3
Forecasting
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
FORECAST:
 A statement about the future value of a
variable of interest such as demand.
 Forecasting is used to make informed
decisions.
 Long-range
 Short-range
3-2
Forecasts
 Forecasts affect decisions and activities
throughout an organization
 Accounting, finance
 Human resources
 Marketing
 MIS
 Operations
 Product / service design
3-3
Uses of Forecasts
Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, workloads
Product/service design
New products and services
3-4
Features of Forecasts
 Assumes causal system
past ==> future
 Forecasts rarely perfect because of
randomness
 Forecasts more accurate for
groups vs. individuals
I see that you will
get an A this semester.
 Forecast accuracy decreases
as time horizon increases
3-5
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
3-6
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Make the forecast
Step 4 Obtain, clean and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
3-7
Types of Forecasts
 Judgmental - uses subjective inputs
 Time series - uses historical data
assuming the future will be like the
past
 Associative models - uses
explanatory variables to predict the
future
3-8
Judgmental Forecasts
 Executive opinions
 Sales force opinions
 Consumer surveys
 Outside opinion

Delphi method
 Opinions of managers and staff
 Achieves a consensus forecast
3-9
Time Series Forecasts
 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
3-10
Forecast Variations
Figure 3.1
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
3-11
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.
3-12
Naïve Forecasts





Simple to use
Virtually no cost
Quick and easy to prepare
Easily understandable
Cannot provide high accuracy
3-13
Uses for Naïve Forecasts
 Stable time series data
 F(t) = A(t-1)
 Seasonal variations
 F(t) = A(t-n)
3-14
Techniques for Averaging
 Moving average
 Weighted moving average
 Exponential smoothing
3-15
Moving Averages
 Moving average – A technique that averages a
number of recent actual values, updated as
new values become available.
Ft = MAn=
At-n + … At-2 + At-1
n
 Weighted moving average – More recent
values in a series are given more weight in
computing the forecast.
Ft = WMAn=
wnAt-n + … wn-1At-2 + w1At-1
3-16
Simple Moving Average
Actual
MA5
47
45
43
41
39
37
MA3
35
1
2
3
Ft = MAn=
4
5
6
7
8
9
10 11 12
At-n + … At-2 + At-1
n
3-17
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
• Premise--The most recent observations
might have the highest predictive value.

Therefore, we should give more weight to
the more recent time periods when
forecasting.
3-18
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
 Weighted averaging method based on
previous forecast plus a percentage of the
forecast error
 A-F is the error term,  is the % feedback
3-19
Example 3 - Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
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
3-20
Picking a Smoothing Constant
Actual
Demand
50
.4
45
 .1
40
35
1
2
3
4
5
6
7
8
9 10 11 12
Period
3-21
Common Nonlinear Trends
Figure 3.5
Parabolic
Exponential
Growth
3-22
Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5




t
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
3-23
Calculating a and b
n  (ty) -  t  y
b =
2
2
n t - (  t)
 y - b t
a =
n
3-24
Linear Trend Equation Example
t
Week
1
2
3
4
5
2
t
1
4
9
16
25
 t = 15
t2 = 55
2
(t) = 225
y
Sales
150
157
162
166
177
ty
150
314
486
664
885
 y = 812  ty = 2499
3-25
Linear Trend Calculation
b = 5 (2499) - 15(812) = 12495-12180 = 6.3
5(55) - 225
275 -225
a = 812 - 6.3(15) = 143.5
5
y = 143.5 + 6.3t
3-26
Techniques for Seasonality
 Seasonal variations
 Regularly repeating movements in series values
that can be tied to recurring events.
 Seasonal relative
 Percentage of average or trend
 Centered moving average
 A moving average positioned at the center of the
data that were used to compute it.
3-27
Associative Forecasting
 Predictor variables - used to predict values
of variable interest
 Regression - technique for fitting a line to a
set of points
 Least squares line - minimizes sum of
squared deviations around the line
3-28
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.
3-29
Linear Regression Assumptions
 Variations around the line are random
 Deviations around the line normally
distributed
 Predictions are being made only within the
range of observed values
 For best results:
 Always plot the data to verify linearity
 Check for data being time-dependent
 Small correlation may imply that other variables
are important
3-30
Forecast Accuracy
 Error - difference between actual value and
predicted value
 Mean Absolute Deviation (MAD)

Average absolute error
 Mean Squared Error (MSE)

Average of squared error
 Mean Absolute Percent Error (MAPE)

Average absolute percent error
3-31
MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
( Actual
 forecas
t
n
/ Actual*100)
3-32
MAD, MSE and MAPE
 MAD
 Easy to compute
 Weights errors linearly
 MSE
 Squares error
 More weight to large errors
 MAPE
 Puts errors in perspective
3-33
Example 10
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Actual
217
213
216
210
213
219
216
212
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
2.75
10.86
1.28
3-34
Controlling the Forecast
 Control chart
 A visual tool for monitoring forecast errors
 Used to detect non-randomness in errors
 Forecasting errors are in control if
 All errors are within the control limits
 No patterns, such as trends or cycles, are
present
3-35
Sources of Forecast errors
 Model may be inadequate
 Irregular variations
 Incorrect use of forecasting technique
3-36
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.
3-37
Choosing a Forecasting
Technique
 No single technique works in every
situation
 Two most important factors
 Cost
 Accuracy
 Other factors include the availability of:




Historical data
Computers
Time needed to gather and analyze the data
Forecast horizon
3-38
Operations Strategy
 Forecasts are the basis for many decisions
 Work to improve short-term forecasts
 Accurate short-term forecasts improve





Profits
Lower inventory levels
Reduce inventory shortages
Improve customer service levels
Enhance forecasting credibility
3-39