The Diagnosis of Blocking Risks in Emergency Network

For the maximum flow f* in the network N, if an arc set B has characteristics: the increase of the capacity of every arc will increase the maximum value v* of the network and meanwhile decrease the total expense Z; then, we call “B” as the “Blocking Set” and the network with blocking set as “ill-conditioned network”. In this paper we first characterize the blocking set and ill-conditioned network and second, present the optimal investment decision for increasing the capacity and removing ill-conditioned network.