Guta, Berhanu (PhD)Getachew, Zinash2021-03-292023-11-042021-03-292023-11-042020-06-25http://etd.aau.edu.et/handle/123456789/25760Mixed integer programming is a linear programming with some of the deci- sion variables are integer and some of them are continuous. Thus, unlike to linear programming it some what complex to solve due to the integer decision variables. Some of the complexities are minimized using di_erent methods such as Gomory's cutting plane, Branch and bound methods. In this project, we presented the solutions of mixed integer linear programming using Go- mory's Fractional cutting plane through removing the unnecessary region from its linear programming relaxation to obtain the integer solution and branch and bound by dividing the problem to smaller sub-problems which are more simple than the original problem. Therefore, based on these con- cepts, the corresponding algorithms are presented with illustrative examples.enLinear ProgrammingSimplex MethodDual Simplex MethodMixed Integer ProgrammingCutting Plane MethodBranch and Bound MethodThesis