Contraflow technique has gained a considerable focus in evacuation planning research over the past several years. In this work, we design efficient algorithms to solve the maximum, lex-maximum, earliest arrival, and quickest dynamic flow problems having constant attributes and their generalizations with partial contraflow reconfiguration in the context of evacuation planning. The partial static contraflow problems, that are foundations to the dynamic flows, are also studied. Moreover, the contraflow model with inflow-dependent transit time on arcs is introduced. A strongly polynomial time algorithm to compute approximate solution of the quickest partial contraflow problem on two terminal networks is presented, which is substantiated by numerical computations considering Kathmandu road network as an evacuation network. Our results show that the quickest time to evacuate a flow of value 100,000 units is reduced by more than 42% using the partial contraflow technique, and the difference is more with the increase in the flow value. Moreover, the technique keeps the record of the portions of the road network not used by the evacuees.

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The research on evacuation planning problem is promoted by the very challenging emergency issues due to large scale natural or man-created disasters. It is the process of shifting the maximum number of evacuees from the disastrous areas to the safe destinations as quickly and efficiently as possible. Contraflow is a widely accepted model for good solution of evacuation planning problem. It increases the outbound road capacity by reversing the direction of roads towards the safe destination. The continuous dynamic contraflow problem sends the maximum number of flow as a flow rate from the source to the sink in every moment of time unit. We propose the mathematical model for the continuous dynamic contraflow problem. We present efficient algorithms to solve the maximum continuous dynamic contraflow and quickest continuous contraflow problems on single source single sink arbitrary networks and continuous earliest arrival contraflow problem on single source single sink series-parallel networks with undefined supply and demand. We also introduce an approximation solution for continuous earliest arrival contraflow problem on two-terminal arbitrary networks.

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