Forecasting Product Life Cycle Curves: Practical Approach and Empirical Analysis

Abstract

We present an approach to forecast customer orders of ready-to-launch new products that are similar to past products. The approach fits product life cycle (PLC) curves to historical customer order data, clusters the curves of similar products, and uses the representative curve of the new product’s cluster to generate its forecast.

We propose three families of curves to fit the PLC: Bass diffusion curves, polynomial curves and simple piecewise-linear curves (triangles and trapezoids). Using a large data set of customer orders for 4,037,826 units of 170 Dell computer products sold over three and a half years, we compare goodness-of-fit and complexity for these families of curves. Fourth-order polynomial curves provide the best in-sample fit with piecewise-linear curves a close second. Using a trapezoidal fit, we find that the PLCs in our data have very short maturity stages; more than 20% have no maturity stage and are best fit by a triangle.

The fitted PLC curves of similar products are clustered either by known product characteristics or by data-driven clustering. Our key empirical finding is that, for our large data set, data-driven clustering of simple triangles and trapezoids, which are simple-to-estimate and explain, performs best for forecasting. Our conservative out-of-sample forecast evaluation, using data-driven clustering of triangles and trapezoids, results in mean absolute errors approximately 2-3% below Dell’s forecasts. We also apply our method to a second data set of a smaller company and find consistent results.

Keywords: Forecasting, Product Life Cycle, Dell, clustering

JEL Classification: C80, C44, C20, C53, C52