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Many real-world systems can be modeled by multi-state flow networks (MFNs) and their reliability evaluation features in designing and control of these systems. Considering the cost constraint makes the problem of reliability evaluation of an MFN more realistic. For a given demand value  d  and a given cost limit  c , the reliability of an MFN at level ( d ,  c ) is the probability of transmitting at least  d  units from the source node to the sink node through the network within the cost of  c . This article addresses the so-called ( d ,  c )-MC problem, i.e., the problem of reliability evaluation of an MFN with cost constraint in terms of minimal cuts. It presents new results on which a new algorithm is based. This algorithm finds all ( d ,  c )-MC candidates without duplicates and verifies them more efficiently than existing ones. The complexity results for this algorithm and an example of its use are provided. Finally, numerical experiments with R language implementations of the presented algorithm and other competitive algorithms are considered. Both the time complexity analysis and numerical experiments demonstrate the presented algorithm to be more efficient than the fastest competing algorithms in 81.41–85.11% of cases.

An efficient algorithm for the reliability evaluation of multistate flow networks under budget constraints