**Urmila Pyakurel 1,†, Hari Nandan Nath 1,\*, Stephan Dempe <sup>2</sup> and Tanka Nath Dhamala <sup>1</sup>**


Received: 9 September 2019; Accepted: 16 October 2019; Published: 19 October 2019

**Abstract:** 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.

**Keywords:** network optimization; dynamic flow; evacuation planning; contraflow configuration; partial lane reversals, algorithms and complexity; logistic supports
