Mathematical optimization problems with a goal function, have many applications in
various fields like financial sectors, management sciences and economic applications.
Therefore, it is very important to have a powerful tool to solve such problems when the
main criterion is not linear, particularly fractional, a ratio of two affine functions. In
this paper, we propose an exact algorithm for optimizing a linear fractional function over
the efficient set of a Multiple Objective Integer Linear Programming (MOILP) problem without
having to enumerate all the efficient solutions. We iteratively add some constraints, that
eliminate the undesirable (not interested) points and reduce, progressively, the
admissible region. At each iteration, the solution is being evaluated at the reduced
gradient cost vector and a new direction that improves the objective function is then
defined. The algorithm was coded in MATLAB environment and tested over different
instances randomly generated
