Optimal Pricing and Rationing Decisions for Short Life Cycle Products with Time-Sensitive Customers

Abstract

We consider a firm that sells a product with a short life cycle to time-sensitive customers. The customers’ product valuations decrease over time and they are grouped into different classes according to their delay sensitivities, the marginal decrease of their product valuation over time. The product is sold at two points of sale (POS’s): pre-sale and regular sale. We study the firm's sales strategy which involves pricing and rationing decisions. The rationing decision involves the firm deciding which customers to satisfy at pre-sale and rationing the other customers to regular sale. We formulate the firm's problem for both capacitated and uncapacitated firms in order to understand the effect of capacity constraints on the firm’s optimal decisions. We show that for both types of firms the set of rationing constraints is equivalent to a simpler set of constraints that is only related to the total sales in each period. Under optimality, we find that the uncapacitated firm either rations all the customer classes or none of them, and the capacitated firm does not carry inventory from pre-sale to regular sale. When the firm sells to homogeneous customers, we fully characterize the firm's optimal decisions: regardless of the capacity constraints, the firm can obtain optimal profits without rationing any of its customers. Surprisingly, the optimal product entry timing for the capacitated firm can actually increase even when customers’ delay sensitivity increases. When the firm sells to two customer classes, rationing can be optimal for both capacitated and uncapacitated firms. Further, for a capacitated firm it is optimal to either ration both customer classes or none, and rationing can be optimal even when the prices decrease from pre-sale to regular sale. Finally, we perform a numerical study in which we examine how optimal sales strategy changes with parameters and identify the scenarios in which different sales strategies are optimal.

Keywords: time-sensitive, rationing, customer classes, delay sensitivity, product launch

JEL Classification: M21, M31