We propose an algorithm for solving mixed integer linear programming problem, which is a combination of branch-and-bound and
decomposition procedure. For branching and bounding we divide a rectangular domain into smaller and smaller subrectangles, and to each generated subrectangle $R$ we associate a lower bound for the objective function with respect to $y\in R$ by using a suitable relaxation involving the continuous linear constraint but not the integer ones. This relaxation thus allows us to decompose the problem into subprograms each of them consists of a linear program and one-dimensional integer linear problems.