Dynamic network flow location models and algorithms for quickest evacuation planning

Dynamic network flow problems have wide applications in evacuation planning. From a given subset of arcs directed network, choosing the suitable for facility location with objective is very important optimization emergency cases. Because decrease capacity an arc by placing it, there may be reduction maximum or increase quickest time. In this work, we consider problem identifying optimal locations so that time minimum. Introducing FlowLoc problem, give strongly polynomial algorithms to solve single case. Realizing NP-hardness multi-facility case, develop mixed integer programming formulation it and propose two heuristics its solution. growing concerns reversals planning, introduce ContraFlowLoc present exact single-facility case complexity. The solutions thus obtained here are practically important, particularly systematize traffic allocation minimizing