  Sustainable Supply Chain (SSC) management aims at integrating economic,
environmental and social goals to assist in the long-term planning of a company
and its supply chains. There is no consensus in the literature as to whether
social and environmental responsibilities are profit-compatible. However, the
conflicting nature of these goals is explicit when considering specific
assessment measures and, in this scenario, multi-objective optimization is a
way to represent problems that simultaneously optimize the goals. This paper
proposes a Lagrangian matheuristic method, called $AugMathLagr$, to solve a
hard and relevant multi-objective problem found in the literature.
$AugMathLagr$ was extensively tested using artificial instances defined by a
generator presented in this paper. The results show a competitive performance
of $AugMathLagr$ when compared with an exact multi-objective method limited by
time and a matheuristic recently proposed in the literature and adapted here to
address the studied problem. In addition, computational results on a case study
are presented and analyzed, and demonstrate the outstanding performance of
$AugMathLagr$.
