Abstract
The evacuation planning problem models the process of shifting residents from emergency areas (sources) to safe places (sinks) as quickly and efficiently as possible. Most of the flow over time models used in the evacuation planning are based on the flow conservation constraints, i.e., the inflow should be equal to the outflow on each node except at the sources and sinks. We investigate the universal maximum flow problem with intermediate storage, i.e., the inflow may be greater than the outflow on intermediate nodes which maximizes the number of evacuees leaving the emergency areas at each point of time. We propose efficient algorithms to solve the problem on two-terminal series-parallel and general networks. We also discuss the solution technique for the problem with arc reversal capability and compare these solutions without and with intermediate storage.
1991 Mathematics Subject Classification. 2010 Mathematics Subject Classification. Primary: 90B10, 90C27, 68Q25; Secondary: 90B06, 90B20.
The first author acknowledges the support to her post doctoral research stay (November 2017 – October 2019) at TU Bergakademie, Freiberg, Germany and return fellowship (November 2019 – October 2020) of Alexander von Humboldt Foundation.
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Pyakurel, U., Dempe, S. (2021). Universal Maximum Flow with Intermediate Storage for Evacuation Planning. In: Kotsireas, I.S., Nagurney, A., Pardalos, P.M., Tsokas, A. (eds) Dynamics of Disasters. Springer Optimization and Its Applications, vol 169. Springer, Cham. https://doi.org/10.1007/978-3-030-64973-9_14
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