Saving a Path and Maximizing Dynamic Contra ow: A Bilevel Programming Approach

Abstract

An important aspect of evacuation planning is to save human population by sending the people in dangerous areas (sources) to the safe places (sinks). Optimization models for evacuation planning focus on regulating the tra_c ow in urban road networks so as to maximize the number of evacuees reaching the safe places or to minimize the evacuation time of evacuees. Recent studies show that reversing the direction of the usual tra_c ow in necessary road segments increases the tra_c ow and decreases the evacuation time signi_cantly. However, this may block the ow of some necessary support towards the source. Based on network ow models, we consider the problem of saving a path from a given node to the source, in a single-source-single-sink network, as a bilevel program. With an objective to minimize a function depending on ow rate and the path chosen, the upper level selects a path from a given node to the source, and the lower level maximizes the dynamic ow allowing arc reversals in the resulting network within a given time horizon. We discuss a solution strategy based on replacing the lower level problem by the corresponding KKT conditions.

GANIT J. Bangladesh Math. Soc. 42.1 (2022) 010- 024