Perishable asset revenue management with Markovian time dependent demand intensities

Many industries face the problem of selling a fixed stock of items over a finite horizon. These industries include airlines selling seats before planes depart, hotels renting rooms before midnight, theaters selling seats before curtain time, and retailers selling seasonal items with long procurement lead times. Given a sunk investment in seats, rooms, or winter coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize expected revenues. In this paper we address the problem of deciding the optimal timing of price changes within a given menu of allowable, possibly time dependent, price paths each of which is associated with a general Poisson process with Markovian, time dependent, predictable intensities. We show that a set of variational inequalities characterize the value functions and the optimal (possibly random) time changes. In addition, we develop an efficient algorithm to compute the optimal value functions and the optimal pricing policy.