Minimum parametric flow over time

Abstract

The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead directly work on the original network, the method implements a labelling algorithm in the parametric dynamic residual network and uses quickest paths from the source node to the sink node in the time-space network along which repeatedly decreases the dynamic flow for a sequence of parameter values, in their increasing order. In each iteration, the algorithm computes both the minimum flow for a certain subinterval of the parameter values, and the new breakpoint for the maximum parametric dynamic flow value function.