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A number of problems in several areas such as power transmission and distribution, communication and transportation can be formulated as a stochastic-flow network (SFN). The system reliability of an SFN can be computed in terms of all the upper boundary points, called d-MinCuts (d-MCs). Several algorithms have been proposed to find all the d-MCs in an SFN. Here, some recent studies in the literature on search for all d-MCs are investigated. We show that some existing results and the corresponding algorithms are incorrect. Then, correct versions of the results are established. By modifying an incorrect algorithm, we also propose an improved algorithm. In addition, complexity results on a number of studies are shown to be erroneous and correct counts are provided. Finally, we present comparative numerical results in the sense of performance profile of Dolan and Moré showing the proposed algorithm to be more efficient than some existing algorithms.

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In the face of budgetary limitations in organizations, identifying critical facilities for investing in quality improvement plans could be a sensible approach. In this paper, hierarchical facilities with specified covering radius are considered. If disruption happens to a facility, its covering radius will be decreased. For this problem, a bi-objective mathematical formulation is proposed. Critical facilities are equivalent to the facilities which attacking them causes the most reduction in the quality of the system performance. Consequently, this problem is studied in the interdiction problem framework. To solve the multi-objective model the weighting-sum approaches are applied. The first interdictor's objective function helps decision makers to identify the vulnerability of the system. Moreover, the second objective function may assist in minimizing the cost of applied quality improvement plans.