Allocating resources via price management systems: a dynamic programming-based approach

In this paper, a novel model for price management systems in resource allocation problems is proposed. Stochastic customer requests for resource allocations and releases are modelled as constrained parallel Birth–Death Processes (BDP). We address both instant (i.e. the customer requires a resource to be allocated immediately) and advance (i.e. the customer books a resource for future use) reservation requests, the latter with both bounded and unbounded time interval options. Algorithms based on Dynamic Programming (DP) principles are proposed for the calculation of suitable price profiles. At the core of such algorithms, there is the resolution of stochastic optimisation problems. In particular, the maximisation of the expected total revenue is formulated via a constrained Stochastic Dynamic Programming (SDP) approach, which becomes time-variant in case of advance reservation requests. Approximate Dynamic Programming (ADP) techniques are adopted in case of large state spaces. Simulations are performed to show the effectiveness of the proposed models and the related algorithms.