Diffusion of Innovations Under Supply Constraints

In this paper we present a canonical setting that illustrates the need for explicitly modeling interactions between manufacturing and marketing/sales decisions in a firm. We consider a firm that sells an innovative product with a given market potential. The firm may not be able to meet demand due to capacity constraints. For such firms, we present a new model of demand, modified from the original model of Bass, to capture the effect of unmet past demand on future demand. We use this model to find production and sales plans that maximize profit during the lifetime of the product in a firm with a fixed production capacity. We conduct an extensive numerical study to establish that the trivial, myopic sales plan that sells the maximal amount possible at each time instant is not necessarily optimal. We show that a heuristic “build-up” policy, in which the firm does not sell at all for a period of time and builds up enough inventory to never lose sales once it begins selling, is a robust approximation to the optimal policy. Specializing to a lost-sales setting, we prove that the optimal sales plan is indeed of the “build-up” type. We explicitly characterize the optimal build-up period and analytically derive the optimal initial inventory and roll-out delay. Finally, we show that the insights obtained in the fixed capacity case continue to hold when the firm is able to dynamically change capacity.