Optimal Product Lifecycles with Similar Durations

Abstract

The question of when to stop marketing a given product and to initiate another lifecycle for that product is addressed in this paper, together with the R&D period and issues of timing. In the proposed model, decision-makers are faced with a given technology and have a single product of their own in the market. The criterion for success is to maximize the discounted net cash flow or the equivalent annuity stream for a given period of time, e.g. a year, a decade etc. The initiation of another cycle is independent of when the current cycle terminates, but is functionally related to its length. Managerial and operational constraints are included, as well as market share constraints. The problem is solved for a representative single cycle assuming that technology is constant i.e. for a low- to mid-technology product. The resulting rules are expressed in managerial terms, for example, as a function of peak of cash flow, cumulative cash flow, level of cash flow, and the length of the R&D period. Some numerical examples for all cases are provided to illustrate the rules resulting from the models.