A Class of Continuous Network Flow Problems

摘要

The solution in discrete time of the problem of maximizing the flow in a network with time-varying arc capacities and storage at the nodes is a straightforward extension of the static case. In this paper, the problem is formulated and solved in continuous time. A continuous version of the Ford-Fulkerson theorem is proved, and an analogue of the labelling algorithm is developed. An example is given to clarify some of the ideas of the paper, and the duality theory for this problem is discussed.