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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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A multi-periodic, multi-echelon green supply chain network consisting of manufacturing plants, potential distribution centers, and customers is developed. The manufacturing plants can provide the products in three modes including production in regular time, production in over time, or by subcontracting. The problem has three objectives including minimization of the total costs of the green supply chain network, maximization of the average safe inventory levels of the manufacturing plants and the distribution centers and minimization of the environmental impacts of the manufacturing plants in producing, holding and dispatching the products and also the environmental impacts of the distribution centers in holding and dispatching the products. The problem is first formulated as a mixed-integer mathematical model. Then, in order to solve the model, the augmented weighted Tchebycheff method is employed and its performance in producing the Pareto optimal solutions is compared with the goal attainment method.