Optimal Pricing, Production, and Inventory for New Product Diffusion Under Supply Constraints

Management of new product introductions is critical for nearly all firms, and one of its most important dimensions is the management of demand during the introduction. Research analyzing this area predominantly uses versions of the diffusion model to capture the demand trajectory of a new product with a fixed potential market. The classic Bass model assumes that demand for innovative products is influenced both by “external” media influence and “internal” word-of-mouth effect, but it excludes price and assumes that capacity is unlimited. In reality, both factors critically influence firms' strategies. Price fluctuations for a new product are common, and price is often a critical lever that helps to shape the demand. Also, firms often have significant capacity constraints, which influence the feasibility of their strategies. In this paper, we consider how a capacity-constrained firm prices products during new product introductions. Thus, the demand rate is influenced by price and, when capacity is insufficient, we allow some customers to be either lost or backlogged, which slows down the word-of-mouth effect. To understand the effect of both pricing and capacity, we consider the integrated optimal pricing, production, and inventory decisions, using control-theory framework (a generalization of the classic Bass model). Most of our results are fairly robust and apply under the assumption of lost sales and partial backlogging, as well as make-to-order and make-to-stock environments. We show that in most cases, the optimal trajectory of demand is unimodal, as in the Bass model, but the optimal price trajectory and the corresponding pricing policy are more complicated when capacity is limited. Using a numerical study, we explore when pricing flexibility is most valuable and whether simple pricing policies may be effective. We find that benefits of pricing flexibility are highest when capacity is neither unlimited (very large) nor very small and when word-of-mouth effect dominates direct impact from media. The ability to adjust prices is significantly more important than the option of producing in advance and holding inventory. We also find that simple pricing policies, appropriately chosen for given capacity, perform very well. In a numerical study, we show that demand uncertainty and increases in capacity over time do not affect our main insights.