Many real-world systems can be modeled by multistate 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 valuedand a given cost limitc, the reliability of an MFN at level (d, c) is the probability of transmitting at leastdunits from the source node to the sink node through the network within the cost ofc.