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The large scale calamities caused by natural or human-created disasters are the challenging issues to protect the life and their surroundings. It is a complex task to develop the significant and universally accepted solution strategy for handling these issues. Appropriate facility locations and transportation facilities are essential components for the efficient evacuation planning flow models. Contraflow, the lane reversal strategy, is one of the widely accepted solution approach for evacuation planning as it maximizes the outbound capacities of roads by reversing the required road directions and makes the traffic smooth. This significantly increases the flow value and decreases the evacuation time. In this work, the network facility location and the contraflow approach are incorporated to the flow models and some efficient algorithms are presented to locate the facility with an objective of minimum flow loss on the evacuation network. Our facility location contraflow solutions obtain the optimal plans with respect to the given and arbitrary locations.

Many large-scale natural and human-created disasters have drawn the attention of researchers towards the solutions of evacuation planning problems and their applications. The main focus of these solution strategies is to protect the life, property, and their surroundings during the disasters. With limited resources, it is not an easy task to develop a universally accepted model to handle such issues. Among them, the budget-constrained network flow improvement approach plays significant role to evacuate the maximum number of people within the given time horizon. In this paper, we consider an evacuation planning problem that aims to shift a maximum number of evacuees from a danger area to a safe zone in limited time under the budget constraints for network modification. Different flow improvement strategies with respect to fixed switching cost will be investigated, namely, integral, rational, and either to increase the full capacity of an arc or not at all. A solution technique on static network is extended to the dynamic one. Moreover, we introduce the static and dynamic maximum flow problems with lane reversal strategy and also propose efficient algorithms for their solutions. Here, the contraflow approach reverses the direction of arcs with respect to the lane reversal costs to increase the flow value. As an implementation of an evacuation plan may demand a large cost, the solutions proposed here with budget constrained problems play important role in practice.