Managing Demand and Sales Dynamics in New Product Diffusion Under Supply Constraint

The Bass diffusion model is a well-known parametric approach to estimating new product demand trajectory over time. This paper generalizes the Bass model by allowing for a supply constraint. In the presence of a supply constraint, potential customers who are not able to obtain the new product join the waiting queue, generating backorders and potentially reversing their adoption decision, resulting in lost sales. Consequently, they do not generate the positive "word-of-mouth" that is typically assumed in the Bass model, leading to significant changes in the new product diffusion dynamics. We study how a firm should manage its supply processes in a new product diffusion environment with backorders and lost sales. We consider a make-to-stock production environment and use optimal control theory to establish that it is never optimal to delay demand fulfillment. This result is interesting because immediate fulfillment may accelerate the diffusion process and thereby result in a greater loss of customers in the future. Using this result, we derive closed-form expressions for the resulting demand and sales dynamics over the product life cycle. We then use these expressions to investigate how the firm should determine the size of its capacity and the time to market its new product. We show that delaying a product launch to build up an initial inventory may be optimal and can be used as a substitute for capacity. Also, the optimal time to market and capacity increase with the coefficients of innovation and imitation in the adoption population. We compare our optimal capacity and time to market policies with those resulting from exogeneous demand forecasts in order to quantify the value of endogenizing demand.