A Bicriteria Approach for Saving a Path Maximizing Dynamic Contraflow

Abstract

The maximum dynamic contraflow problem in transportation networks seeks to maximize the flow from a source to a sink within a given time horizon with a possibility of arc reversals. This may result into blockage of paths of desired length from some node of the network towards the source. In some cases such as the evacuation planning, we may require a path towards the source to move some facilities, for example, emergency vehicles. In this work, we model the problem of saving such a path as a bicriteria optimization problem which minimizes the length of the path and maximizes the dynamic flow with arc reversals. We use the [Formula: see text]-constraint approach to solve the problem and propose a procedure that gives the set of all Pareto optimal solutions in a single-source-single-sink network with integer inputs. We also present computational performance of the algorithm on a road network of Kathmandu city, and on randomly generated networks. The results are of both theoretical and practical importance.