Maximum Dynamic Flow Model for Hesitant Fuzzy Evacuation with Intermediate Storage at Nodes

Fuzzy logic is a modern tool which can be used to deal with uncertainty inherent in evacuation emergency tasks. During evacuation, the main goal is to transport the maximum amount of aggrieved from the hazardous area to the secure shelter, considering arc capacities and dynamic flows. In most cases, evacuation tasks do not consider storage at intermediate nodes, although this opportunity allows transporting the increased flow value. Moreover, transit flows depending on the flow departure time should be taken in account. To address this problem, the method for the maximum dynamic evacuation with intermediate storage will be presented in this paper. To convey the maximum possible flow in the dynamic network with intermediate storage to the sink, the priority order of intermediate nodes must be defined. For this reason, a decision-maker assess the nodes by means of hesitant fuzzy sets such as hesitant fuzzy hybrid average aggregation operators. The proposed method handles a fuzzy network, whose nodes along with arcs have capacities in order to store the flow. Based on the operators of hesitant fuzzy hybrid average aggregation, the priority order of intermediate nodes is calculated in order to gain extra flow leaving the source that can be additionally stored in intermediate nodes. The aim of the proposed algorithm is to convey the maximum amount of people from origin to destination considering intermediate storage at nodes with various priority levels according to the degree of approachability, reliability, and transportation costs. A case study is given to support the algorithm.