Dynamic Pricing Problems with Elastic Demand

We study a dynamic pricing problem for a company that sells a single product to a group of customers over a finite time horizon. These customers are price sensitive and the price of today influences the group of customers of tomorrow. The objective is to set the prices over time so as to maximize revenue. We study two customer models: a multiplicative and an additive model. Our main contribution is considering the case when the demand is deterministic. We give a polynomial time algorithm for the multiplicative model, and prove that the additive model is (weakly) NP-hard and allows a fully polynomial approximation scheme. Further, when the choice of prices is limited we prove that the optimal solution has a specific structure. Complementing the results for the deterministic setting, we finally provide two algorithms when the demand is stochastic.