In this paper, a branch and bound multi-objective based method is proposed for reaching the non-dominated set. Two types of nodes are considered in the tree-search. The first type characterises the non-integer solutions found which are transformed to integer solutions by applying a branching procedure. The second type of nodes contains an integer solution and in this case efficient cuts are established in order either to remove dominated integer vectors or to fathom them. The method is compared advantageously with two exact methods of the literature tailored for the general case and also analysed computationally on benchmarks of MCDM library.