A simple method for the multi-state quickest path flow network reliability problem

In order to conform to the real world systems such as distribution systems and supply chain management system, we assume the capacity of each arc in the quickest path problem is stochastic (multi-state). In this study, we propose a simple algorithm to evaluate the probability that d units of data can be sent from the source node to the sink node through the multi-state quickest path flow network within T units of time. The proposed algorithm based on the k-th shortest path algorithm only has less time complexity than the best-known algorithms which were required to solve the NP-hard problem to find all minimal paths in advance.