Dynamic Pricing with Periodic Review and a Finite set of Prices with Cancellation

In this paper, three dynamic pricing models are developed and analyzed. We assume a limited number of a particular asset is offered for sale over a period of time. This asset is perishable and can be an inventory or a manufacturing capacity. During each period, the seller sets a price for this asset. This price is selected from a predetermined discrete set. The maximum amount which a customer is willing to pay is called "reservation price". Different customers have different reservation prices. The distribution function of the reservation prices for all potential customers is known. Demands arrive according to a nonhomogeneous Poisson process. To maximize the expected revenue, the price of this asset is controlled periodically, as sales evolve. Demand cancellation is also considered. Furthermore, we study the effect of cancellation as well as setting a sale limit for each period. The analysis of the models indicates that their properties are different from those of the basic models studied previously. By randomly generated examples, we show that the properties of “Inventory Monotonocity” and “Time Monotonocity” do not hold in our models, while these properties hold for continuous price review models.