The problem of managing the price for resource allocation arises in several applications, such as purchasing plane tickets, reserving a parking slot, booking a hotel room or renting SW/HW resources on a cloud. In this paper, we model a price management resource allocation problem with parallel Birth-Death stochastic Processes (BDPs) to account for the fact that the same resource can be possibly purchased by customers at different prices. In addition, customers can hold the resource at the purchase price to the necessary extent. The maximization of the revenue in both the finite and infinite time horizon cases is addressed in this paper with Stochastic Dynamic Programming (DP) approaches. To overcome the difficulty in solving the corresponding optimization problem due to the state space explosion, Approximate Dynamic Programming (ADP) techniques (in particular, the Least Square Temporal Difference method along with Monte Carlo simulations) are adopted. Furthermore, a MATLAB Toolbox is developed with the aim of solving stochastic DP/ADP problems and supporting probabilistic analysis. Extensive simulations are performed to show the effectiveness of the proposed model and the optimization approach.
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