Cindy Wu Advisor: Charles V. Trappey,

An Evaluation of the Time-varying Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products Cindy WuAdvisor: Charles V. Trappey, MR Final Report

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 MR Final Report

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. MR Final Report

Product Life Cycle • Introduction: slow sales growth • Growth: rapid sales growth • Maturity: sales growth declines • Decline: sales growth falls MR Final Report

Cumulative sales Growth Decline Introduction Mature Time 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 MR Final Report

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. MR Final Report

Technological Forecasting Models • Simple Logistic Curve Model • Gompertz Model • Extended Logistic Model MR Final Report

: the variable care to forecast : is the upper bound of e : natural logarithm a b : parameter Simple Logistic Curve Model MR Final Report

: the variable care to forecast : is the upper bound of e : natural logarithm a b : parameter Gompertz Model MR Final Report

A L1 L2 B Time 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 MR Final Report

is extended to 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 MR Final Report

Technological Forecasting Models • Extended Logistic Model is the time-varying capacity and is the function which is similar to logistic curve MR Final Report

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 MR Final Report

Data Collection - Penetration rate MR Final Report

Data Collection – Cumulative sales MR Final Report

Market Growth for Saturation Data Sets MR Final Report

Market Growth for Cumulative Data Sets MR Final Report

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 MR Final Report

Results (Penetration Data Set) MR Final Report

Results (Cum. Sales Data Set) MR Final Report

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. MR Final Report

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. MR Final Report

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. MR Final Report

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 MR Final Report

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 1995;11:199-215. MR Final Report

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. MR Final Report

Thank you. MR Final Report

Cindy Wu Advisor: Charles V. Trappey,