New Product Diffusion Decisions Under Supply Constraints

Two recent papers on managing new product diffusion decisions under production constraints reach somewhat contradictory conclusions. Ho et al. (Ho, T.-H., S. Savin, C. Terwiesch. 2002. Managing demand and sales dynamics in new product diffusion under supply constraint. Management Sci. 48(2) 187-206) show that it is never optimal to refuse to satisfy any customers when the firm has inventory of the product. On the other hand, in a very similar model, Kumar and Swaminathan (Kumar, S., J. M. Swaminathan. 2003. Diffusion of innovations under supply constraints. Oper. Res. 51(6) 866-879) show that production constraints may in fact lead a firm to reject customers' orders even when the firm has the inventory to satisfy them (to slow down new product diffusion). We provide a counterexample to the results of Ho et al. (2002) and show that in their and Kumar and Swaminathan's (2003) models, it may be optimal to deny customers a product in inventory. We provide a generalization of both models that includes the ability to dynamically price the product (and also allows capacity and production costs to vary over time). We show that the unintuitive but optimal behavior of denying customers products that are in inventory disappears when the firm can dynamically set prices.