American Journal of Applied Mathematics
Volume 8, Issue 4, August 2020, Pages: 207-215
Received: Apr. 8, 2020;
Accepted: Jul. 20, 2020;
Published: Jul. 28, 2020
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Iswar Mani Adhikari, Prithvi Narayan Campus, Tribhuvan University, Pokhara, Nepal
Tanka Nath Dhamala, Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal
The evacuation planning problem can be viewed as different variants of dynamic flow maximization and time minimization problems. An optimal solution to the latter problem sends a given amount of flow from disaster zones to safe zones in minimum time. We solve this problem on an embedded integrated network of a prioritized primary and a bus-routed secondary sub-networks. For a lexicographically maximum (lex-max) dynamic flow problem, we are given a time horizon and a prioritized network, where we need a feasible dynamic flow that lexicographically maximizes the flow amount leaving each terminal respecting the priority. Here, we use the quickest transshipment partial arc reversal strategy to collect the evacuees in minimum time from the disaster zones to the pickup locations of the primary sub-network. By treating such pickup locations as sources, the available set of transit-buses is assigned in the secondary sub-network to shift the evacuees finally to the sinks on the first-come-first-serve basis. This novel approach proposed here is better suited for the simultaneous flow of evacuees with minimum waiting delay at such pickup locations in the integrated evacuation network topology. The lane reversal strategy significantly reduces the evacuation time, whereas reversing them only partially has an additional benefit that the unused road capacities can be used for supplying emergency logistics and allocating facilities as well.
Iswar Mani Adhikari,
Tanka Nath Dhamala,
Minimum Clearance Time on the Prioritized Integrated Evacuation Network, American Journal of Applied Mathematics.
Vol. 8, No. 4,
2020, pp. 207-215.
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