A Continues Time Revenue Management Model With Multi-product

Consider a firm that owns a multiple types of products which should be sold in a finite horizon. The savage value of unsold products at the end of the period is zero. The firm strives to maximize its total expected revenues over a finite horizon by choosing a dynamic pricing strategy for each type. For example, an airline company sells tickets of the first class, business class, and economy class for a flight. Demand for each type of products is considered as a homogenous Poisson process with the intensity being a function of the price vector. A HJB equation that the maximal expected revenue and the optimal pricing policy satisfied is obtained. And an algorithm to solve the HJB equation is given. Furthermore, the deterministic version of the problem with its optimal pricing policy is obtained. We show that the optimal policy of the deterministic problem is an ^-optimal policy of the stochastic problem under certain conditions.