  Optimal transport is a framework that facilitates the most efficient
allocation of a limited amount of resources. However, the most efficient
allocation scheme does not necessarily preserve the most fairness. In this
paper, we establish a framework which explicitly considers the fairness of
dynamic resource allocation over a network with heterogeneous participants. As
computing the transport strategy in a centralized fashion requires significant
computational resources, it is imperative to develop computationally light
algorithm that can be applied to large scale problems. To this end, we develop
a fully distributed algorithm for fair and dynamic optimal transport with
provable convergence using alternating method of multipliers. In the designed
algorithm, each corresponding pair of resource supplier and receiver compute
their own solutions and update the transport schemes through negotiation
iteratively which do not require a central planner. The distributed algorithm
can yield a fair and efficient resource allocation mechanism over a network. We
corroborate the obtained results through case studies.
