Dynamic pricing problems with elastic demand

We consider a dynamic pricing problem for a company that sells a single product to a group of price-sensitive customers over a finite time horizon. The objective is to set the prices over time so as to maximize revenue. Two price-sensitivity models are studied: multiplicative and additive demand change. We develop a polynomial-time algorithm for the multiplicative model. In contrast, we prove that the problem under additive demand change is NP-hard and admits an FPTAS.