Enhancing computations of nondominated solutions in MOLFP via reference points

In previous work, Costa and Alves (J Math Sci 161:(6)820–831, <CitationRef CitationID="CR2">2009</CitationRef>; <CitationRef CitationID="CR3">2011</CitationRef>) have presented Branch & Bound and Branch & Cut techniques that allow for the effective computation of nondominated solutions, associated with reference points, of multi-objective linear fractional programming (MOLFP) problems of medium dimensions (ten objective functions, hundreds of variables and constraints). In this paper we present some results that enhance those computations. Firstly, it is proved that the use of a special kind of achievement scalarizing function guarantees that the computation error does not depend on the dimension of the problem. Secondly, a new cut for the Branch & Cut technique is presented. The proof that this new cut is better than the one in Costa and Alves (<CitationRef CitationID="CR3">2011</CitationRef>) is presented, guaranteeing that it reduces the region to explore. Some computational tests to assess the impact of the new cut on the performance of the Branch & Cut technique are presented. Copyright Springer Science+Business Media New York 2013