# Optimal transport on supply-demand networks

## TL;DR

This paper introduces a new transport model for supply-demand networks with heterogeneous nodes, proposing an optimization method that significantly improves transport capacity by strategically placing supply nodes.

## Contribution

It develops a general model for supply-demand networks and introduces a simulated annealing algorithm to optimize supply node placement, enhancing transport capacity.

## Key findings

- Optimal supply node placement improves capacity significantly.
- The proposed method outperforms degree, betweenness, and greedy algorithms.
- Transport capacity depends strongly on supply node locations.

## Abstract

Previously, 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 grid and supply chain networks, show a far different scenario in which the nodes are classified into two categories: the supply nodes provide some kinds of services, while the demand nodes require them. In this paper, we propose a general transport model for those supply-demand networks, associated with a criterion to quantify their transport capacities. In a supply-demand network with heterogenous degree distribution, its transport capacity strongly depends on the locations of supply nodes. We therefore design a simulated annealing algorithm to find the optimal configuration of supply nodes, which remarkably enhances the transport capacity, 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.