Modelling product life cycles for consumer durables

Abstract

This thesis is concerned with mathematical modelling of consumer durable product form sales over entire product life cycle (PLC). The PLC is defined as the curve which represents unit sales for some product, extending from time it is first placed in market until it is removed. This work was motivated by need to explain many variations of PLC shapes which occur for different products in order to render PLC concept more useful. The thesis deals with dynamic modelling of PLC shapes. This is determined by factors from both demand and supply side of market. As a result, comprehensive modelling of PLCs needs a dynamic characterization of both sides of market and their interactions. Such a model is too complex, and we focus our attention on a simpler case in which only demand side factors are modelled dynamically. As such, thesis' contribution should be viewed as a first step towards building of a more complete model which considers both sides dynamically. In our model, supply side factors which influence demand side are considered exogenous variables and effect of demand side on supply side dynamics is not considered. The traditional PLC concept portrays evolution of sales by four stages:introduction -> growth -> maturity -> decline A alternative representation of PLC concept for consumer durable product forms is developed. The following four phases of PLC are identified by dividing total sales into various components: innovator -> imitator -> repeat -> substitute It is proposed that key time and magnitude scales associated with each of above components of sales determine predominant trends of PLC. Advantages of this new approach include ability to explain variations in PLC shapes and providing a richer base for decision making, since sub-components of total sales are modelled explicitly. Using this new PLC concept and a simple illustrative example, it is shown that most empirically reported PLC shapes can be emulated by proper choice of these time and magnitude scales. Further refinement of this new approach involves more detailed modelling of each of sales components. New models were developed for: first purchase sales of new products (innovator and imitator); repeat purchase sales (replacement and multiple); and, product substitution. A new model for first purchase sales is developed in diffusion paradigm which relates innovative and imitative purchasing behaviour to type of product information required before purchasing. Model analysis revealed model is more flexible than earlier simple diffusion models in terms of emulating bimodal sales curves. Three new models for replacement purchase sales are developed which model mean replacement age (MRA) as changing over time. One model considers MRA to be a function of time, while another represents MRA as a function of price. Yet another model considers changes in forced and induced replacements over time. Two new models for multiple purchase sales are developed which incorporate an upper limit on potential multiple purchases. Four new models for product substitution are developed within diffusion paradigm. New elements incorporated into these models include explicitly modelling both forced and induced substitute purchases, and substitute decisions dependent on age of consumer's currently owned unit of incumbent product. The models presented represent new theoretical contributions. While empirical testing of these models is performed with data available, limited nature of this data does not permit complete validation of these models. The results of testing first purchase model are encouraging with model fitting data better than previous similar models. Unfortunately data available for testing replacement purchase models is not of sufficient quality to properly validate new models. In case of multiple purchases and product substitution models, data for only one product was available. The results for both cases are tentatively encouraging, with models fitting data quite well, though addition data is again needed for both cases.