Non-Conservative Maximum Flow in Belief Degree Approach

Abstract

In many real-world problems, we have to face situations where there is not enough data or no data. The belief degree approach is one of the suitable techniques that can be applied to solve such real-life problems. Domain experts, utilizing uncertainty theory, excel in these situations. The goal of this study was to design the maximum flow model with deterministic excess flow storage at the intermediate vertices and uncertainty in arc capacities of a network at a predefined confidence level ꞵ. Through the application of an uncertain measure and the inverse distribution formed by the uncertain variable, the classical maximum flow model is converted into its deterministic counterpart. This problem is solved by developing a polynomial procedure. A numerical example is provided that illustrates the suggested model and the algorithm. Lastly, a graphic comparison is made between conservative and non-conservative maximum flows for different values of confidence level, which verifies the dominance of non-conservative flows over the conservative ones.