Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal

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.

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

“…The remaining graph structure and data are unaltered. In the transformed network ZZZ , we have solved the lex-max dynamic flow problem on each arc as in [18] and saved all unused arc capacity as in [17].…”

“…For each H ∈ T and > ∈ , if > is reversed, j = Z -v ] and j ] = 0 . If neither > nor > ] is reversed, j = -v where j is saved capacity of >, [17]. 5.…”

“…In the transformed dynamic network ZZZ we compute the lex-max number of evacuees reached to each of the prioritized pickup locations as the lex-max dynamic flow as in [18]. Moreover, the obtained solution is equivalent to the solution of the quickest arrival of evacuees at in with the partial arc reversal up to the necessary capacity as in Step 3, [17]. Capacities of the arcs not used by the flow after partial arc reversals are computed in Consider the primary sub-network for evacuee arrival as in Figure 2(i).…”

“…The partial contraflow with path reversals leads to a significant improvement in increasing the flow values, decreasing the evacuation time, and utilization of the unused capacities of paths for humanitarian logistics and vehicle movements, [16]. Authors in [17] have introduced the partial lane reversal strategy and presented efficient dynamic flow algorithms for quickest and maximum flow evacuation planning problems. In the quickest transshipment problem, a given number of evacuees has to be shifted in minimum time.…”

Supported Evacuation for Disaster Relief through Lexicographic Goal Programming

“…Pyakurel et al [28] established that an evacuation optimizer looks for a plan on an evacuation network for an efficient transfer of the maximum quantity of evacuees from the dangerous points (sources) to safer ones (sinks) as quickly as possible. Other analyses related with evacuation planning in order to save human lives and support humanitarian relief can be found in [29,30].…”