Optimal policies in continuous time inventory control models with limited supply

In this paper, we deal with the problem of a fixed number of units of a certain perishable commodity over a continuous time horizon. Airline seats, hotel rooms, advertising space in newspapers, and some seasonal products that must be sold before the end of the season are examples of such commodities that cannot be carried over and are not storable for consumers. This paper considers such a problem of continuous time perishable inventory control by applying semi-Markov decision processes over a finite time horizon. It is shown that there is an optimal policy that is simple and stationary. Furthermore, some analytical properties of this optimal policy and its value function are explored under certain specific assumptions.