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.
Highlights
Because of the significant occurrences of many predictable and unpredictable large-scale disasters worldwide, regardless of various discoveries and urbanization, an efficient, implementable, and reliable evacuation planning is indispensable for saving life and supporting humanitarian relief with optimal use and equitable distribution of available resources
We find the static flow corresponding to the quickest flow in the bow graph, and we push the flow to the slowest arc to find the approximate dynamic flow corresponding to the quickest flow
The maximum dynamic and earliest arrival contraflow problems are generalized on lossy networks with partial contraflow reconfiguration
Summary
Because of the significant occurrences of many predictable and unpredictable large-scale disasters worldwide, regardless of various discoveries and urbanization, an efficient, implementable, and reliable evacuation planning is indispensable for saving life and supporting humanitarian relief with optimal use and equitable distribution of available resources. Kim et al [27] present two greedy and bottleneck heuristics for possible numerical approximate solutions to the quickest contraflow problem, and they show that at least 40% evacuation time can be reduced by reverting at most 30% arcs in their case study They model the problem of lane reversals mathematically as an integer programming problem by means of flows on network and prove that it is N P -hard. With the given supplies at the sources and demands of the sink, the earliest arrival transshipment contraflow problem is modeled in discrete time [32] and solved on multisource network with polynomial algorithm.
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