Chance distribution of the maximum flow of uncertain random network

Abstract

A network is called uncertain random network if some arc capacities of the network are uncertain variables and others are random variables. The main purpose of this paper is to study the maximum flow in an uncertain random network. Under the framework of chance theory, this paper obtains chance distribution of the maximum flow of an uncertain random network. At the same time, the expected value of maximum flow is given for an uncertain random network. A new method is derived to calculate chance distribution of the maximum flow for an uncertain random network.

A novel single-period inventory problem with uncertain random demand and its application

“…As a general theoretical framework to model the practical problems with unknown parameters, uncertain random programming was introduced by Liu [13] and then extended to uncertain random multi-objective programming [33], uncertain random multilevel programming [7] and uncertain random goal programming [21]. As applications, Sheng and Gao [26] considered arc capacities of a network as random variables or uncertain variables and then derived the chance distribution of the maximum flow. Qin [22] presented a mean-variance model for portfolio optimization problem with mixture of random and uncertain returns.…”

On the convergence of uncertain random sequences

“…In addition, Liu (2014) presented a concept of uncertain random network and obtained the shortest path distribution of an uncertain random network. Sheng and Gao (2014) obtained the maximum flow of chance distribution of an uncertain random network.…”

Uncertain Distribution-Minimum Spanning Tree Problem

“…Refs. [20][21][22][23]. Particularly, on the basis of the uncertainty theory, Peng and Li 24 considered the uncertain minimum spanning tree (UMST) problem where the edge weights are assumed to be uncertain variables.…”