Optimal transport on supply-demand networks.

In the literature, transport networks are usually treated as homogeneous networks, that is, every node has the same function, simultaneously providing and requiring resources. However, some real networks, such as power grids and supply chain networks, show a far different scenario in which nodes are classified into two categories: supply nodes provide some kinds of services, while demand nodes require them. In this paper, we propose a general transport model for these supply-demand networks, associated with a criterion to quantify their transport capacities. In a supply-demand network with heterogeneous degree distribution, its transport capacity strongly depends on the locations of supply nodes. We therefore design a simulated annealing algorithm to find the near optimal configuration of supply nodes, which remarkably enhances the transport capacity compared with a random configuration and outperforms the degree target algorithm, the betweenness target algorithm, and the greedy method. This work provides a start point for systematically analyzing and optimizing transport dynamics on supply-demand networks.