The α-maximum flow model with uncertain capacities

This paper investigates uncertain maximum flow problem. To obtain the uncertainty distribution of the maximum flow, an α-maximum flow model is formulated under uncertainty theory framework. It is proved that there exists an equivalence relationship between the α-maximum flow model and the classic deterministic maximum flow model. Furthermore, some important properties of α-maximum flow model are analyzed, based on which a polynomial algorithm is proposed. Finally, a numerical example is presented to illustrate the model and the algorithm.