Abstract network flow with intermediate storage for evacuation planning

The abstract network is a generalization of the classical network which is associated with the set of elements and linearly ordered subset of elements, known as paths, that satisfy switching property. Each element is equipped with an integral capacity of two types, movement capacity which transships the flow from the element and storage capacity which stores the flow at the element. In the evacuation process, every individual may not be sent to the final destination due to capacity or time constraints. So, the storage of evacuees at intermediate elements can be a milestone to save the life of people. In this paper, we present polynomial time algorithms to solve maximum static, lexicographic maximum static and maximum dynamic flow problems in an abstract network. We also present the solution procedure to these problems in the abstract contraflow networks having symmetric as well as asymmetric transit times between the pair of adjacent elements.(c) 2022 Elsevier B.V. All rights reserved.