Guta, Berhanu (PhD)Genene, Aster2021-01-212023-11-042021-01-212023-11-042020-12-12http://etd.aau.edu.et/handle/123456789/24732Optimization is a mathematical problem that has many real-world applica- tions. It is used to determine minimizers or maximizers of a multi-variable real function, under a restricted domain. The thesis presented here aims in determining an optimal joint inventory with transportation proposed by [10]. These problems are characterized by the presence of both transportation and inventory considerations, either as parameters or constraints. A supply chain class which helps to determine joint transport and inventory cost does have a wide variety of advantages for both company and customer. One of the op- timization parts which is mixed integer programming is applied to nd the optimal solution to Joint Transportation-and-Inventory Problems (JTIPs) which portioning of customers as well as the route and date of delivery. Two mixed-integer programming models will be discussed: time-discretized inte- ger programming and the new approach with prede ned quantities of delivery with the date of delivery. As is shown in this thesis, the approach allows us to use a simplex method and the technique for solving mixed-integer program- ming i.e., branch and bound Method, and cutting plane method. Solution procedures are clearly illustrated based on a hypothetical applications and modi cation of the model are present in this thesis.enInventory Routing ProblemMixed Integer Programming Prob- LemBranch and Bound MethodCutting Plane MethodThesis