Browsing by Author "Getachew Beyene"

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    On Application of Network Simplex Method to Solve Minimum Cost Network Flow Problem
    (Addis Ababa University, 2024-09) Getachew Beyene; Mesfin Masre
    The problem of the minimum cost flow (MCF) is to send a flow from a set of supply nodes to a set of demand nodes via the arc of a network at a minimum total cost, without violating the lower and upper limits of the flow through the arc. The framework work of the MCF is particularly broad and can be used to model a number of specialized network problems, including assignment, transport and transfer problems, the shortest path problem and the maximum flow problem. The network simplex method is described to solve the minimum cost network flow problem, one of the most fundamental and a significant problem of network optimal design, and is applied to the network flow programming problem using simplex algorithms. The Network Simplex method describes the basic solutions for the problem of network flow programming and provides procedures for calculating the basic and double solutions associated with a given basis to find the optimal solution.