
Ft = forecast value in period t
n = number of period
Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5
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t
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
Calculating a and b
n  (ty) -  t  y
b =
n t 2 - (  t) 2
 y - b t
a =
n
Linear Trend Equation
Example
t
Week
1
2
3
4
5
2
t
1
4
9
16
25
 t = 15
 t = 55
2
( t) = 225
2
y
Sales
150
157
162
166
177
ty
150
314
486
664
885
 y = 812  ty = 2499
Linear Trend Calculation
b =
5 (2499) - 15(812)
5(55) - 225
=
12495-12180
275 -225
812 - 6.3(15)
a =
= 143.5
5
y = 143.5 + 6.3t
= 6.3
Casual Forecasting Models
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Regression
Correlation Coefficient
Coefficient of Determination
Multiple Regression
Autogressive Model
Stepwise Regression
Associative Forecasting
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Regression - technique for fitting a
line to a set of points
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Least squares line - minimizes sum of
squared deviations around the line
Causal Forecasting Models
(Regression)
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Regression analysis is a statistical
technique that can be used to develop
an equation to estimate mathematically
how two or more variables are related.
Y = bo + b1x
b1 = n xy – x y
n  x2 – (  x)2
bo = y - b1x
Linear Model Seems Reasonable
X
7
2
6
4
14
15
16
12
14
20
15
7
Y
15
10
13
15
25
27
24
20
27
44
34
17
Computed
relationship
50
40
30
20
10
0
0
5
10
15
20
25
A straight line is fitted to a set of sample points.
Correlation Coefficient
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The coefficient of correlation, r, explains the
relative importance of the association between y
and x. The range of r is from -1 to +1.
r = n  xy -  x  y______________
 [ n  x2 – (x)2][n  y2 -(  y)2]
Although the coefficient of correlations is helpful in
establishing confidence in our predictive model,
terms such as strong, moderate, and weak are not
very specific measures of a relationship.
Coefficient of Determination
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The coefficient of determination, r2, is
the square of the coefficient of
correlation.
This measure indicates the percent of
variation in y that is explained by x.
Multiple Regression

Multiregression analysis is used when two or
more independent variables are incorporated into
the analysis.
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In forecasting the sale of refrigerators, we might
select independent variable such as:

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Y= annual sales in thousands of units
X1 = price in period t
X2 = total industry sales in period t-1
X3 = number of building permits for new houses in
period t-1
Multiple Regression
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X4 = population forecast for period t
X5 = advertising budget for period t
Y = bo +b1X1+b2X2+b3X3+b4X4+b5X5
Autogressive Models
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Regression models where the
independent variables are previous
values of the same time series
Yt = bo+b1Yt-1+b2Yt-2+b3Yt-3
Stepwise Regression
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In regular multiple regression analysis,
all the independent variables are
entered into the analysis concurrently.
In stepwise regression analysis,
independent variables will be selected
for entry into the analysis on the basis
of their explanatory (discriminatory)
power.
Choosing a Forecasting
Technique
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No single technique works in every situation
Two most important factors
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Cost
Accuracy
Other factors include the availability of:
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Historical data
Computers
Time needed to gather and analyze the data
Forecast horizon
Exponential Smoothing
Linear Trend Equation
Simple Linear Regression