Estimating the Timing and Magnitude of Peak Sales in New Consumer Durables

Consider the problem of estimating the timing and magnitude of peak sales for a new consumer durable product which is infrequently purchased and initially has few replacement purchases (as compared to initial purchases) . In such a case typically the sales rate climbs to a peak over a period of years and then declines somewhat, with replacement purchases becoming a larger component of total sales and initial purchases correspondingly declining. A good estimate of the magnitude of the peak sales rate is a critical input to production capacity expansion planning, while a good estimate of the timing of the peak sales rate is critical to proper control of inventories as sales attains and passes its peak rate. We explore a model proposed by Bass for this situation, pointing out a possible shortcoming and suggesting a modification of his model which involves a decision-theoretic approach.