Uncertain minimum cost flow problem.

The aim of this paper is to give an uncertainty distribution of the least cost of shipment of a commodity through a network with uncertain capacities. Uncertainty theory is used to deal with uncertain capacities, and an $$\alpha $$ -minimum cost flow problem model is proposed. After defining the $$\alpha $$ -minimum cost flow, the properties of the model are analyzed, and then an algorithm for uncertain minimum cost flow problem is developed. The algorithm can be considered as a general solution to the uncertain minimum cost flow problem. To demonstrate the efficiency of the proposed algorithm, a numerical example is illustrated. [ABSTRACT FROM AUTHOR]