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2007/12/21 MR Final Report 1
An Evaluation of the Time-varying Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products
Cindy Wu
Advisor: Charles V. Trappey,
2007/12/21 MR Final Report 2
Introduction
With the rapid introduction of new technologies, product life cycles (PLC) for electronic goods become shorter and shorter.
Less data becomes available for analysis
Using smaller data sets to forecast future trends is important
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Research Purpose
This research studies the forecast accuracy of long and short lifecycle products data sets using the simple logistic, Gompertz, and extended logistic models.
Time series datasets for 22 electronic products and services were used to evaluate and compare the performance of the three models.
2007/12/21 MR Final Report 4
Product Life Cycle
Introduction: slow sales growth Growth: rapid sales growth Maturity: sales growth declines Decline: sales growth falls
IntroductoryStage
GrowthStage
MaturityStage
Decline Stage
Time
MarketSales
2007/12/21 MR Final Report 5
S-curve
Time
Cumulative sales
Introduction
Growth
Mature
Decline
Technology product growth follows S-curve Initial growth is often slow Followed by rapid exponential growth Falls off as a limit to market share is approached
2007/12/21 MR Final Report 6
Growth Curve Model
Growth curves models are widely used in technology forecasting and have been developed to forecast the penetration rate of technology based products.
Growth curve models are expressed by logistic form, so they are also referred as “S-shaped” curves.
Simple logistic curve and Gompertz curve are the most frequently referenced.
2007/12/21 MR Final Report 7
Technological Forecasting Models
Simple Logistic Curve Model
Gompertz Model
Extended Logistic Model
2007/12/21 MR Final Report 8
Simple Logistic Curve Model
btT ae
Ly
1
btayLyY ttt lnln
L ty: is the upper bound of
e : natural logarithm
a b : parameter
: the variable care to forecastty
2007/12/21 MR Final Report 9
Gompertz Model
btaet Ley
btayLY tt lnlnln
L ty: is the upper bound of
e : natural logarithm
a b : parameter
: the variable care to forecastty
2007/12/21 MR Final Report 10
Limitation of the Models
The upper limit of the curve should be set correctly or the prediction will become inaccurate.
Setting the upper limit to growth is difficult and ambiguous Necessity productShort life cycle product
L1
Time
L2
A
B
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Extended Logistic Model
Meyer and Ausubel (1999)The upper limit of the curve is not
constant but dynamic over timeExtending the simple logistics model with
a carrying capacity
k
ybydt
df1
tk
ybydt
df1is extended to
2007/12/21 MR Final Report 12
Technological Forecasting Models
Extended Logistic Model
is the time-varying capacity and is the function which is similar to logistic curve
ateDtk 1
bt
at
btteC
eD
eC
tky
1
1
1
2007/12/21 MR Final Report 13
The Measurements of Fit and Forecast Performance
n
ff
MAD
n
iii
1
ˆ
n
ff
RMSE
n
iii
1
2ˆ
Mean Absolute Deviation (MAD)
Root Mean Square Error (RMSE)
The smaller the MAD and RMSE, the better performance
2007/12/21 MR Final Report 14
Data Collection - Penetration rate
Product SamplePeriod
SampleSize
Color TV 1974 ~ 2004 31
Telephone 1964 ~ 2004 35
Washing Machine 1974 ~ 2004 31
ADSL subscription 2000 ~ 2006 26
Mobile internet subscription 2000 ~ 2006 20
Broadband network 2000 ~ 2006 26
2007/12/21 MR Final Report 15
Data Collection – Cumulative sales
Product SamplePeriod
SampleSize
LCD-TV 2003 ~ 2007 18
19”LCD monitor 2003 ~ 2007 18
CCD DC 2003 ~ 2007 18
DC >5m 2003 ~ 2007 18
WLAN (802.11g) 2003 ~ 2007 18
Cable Modem 2003 ~ 2007 18
Combo ODD 2003 ~ 2007 18
Barebones 2003 ~ 2007 18
2007/12/21 MR Final Report 16
Data Collection – Cumulative sales
Product SamplePeriod
SampleSize
China PAS 2003 ~ 2007 18
LCD panel for TV 2003 ~ 2007 18
LCD panel for notebook 2003 ~ 2007 18
Color-65k mobile phone
2003 ~ 2007 18
Server 2003 ~ 2007 18
LCD-TV >30” 2004 ~ 2007 14
VoIP IAD 2004 ~ 2007 14
VoIP router 2004 ~ 2007 14
2007/12/21 MR Final Report 17
Market Growth for Saturation Data Sets
0
20
40
60
80
100
120
1964
1970
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
.06
2000
.12
2001
.06
2001
.12
2002
.06
2002
.12
2003
.06
2003
.12
2004
.06
2004
.12
2005
.06
2005
.12
2006
.06
Time
Satu
ratio
n (%
)
Color TV Telephone Washing machine ADSL Mobile internet Broadband network
2007/12/21 MR Final Report 18
Market Growth for Cumulative Data Sets
0
20000
40000
60000
80000
100000
120000
140000
160000
2003
Q1
2003
Q2
2003
Q3
2003
Q4
2004
Q1
2004
Q2
2004
Q3
2004
Q4
2005
Q1
2005
Q2
2005
Q3
2005
Q4
2006
Q1
2006
Q2
2006
Q3
2006
Q4
2007
Q1
2007
Q2
Time
Cum
ulat
ive
sale
s vo
lum
e (t
hous
and)
LCD-TV 19”LCD monitor CCD DC DC >5mWLAN (802.11g) Cable Modem Combo ODD BareboneChina PAS LCD panel for TV LCD panel for notebook Mobile color-65kServer LCD-TV >30” VoIP IAD VoIP Router
Note: the unit of wireless internet is ten thousand. Source: ASIP, Market Intelligence Center, Taiwan
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Analysis Steps
The first step (Fit performance) Reserve the last five data points Fit the remaining data points into the three models Compute the coefficients of the models and the
statistics for MAD and RMSE
The second step (Forecast performance) Uses the derived models to forecast the five data
points Compare the forecast with the true observations Compute MAD and RMSE for forecast performance
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Results (Penetration Data Set)
Product
Fitting Forecasting
Extended logistic
GompertzSimple logistic
Extended logistic
GompertzSimple logistic
Color TV 1 2 3 1 2 3
Phone 1 2 3 1 2 3
Washing Machine
1 2 3 1 2 3
ADSL 1 2 3 1 2 3
Mobile Internet
1 2 3 1 2 3
BroadbandNetwork
1 3 2 1 2 3
2007/12/21 MR Final Report 21
Results (Cum. Sales Data Set)
Product
Fitting Forecasting
Extended logistic
GompertzSimple logistic
Extended logistic
GompertzSimple logistic
LCD-TV 1 2 3 1 2 3
19”LCD monitor 1 2 3 2 1 3
CCD DC 1 2 3 1 2 3
DC >5m 1 2 3 2 1 3
WLAN (802.11g) 1 2 3 1 2 3
Cable Modem 1 2 3 1 2 3
Combo ODD 1 2 3 1 2 3
Barebones 1 2 3 1 2 3
China PAS 1 2 3 1 2 3
LCD panel for TV 1 2 3 2 1 3
LCD-TV >30” 1 3 2 3 2 1
VoIP IAD 1 2 3 2 1 3
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Conclusion
This study compares the fit and prediction performance of the simple logistic, Gompertz, and the extended logistic models for four electronic products.
Since the simple logistic and Gompertz curves require the correct setting of upper limits for accurate market growth rate predictions, these two models may not be suitable for short life cycle products with limited data.
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Conclusion
The time-varying extended logistic model fits short life cycle product datasets better than the simple logistic, and Gompertz models for 70% of the 18 product data sets for which the extended logistic model could be fitted.
Besides, the time-varying extended logistic model is better suited to predict market capacity with limited historical data as is typically the case for short lifecycle products and services.
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Limitations
Since the capacity of extended logistic model is time-varying and is a logistics function of time, it is not suitable for the data with linear curve.
The data sets for LCD panel for notebooks, color-65k mobile phones, servers, and VoIP routers would not converge when using the time-varying extended logistic model to estimate the coefficients.
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Limitations
LCD panel for notebooks, servers, and VoIP routers data sets are linear
The curve for the color-65k mobile phone has an obvious jump
0
20000
40000
60000
80000
100000
120000
140000
160000
2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2Time
Cu
mu
lati
ve
sale
s v
olu
me
(th
ou
san
d)
LCD panel for notebook Mobile color-65k Server VoIP Router
Note: the unit of wireless internet is ten thousand. Source: ASIP, Market Intelligence Center, Taiwan
2007/12/21 MR Final Report 26
Meade & Islam (1995)
Source: Meade N, Islam T. Forecasting with growth curves: An empirical comparison. International Journal of Forecasting 1995;11:199-215.
Using telephone data from Sweden to compare the simple logistic, extended logistic, and the local logistic models
The extended logistic model had the worst performance
2007/12/21 MR Final Report 27
Future Research
A possible solution for those types of data sets with linear data or with many anomalous data points may be to apply smoothing techniques or data re-interpretation techniques.
Further research can be conducted using Tukey smoothing and data re-interpretation to see if the extended logistic model can be forced to converge and therefore find broader applications for short life cycle data sets.
2007/12/21 MR Final Report 28
Thank you.
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