Lexicographic Maximum Flow Allowing Intermediate Storage

In a capacitated network, an optimum solution of the maximum flow problem is to send as much possible from source node sink efficiently by satisfying capacity and conservation constraints. But, because limited on arcs, total amount out going may not reach sink. If excess can be stored at intermediate nodes, outgoing increased significantly. Similarly, different destinations have their own importance with respect some circumstances. Motivated these scenarios, we introduce lexicographic problems storage in static dynamic networks assigning priority order nodes. We extend this notion arc reversals approach, maximization technique, which widely accepted evacuation planning it increases outbound capacities using opposite direction well. Travel times along anti-parallel arcs considered unequal take into account travel time reversed equal non-reversed towards reversed. present polynomial algorithms for problems.