Reliable and economic resource allocation in an unreliable flow network

In this paper a reliable and economic resource allocation strategy under cost constraints is developed for an unreliable multi-source multi-sink flow network. A multi-source multi-sink flow network is composed of nodes, characterized as source nodes, sink nodes and intermediate nodes, as well as directed arcs, joining pairs of nodes. In the presence of unreliable intermediate nodes and arcs, it is important to distribute resources at source nodes in a reliable and cost-effective manner so that resources are more likely to be transmitted successfully to sink nodes through the flow network. By modelling the capacities of intermediate nodes and arcs as statistically independent random variables, an integrated approach is proposed in this study that combines the existing methodologies to determine a reliability-maximizing resource allocation strategy which meets demand at sink nodes and a predetermined transmission cost requirement. Examples of cyclic and acyclic flow networks with unreliable intermediate nodes and arcs are given to illustrate the application of the proposed approach.