FlowLoc problems with maximum excess flow

Abstract

In order to reduce huge losses from natural and human caused disasters, an appropriate strategy of evacuation planning, preparedness, response and recovery is very essential. The placement of facilities in appropriate arcs of a network plays an important role for the optimal evacuation planning. Such an efficient assignment should respect the least decreases on the arc capacity and hence should minimize the reduction of the optimal flow value. On the other hand, due to the bottleneck capacity, not all flows out from the sources may reach to the sinks. To maximize the flow value, the resulting excess flow can be stored at intermediate nodes that are comparatively safer than the sources.By integrating both concepts, we introduce the single-source single-sink maximum static and dynamic flow location (FlowLoc) problems with excess flow storage allowed. Our objective here is to minimize the reduction of maximum flow in an evacuation network where given facilities are placed on arcs and excess flow is stored at intermediate nodes. We provide their mathematical models and also present polynomial time algorithms to solve them. For the maximum static and dynamic multi-FlowLoc problems where multiple facilities are located, we give their mathematical models and present polynomial time heuristics. These solutions here are practically important, especially in evacuation planning, to maximize the flow value out of the disastrous places by locating the facilities.