An Evaluation of the Time-varying Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products

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An Evaluation of the Time-varying Extended
Logistic, Simple Logistic, and Gompertz Models
for Forecasting Short Lifecycle Products

• Cindy WuAdvisor Charles V. Trappey,

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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.

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Product Life Cycle

• Introduction slow sales growth
• Growth rapid sales growth
• Maturity sales growth declines
• Decline sales growth falls

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S-curve

• 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

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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.

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Technological Forecasting Models

• Simple Logistic Curve Model
• Gompertz Model
• Extended Logistic Model

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Simple Logistic Curve Model
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Gompertz Model
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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 product
• Short life cycle product

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Extended Logistic Model

• Meyer and Ausubel (1999)
• The upper limit of the curve is not constant but
  dynamic over time
• Extending the simple logistics model with a
  carrying capacity

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Technological Forecasting Models

• Extended Logistic Model
• is the time-varying capacity and is the function
  which is similar to logistic curve

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The Measurements of Fit and Forecast Performance
Mean Absolute Deviation (MAD)
Root Mean Square Error (RMSE)
The smaller the MAD and RMSE, the better
performance
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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
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Data Collection Cumulative sales
Product SamplePeriod SampleSize
LCD-TV 2003 2007 18
19LCD monitor 2003 2007 18
CCD DC 2003 2007 18
DC gt5m 2003 2007 18
WLAN (802.11g) 2003 2007 18
Cable Modem 2003 2007 18
Combo ODD 2003 2007 18
Barebones 2003 2007 18
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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 gt30 2004 2007 14
VoIP IAD 2004 2007 14
VoIP router 2004 2007 14
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Market Growth for Saturation Data Sets
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Market Growth for Cumulative Data Sets
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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 Fitting Fitting Forecasting Forecasting Forecasting
Product Extended logistic Gompertz Simple logistic Extended logistic Gompertz Simple 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
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Results (Cum. Sales Data Set)
Product Fitting Fitting Fitting Forecasting Forecasting Forecasting
Product Extended logistic Gompertz Simple logistic Extended logistic Gompertz Simple logistic
LCD-TV 1 2 3 1 2 3
19LCD monitor 1 2 3 2 1 3
CCD DC 1 2 3 1 2 3
DC gt5m 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 gt30 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

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Meade Islam (1995)

• 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

Source Meade N, Islam T. Forecasting with growth
curves An empirical comparison. International
Journal of Forecasting 199511199-215.
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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.

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Thank you.