Forecasting
–
–
–
–
–
Introduction to forecasting
Do you need a forecasting system?
Forecasting models
Qualitative judgments in forecasting
Reading: Chapter 8
MGT3303
Michel Leseure
Forecasting
• All operational systems operate in an
environment of uncertainty
• Information is an asset - managing it a
necessity
• “Reliable” information about the future is a
source of competitive edge
• Forecasting supplements the intuitive
feelings of managers and decision
makers.
MGT3303
Michel Leseure
Users
%
Budgets
86
Market planning
70
Production planning
59
Capital investment
57
Sales quota
44
Production scheduling
42
Product introduction
31
Others
10
The Uses
of
Demand
Forecasts
Forecasting practices of
Canadian Firms
Int. J. Production Economics
70(2001) 163-174
MGT3303
Michel Leseure
Forecasting in the hand tool
industry (1997 survey)
• 84% of hand tool manufacturers (UK+US)
use forecasting techniques
• Out of the manufacturers using
forecasting techniques:
– 0% think they are inaccurate and not
helpful
– 38 % think they are inaccurate but helpful
– 50% think they are somewhat accurate
– 12% think they are accurate
MGT3303
Michel Leseure
Forecasting « Laws »
• Forecasts are always wrong
• Forecasts always change
• The further into the future, the less reliable the
forecast.
– (greatest uncertainty and potential for a large error
when there is still time to prepare)
• Forecasts for group statistics tend to be more
accurate than forecasts for individuals
(risk/uncertainty pooling concept)
• Learning not predicting
MGT3303
Michel Leseure
Forecasting Error Trumpet
When the start of the new season is
farthest off,
 We still have time to produce in anticipation of start of season
demand
 We have the least accurate picture of what the demand will
look like
40%
20%
+10%
-10%
Time
Start of season
16 weeks
26 weeks
MGT3303
Michel Leseure
Time scope in manufacturing
forecasting
• Short-term forecasting:
– planning and scheduling manufacturing
operations, purchasing, staffing - mostly
quantitative
• Long-term forecasting:
– planning for capital investment, facility
layout, job shop design, etc. - subjective
and qualitative considerations
MGT3303
Michel Leseure
Frequency of Forecasting
Frequency of forecasting
%
Daily
2
Weekly
7
Monthly
38
Quarterly
24
Semi-annual
8
Yearly
21
Total
100
Forecasting
practices of
Canadian Firms
Int. J. Production
Economics
70(2001) 163-174
MGT3303
Michel Leseure
Do you need a forecasting
system?
• Difficult to estimate all the benefits (or
losses avoided)
• Not an excuse for not knowing the
economics of a forecasting system
MGT3303
Michel Leseure
Benefits of a forecasting system
• Cost of inventory
• Loss of business because of stockout
• Permanent loss of customers because of
stockout
• Cost of obsolescence
• Increase in the cost of production for
producing what is not in stock
MGT3303
Michel Leseure
Computing the value of the
benefits
• Sales = £800,000
• Markup= 100%
• Cost of inventory = 9% of Cost of Goods
Sold
MGT3303
Michel Leseure
Computing the value of the
benefits
•
•
•
•
•
•
Inventory reduced by 5 days
Decrease in order cancellation: 1% of sales
Reduction of lost customers: 0.25% of sales
Reduction of obsolescence: 1% of sales
Reduction of product cost: 2%
How much can you invest in forecasting without
decreasing profits?
MGT3303
Michel Leseure
Computing the value of the
benefits
•
•
•
•
•
Annual CGS: 800,000*0.5= £ 400,000
Product Cost of 5 days worth of inventory: £5,479
of which inventory costs: 9% = £493
Decrease in order cancellation: 1%=£4000
Reduction of lost customers: 0.25% of sales =
£1000
• Reduction of obsolescence: 1% of sales = £4000
• Reduction of product cost: 2% = £8,000
• TOTAL = £17,493
MGT3303
Michel Leseure
Forecasting System Expenditures
Expenditures
(thousand C$)
No. of firms
0-50
Median
Product
69
25K
1725
50-100
16
75
1200
100-250
11
175
1925
625
5000
250-1000 8
>1000
6
Sum
110
1000
6000
15850
Mean =
15,850/110
= 144 K
Forecasting practices of
Canadian Firms
Int. J. Production
Economics
70(2001) 163-174
MGT3303
Michel Leseure
Forecasting Techniques
MGT3303
Michel Leseure
Types of Forecasting
Approaches & Methods
Unpredictable
Quantitative
Time-Series Methods
Causal / Explanatory Methods
Moving Avarages
Exponential Smoothing
Simple (No Trend)
Double (Linear Trend)
Triple (Curvilinear Trend)
Simple Regression
Linear Trend
Quadratic Trend
Exponential Trend
Multiple Regression
Econometric Modeling
Leading Indicator Analysis
Diffusion Indexes
Qualitative
Delphi Technique
Expert Opinion
Factor Listing Method
MGT3303
Michel Leseure
Overview of forecasting models
• Naïve models
• Time series
– Moving average
– weighting past value
– The decomposition method
• Associative models
– Correlation analysis
– Regression analysis
MGT3303
Michel Leseure
Year
1991
Sales of saws for
the Acme Tool
Company (19911996)
1992
1993
1994
Sales
800
700
600
500
1995
400
300
200
100
0
1996
0
5
10
15
20
25
30
Quarter
T
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Sales
500
350
250
400
450
350
200
300
350
200
150
400
550
350
250
550
550
400
350
600
750
500
400
650
MGT3303
Michel Leseure
Time series analysis
• Time series:
– A time-ordered sequence of observations
taken at regular interval over a period of
time
• Time series are analysed to discover past
patterns of growth and change that can be
used to predict future patterns and needs
for business operations
MGT3303
Michel Leseure
Naïve model
• The forecast for any period equals the
previous period’s actual value
X t 1  X t
 Example,
650
for the Acme tool company, X25=
MGT3303
Michel Leseure
Jazzing-up the naïve model
• Incorporating a trend:
X t 1  X t  ( X t  X t 1 )
 This
model takes into account the
amount of change that occurred
between the last two periods
 X25=X24+(X24-X23)=650 + (650400)=900
MGT3303
Michel Leseure
Jazzing-up the naïve model
• Incorporating seasonal variations:
X t 1  X t 3
 Visual
inspection of the data indicates
that seasonal variations seems to exist.
Sales in the fourth quarter are typically
larger than any of the other quarters
 X25= X21= 750
MGT3303
Michel Leseure
Moving Averages
• Many possible extensions of the naïve model,
moving averages is one
• Averages a number of recent actual values,
updated as new values become available
n
MA n 
Y
i
i 1
n
i: “age” of the data
n= number of periods
in the moving average
Ai: actual value with
age i
MGT3303
Michel Leseure
Application to Acme Tools
• Forecast during the
third quarter of 1996,
with n=4
• Actual value = 650
600  750  500  400
MA 4 
4
MA 4  562 . 5
• Forecast during the
fourth quarter of 1996,
with n=4
750  500  400  650
4
MA 4  575
MA 4 
MGT3303
Michel Leseure
Smoothing effect
800
700
600
500
400
Sales
300
MA4
200
100
0
0
5
10
15
20
25
30
MGT3303
Michel Leseure
12
Period
Index
Months
Moving
Average
Spreadsheet
2 Months
Moving
Error 12
Error 2
Average
1
108
2
108
3
110
4
106
5
108
6
108
7
105
8
100
9
97
10
95
11
95
12
92
13
95
102.67
93.50
-7.67
1.50
14
95
101.58
93.50
-6.58
1.50
15
98
100.50
95.00
-2.50
3.00
16
97
99.50
96.50
-2.50
0.50
17
101
98.75
97.50
2.25
3.50
18
104
98.17
99.00
5.83
5.00
19
101
97.83
102.50
3.17
-1.50
20
99
97.50
102.50
1.50
-3.50
21
95
97.42
100.00
-2.42
-5.00
22
95
97.25
97.00
-2.25
-2.00
23
96
97.25
95.00
-1.25
1.00
24
96
97.33
95.50
-1.33
0.50
25
97
97.67
96.00
-0.67
1.00
26
98
97.83
96.50
0.17
1.50
27
94
98.08
97.50
-4.08
-3.50
28
92
97.75
96.00
-5.75
-4.00
MGT3303
Michel Leseure
8.00
6.00
4.00
2.00
0.00
28
25
22
19
16
13
7
-2.00
10
Results
4
1
Error 12
Error 2
-4.00
-6.00
-8.00
-10.00
115
Index
110
105
12 Months Moving
Average
100
2 Months Moving
Average
95
90
0
5
10
15
20
25
30
MGT3303
Michel Leseure
Using weighted averages
• Using weights in moving averages allows
to give more or less importance to
different periods
• An example is exponential smoothing, a
procedure for continually revising an
estimate in light of more recent
experiences
• Adaptive filtering is a procedure which
identifies the best set of weights for the
actual data
MGT3303
Michel Leseure
Exponential Smoothing
 Form of Weighted Moving Average
 Weights Decline Exponentially
 Most Recent Data Weighted Most
 Each Smoothing Calculation or Forecast Depends On
All Previously Observed Values
 Used for Smoothing to provide an overall impression of
data over time & short-term Forecasting (one period into
the future)
 Assumes No Trend
 Requires Smoothing Coefficient ()
 Subjectively Chosen
 Ranges from 0 to 1
MGT3303
Michel Leseure
Exponential Smoothing
• Ft+1= Dt + (1- )Ft
– Ft+1: Forecast for period t+1
– Dt: Demand for period t
– Ft: Forecast for period t
– : smoothing constant
MGT3303
Michel Leseure
Exponential Smoothing
112
110
108
106
104
102
Data
100
Smoothing (0.5)
98
96
94
92
90
0
5
10
15
20
25
30
MGT3303
Michel Leseure
Choice of Alpha
112
110
108
106
Data
104
Smoothing (0.2)
102
Smoothing (0.4)
100
Smoothing (0.6)
98
Smoothing (0.8)
96
94
92
90
0
5
10
15
20
25
30
The greater is , the greater the reaction to the most
recent demand.
MGT3303
Michel Leseure
Adjusted Exponentially Smoothing
• Exponentional smoothing with a trend
component
• AFt+1= Ft+1+Tt+1
• AF is the adjusted forecast
• T is an exponentially smoothed trend
• Tt+1= (Ft+1 – Ft )+ (1- )Tt
• F is the normal forecast based on the
smoothing constant 
MGT3303
Michel Leseure
Adjusted Exponentially Smoothing
450000
400000
350000
300000
Actual
250000
Regression
200000
4-MAV
150000
FIT
100000
50000
0
-50000
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35
MGT3303
Michel Leseure
The decomposition method
• The most widely used method to forecast
time series
• Three components are found in annual
time series: the trend, the cyclical
variation, and irregular fluctuations
• In short-term time series (i.e. classified by
quarters, months, weeks) an additional
seasonal component is added
MGT3303
Michel Leseure
The trend
Y  27627
. 10.56t
•
•
800
700
•
600
500
Sales
400
Trend
300
•
200
100
0
0
5
10
15
20
25
The long-term
component of a time
series
Underlies the growth
(or decline) in the
series
usually assumed to
be linear (regression
analysis of Y(t)
in the same unit than
Y
30
MGT3303
Michel Leseure
The cyclical component C
• Only for long term time series - scale of
the economic cycles
• Compute C=Y/TS
• Search for a published economic index
which is correlated with C (leading,
coincident, lagging indicators)
• Use published forecasts of the indicator
MGT3303
Michel Leseure
The seasonal component
• Important in manufacturing, where the
model Y=TCSI is often reduced to Y=TSI
• S is usually a centered moving average
• Computations of the seasonal indexes can
be long - the use of time serie and
forecasting software is more appropriate
MGT3303
Michel Leseure
Centered moving average
• A moving average positioned at the center
of the data that were used to compute it
• Period index = actual/centered average
Period
Centered
average Index
Y
1
1
3
40
46
42
42.67 107.8041
MGT3303
Michel Leseure
The irregular component: I
• what is leftover when dividing the actual
values of Y by T, C and
• is plotted to identify any significant
patterns (rare event, e.g. strike, etc.)
• usually, I=1.0 when forecasting
MGT3303
Michel Leseure
A simple
application
• Acme data,
C=I=1.0 for all
quarters
• Y=TS
• T= 276.27
+10.56t
Results of SEASON
procedure for variable
SALES
Multiplicative Model.
Centered MA method.
Period = 4.
Seasonal
index
Period
(* 100)
1
134.133
2
87.481
3
64.285
4
114.102
MGT3303
Michel Leseure
Time series Analysis with SPSS
G1. SALES
800
700
600
500
400
300
200
B1.Original series
E1.Mod. for extremes
100
1ST91
1ST92
1ST93
1ST94
1ST95
1ST96
3RD91
3RD92
3RD93
3RD94
3RD95
3RD96
with 0 final weight
Date
MGT3303
Michel Leseure
Measuring forecast error
• The mean squared error is the most
common method
• Plotting out actual and forecasted points
n
MSE 
 (Y  F )
i
2
i
i 1
n
MGT3303
Michel Leseure
Associative forecasting models
• The fluctuations of the quantity to forecast
(the independent variable Y)are “linked” to
the fluctutations of a dependent variable X
• Time series trend analysis X=t
• if there is a single X, regression analysis
• if there are several X, multivariate
regression analysis
MGT3303
Michel Leseure
Correlation Analysis
• The first step of associative forecasting
models: finding and testing the correlation
of Y with potential Xs
• The correlation measures the strength
and direction of relationship between two
variables
MGT3303
Michel Leseure
Correlation Coefficient
• A correlation of +/-1 indicates a change in one
variable is always matched by a change in the
other, and indicates a strong linear relationship
between the two variables
• r=0 indicates a poor correlation
r
n(  xy )  (  x )(  y )
n(  x 2 )  (  x ) 2  n(  y 2 )  (  y ) 2
MGT3303
Michel Leseure
Application - Correlation
• r= -0.966
• Good explanatory
power
• U explains 96.6% of
sales variations
• not necessarily
statistically significant
Units Sold
45
40
35
30
25
20
15
10
5
0
0
Period
Unemployement
Units Sold
1
7.2
20
2
4
41
3
7.3
17
1
2
4
5.5
35
3
4
5
6.8
25
5
6
6
6
31
7
8
7
5.4
38
MGT3303
Michel Leseure
Regression Analysis-Graphical
• If two variables are correlated, express
their linear relationship
• Y= a+ bX y
dy
a
dx
b=dy/dx
x
MGT3303
Michel Leseure
Regression Analysis - least
square method
• A computational method to fit the best line
through a collection of points
• available on all spreadsheets
• precise (?), convenient
• but cannot detect outliers, noise in the
data, etc.
• Always plot the data
MGT3303
Michel Leseure
Subjective judgments in
forecasting
• A wide variety of tools and techniques
– example: Delphi technique
• problem of the availability of data
• problem of the quality of data
• these tools and techniques force
managers to a thorough analysis of their
businesses -what counts
• supplement “gut feelings”
MGT3303
Michel Leseure
Newer Methods
•
•
•
•
Chaos theory
Expert systems
Genetic algorithms
Neural networks
MGT3303
Michel Leseure
Suggested Homework
•
•
•
•
•
•
Use excel
Solved problems p 376-377
Problem 8-1, p. 378
Problem 8-7, p. 380
Problem 8-14, p. 381
Case problem 8-1, p. 388
MGT3303
Michel Leseure