Guta Berhanu (PhD)Tsegay Tsadkan2020-12-162023-11-042020-12-162023-11-042014-06-06http://etd.aau.edu.et/handle/123456789/24117Maximum ow minimum cost(MFMC) problem combines sending as much ow as possible from the source node to the sink node with minimum cost.Here the attributes for the network are the capacity,ow and cost per unit ow of an arc which varies linearly with the amount of ow.The problem has two special problems namely the shortest path problem and maximum ow problem for which we set all the capacities and cost are set to be zero respectively.Solving maximum ow minimum cost involves two steps;_nding the maximum ow and then _nd the minimum cost using the feasible ow as an input.enMaximum-Flow Minimum CostS-T CutFord Fulkerson Labeling AlgorithmNetwork Simplex AlgorithmThesis