Modelling and solving resource allocation problems via a dynamic programming approach

In this paper, resource allocation problems are formulated via a set of parallel birth–death processes (BDP). This way, we can model the fact that resources can be allocated to customers at different prices, and that customers can hold them as long as they like. More specifically, a discretisation approach is applied to model resource allocation problems as a set of discrete-time BDPs, which are then integrated into one Markov decision process. The stochastic dynamics of the resulting system are also investigated. As a result, revenue management becomes a stochastic decision-making problem, where price managers can propose suitable prices to the allocation requests such that the maximum expected total revenue is obtained at the end of a predefined finite time horizon. Stochastic Dynamic Programming is employed to solve the related optimisation problem with the support of an ad-hoc Matlab-based application. Several simulations are performed to prove the effectiveness of the proposed model and the optimisation approach.