1. 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,

2. 2007/12/21MR Final Report2 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

3. 2007/12/21MR Final Report3 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.

4. 2007/12/21MR Final Report4 Product Life Cycle Introduction: slow sales growth Growth: rapid sales growth Maturity: sales growth declines Decline: sales growth falls

5. 2007/12/21MR Final Report5 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

6. 2007/12/21MR Final Report6 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.

7. 2007/12/21MR Final Report7 Technological Forecasting Models Simple Logistic Curve Model Gompertz Model Extended Logistic Model

8. 2007/12/21MR Final Report8 Simple Logistic Curve Model : is the upper bound of e : natural logarithm a b : parameter : the variable care to forecast

9. 2007/12/21MR Final Report9 Gompertz Model : is the upper bound of e : natural logarithm a b : parameter : the variable care to forecast

10. 2007/12/21MR Final Report10 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 L1 Time L2 A B

11. 2007/12/21MR Final Report11 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 is extended to

12. 2007/12/21MR Final Report12 Technological Forecasting Models Extended Logistic Model is the time-varying capacity and is the function which is similar to logistic curve

13. 2007/12/21MR Final Report13 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

14. 2007/12/21MR Final Report14 Data Collection - Penetration rate ProductSample Period Sample Size Color TV1974 ~ 200431 Telephone1964 ~ 200435 Washing Machine1974 ~ 200431 ADSL subscription2000 ~ 200626 Mobile internet subscription2000 ~ 200620 Broadband network2000 ~ 200626

15. 2007/12/21MR Final Report15 Data Collection – Cumulative sales ProductSample Period Sample Size LCD-TV 2003 ~ 200718 19”LCD monitor 2003 ~ 200718 CCD DC 2003 ~ 200718 DC >5m 2003 ~ 200718 WLAN (802.11g) 2003 ~ 200718 Cable Modem 2003 ~ 200718 Combo ODD 2003 ~ 200718 Barebones 2003 ~ 200718

16. 2007/12/21MR Final Report16 Data Collection – Cumulative sales ProductSample Period Sample Size China PAS 2003 ~ 200718 LCD panel for TV 2003 ~ 200718 LCD panel for notebook 2003 ~ 200718 Color-65k mobile phone 2003 ~ 200718 Server 2003 ~ 200718 LCD-TV >30” 2004 ~ 200714 VoIP IAD 2004 ~ 200714 VoIP router 2004 ~ 200714

17. 2007/12/21MR Final Report17 Market Growth for Saturation Data Sets

18. 2007/12/21MR Final Report18 Market Growth for Cumulative Data Sets

19. 2007/12/21MR Final Report19 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

20. 2007/12/21MR Final Report20 Results (Penetration Data Set) Product FittingForecasting Extended logistic Gompertz Simple logistic Extended logistic Gompertz Simple logistic Color TV123123 Phone123123 Washing Machine 123123 ADSL123123 Mobile Internet 123123 Broadband Network 132123

21. 2007/12/21MR Final Report21 Results (Cum. Sales Data Set) Product FittingForecasting Extended logistic Gompertz Simple logistic Extended logistic Gompertz Simple logistic LCD-TV123123 19”LCD monitor123213 CCD DC123123 DC >5m123213 WLAN (802.11g)123123 Cable Modem123123 Combo ODD123123 Barebones123123 China PAS123123 LCD panel for TV123213 LCD-TV >30”132321 VoIP IAD123213

22. 2007/12/21MR Final Report22 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.

23. 2007/12/21MR Final Report23 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.

24. 2007/12/21MR Final Report24 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.

25. 2007/12/21MR Final Report25 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

26. 2007/12/21MR Final Report26 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

27. 2007/12/21MR Final Report27 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.

28. 2007/12/21 MR Final Report 28 Thank you.