PERTEMUAN 14
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Forecasting
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to:
1. Understand and know when to use
various families of forecasting
models
2. Compare moving averages,
exponential smoothing, and trend
time-series models
3. Seasonally adjust data.
4. Understand Delphi and other
qualitative decision-making
approaches
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives continued
Students will be able to:
5. Identify independent and
dependent variables and use
them in a linear regression
model.
6. Compute a variety of error
measures.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
5.1 Introduction
5.2 Types of Forecasts
5.3 Scatter Diagrams
5.4 Measures of Forecast Accuracy
5.5 Time-Series Forecasting Models
5.6 Causal Forecasting Models
5.7 Monitoring and Controlling
Forecasts
5.8 Using the Computer to Forecast
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Introduction
Eight steps to forecasting:
1. Determine the use of the forecast
2. Select the items or quantities to be
forecasted
3. Determine the time horizon of the
forecast
4. Select the forecasting model or
models
5. Gather the data needed to make the
forecast
6. Validate the forecasting model
7. Make the forecast
8. Implement the results
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-6
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Forecasting Models Fig. 5.1
Forecasting
Techniques
Qualitative
Models
Time Series
Methods
Causal
Methods
Delphi
Methods
Moving
Average
Regression
Analysis
Jury of
Executive
Opinion
Exponential
Smoothing
Multiple
Regression
Sales Force
Composite
Consumer
Market
Survey
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for Management, 8e
by Render/Stair/Hanna
Trend
Projections
Decomposition
5-7
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Annua l Sa le s
Scatter Diagram for Sales
Fig. 5.2
450
400
350
300
250
Televisions
200
150
100
50
0
0
2
4
6
8
10
Time (Years)
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for Management, 8e
by Render/Stair/Hanna
5-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
12
Decomposition of Time
Series
Time series can be decomposed
into:
• Trend (T): gradual up or down
movement over time
• Seasonality (S): pattern of
fluctuations above or below trend
line that occurs every year
• Cycles(C): patterns in data that
occur every several years
• Random variations (R): “blips”in
the data caused by chance and
unusual situations
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-9
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decomposition of Time
Series
Two Models
Multiplicative model:
demand = T * S * C * R
Additive model:
demand = T + S + C + R
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Product Demand
Showing Components
650
Actual Data
Demand
550
Trend
450
350
250
150
Cyclic
50
-50
Random
-150
0
1
2
3
4
Time (Years
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for Management, 8e
by Render/Stair/Hanna
5-11
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
5
Moving Averages
Moving average:
 demand in previous n periods
n
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for Management, 8e
by Render/Stair/Hanna
5-12
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Calculation of ThreeMonth Moving Average
Month
Actual
Shed
Sales
Three-Month
Moving Average
January
10
February
12
March
13
April
16
(10+12+13)/3 = 11 2/3
May
19
(12+13+16)/3 = 13 2/3
June
23
(13+16+19)/3 = 16
July
26
(16+19+23)/3 = 19 1/3
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-13
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Table 5.2
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for Management, 8e
by Render/Stair/Hanna
5-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Weighted Moving
Averages
Weighted moving average =
Σ(weight for period n)  (demand in period n)
Σweights
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Calculating Weighted
Moving Averages
Weights
Applied
Period
Last month
3
Two months ago
2
Three months ago
1
3*Sales last month +
2*Sales two months ago +
1*Sales three
months ago
Sum of weights
6
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Calculation of ThreeMonth Moving Average
Month
Actual
Three-Month
Moving Average
Shed
Sales
January
10
February
12
March
13
April
16
[3*13+2*12+1*10]/6 = 12 1/6
May
19
[3*16+2*13+1*12]/6 =14 1/3
June
23
[3*19+2*16+1*13]/6 = 17
July
26
[3*23+2*19+1*16]/6 = 20 1/2
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-17
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Table 5.3
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-18
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Exponential Smoothing
New forecast =
previous forecast + (previous actual
- previous)
or:
where
Ft = Ft-1 + (At-1 - Ft-1)
Ft = new forecast
Ft-1 = previous forecast
 = smoothing constant
At-1 = previous period actual
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-19
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Selecting the Smoothing
Constant ()
Select  to minimize:
Mean Absolute Deviation = MAD
Σ | forecast errors |

n
Mean Square Error = MSE
Σ(forecast errors) 2

n
Mean Absolute Percent Error = MAPE
1  forecast error 
 Σ

n 
actual

Bias = forecast errors
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-20
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Table 5.4
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-21
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Table 5.5
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-22
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Exponential Smoothing
with Trend Adjustment
Forecast including trend (FITt+1) =
new forecast (Ft) + trend
correction(Tt)
Tt = (1 - )Tt-1 + (Ft – Ft-1)
where
Ti = smoothed trend for period 1
Ti-1 = smoothed trend for the preceding period
 = trend smoothing constant
Ft = simple exponential smoothed forecast for
period t
Ft-1 = forecast for period t-1
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-23
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Exponential Smoothing
with Trend Adjustment
• Simple exponential smoothing first-order smoothing
• Trend adjusted smoothing second-order smoothing
• Low  gives less weight to
more recent trends, while high 
gives higher weight to more
recent trends
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-24
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Trend Projection
General regression equation:
Ŷ  a  bX
where
Ŷ  computed value
of the variable to
be predicted
(dependent variable)
a  Y - axis intercept
XY - nXY
b
2
2
X  nX
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-25
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Midwestern
Manufacturing’s Demand
160
150
140
130
120
110
100
90
80
70
60
Trend Line
Forecast points
Actual demand line
1993 1994 1995 1996 1997 1998 1999 2000 2001
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for Management, 8e
by Render/Stair/Hanna
5-26
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Seasonal Variations
Month
Sales
Demand
Average
Two-Year
Demand
Average
Monthly
Demand
Seasonal
Index
Year Year
2
1
Jan
80
100
90
94
0.957
Feb
75
85
80
94
0.851
Mar
80
90
85
94
0.904
Apr
90
110
100
94
1.064
May
115
131
123
94
1.309
…
…
…
…
…
…
Total Average Demand 1,128
Seasonal Index:
= Average 2 -year demand/Average monthly
demand
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-27
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Using Regression
Analysis to Forecast
Y
X
Triple A' Sales
Local Payroll
($100,000's)
($100,000,000)
2.0
1
3.0
3
2.5
4
2.0
2
2.0
1
3.5
7
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for Management, 8e
by Render/Stair/Hanna
5-28
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Using Regression Analysis
to Forecast - continued
Sales, Y Payroll, X
X2
XY
2.0
1
1
2.0
3.0
3
9
9.0
2.5
4
16
10.0
2.0
2
4
4.0
2.0
1
1
2.0
3.5
7
49
24.5
Y = 15
X = 18
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for Management, 8e
by Render/Stair/Hanna
X2 = 80
XY = 51.5
5-29
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Upper Saddle River, NJ 07458
Using Regression Analysis
to Forecast - continued
Calculating the required
parameters:
X
ΣX
18

3
6
3
Y
ΣY
15

 2.5
6
6
b

ΣXY  nX Y
ΣX 2  nX 2
51.5  6 * 3 * 2.5
 0.25
2
80  6 * 3
a  Y - bX  2.5 - 0.25 * 3  1.75
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-30
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Tr iple A's Sale s ($100,000)
Standard Error of the
Estimate
4
3
2
1
0
0
1
2
3
4
5
6
7
Area Payroll ($100,000,000)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-31
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
8
Standard Error of the
Estimate - continued
S
Y ,X

 (Y  Y )2
c
n2
where
Y  Y  value of each data point
Y  value of the dependent variable
c
computed from the regression equation
n  number of data points
or:
S 
Y,X
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by Render/Stair/Hanna
 Y 2 aY b XY
n 2
5-32
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Triple A’s Calculations
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-33
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Triple A’s Calculations
- continued
SY ,X 
SY ,X 
 Y 2  a  Y  b  XY
n 2
39.5  (1.75 )(15.0 )  (0.25 )(51.5 )
6 2
 0.09375  0.306
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5-34
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Correlation Coefficient
r
nX
nX  ΣXΣY
2

 (X) 2 nY 2  (Y) 2
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by Render/Stair/Hanna
5-35
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458

Triple A’s Calculations
- continued
r



nΣΣ
nΣΣ  ΣXΣY
2

 (ΣΣX nΣΣ  (ΣΣY
2
2
6 * 51.5 - 18 * 15.0
(6 * 80 - 18 2 ) (6 * 39.5 - 15.0 2 )
309 - 270
156 * 12
39
1872
39

43.3
 0.901
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by Render/Stair/Hanna
5-36
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
2

Correlation Coefficient
- Four Values - Fig. 5.7
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Monitoring/Controlling
Forecasts
The Tracking Signal
RSFE
TrackingSi gnal 
MAD
Σ(actual demand in period i  forecast demand in period i)

MAD
where
Σ | forecast errors |
MAD 
n
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-38
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Monitoring/Controlling
Forecasts
The Tracking Signal
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
5-39
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458