# An efficient Lagrangian-based heuristic to solve a multi-objective sustainable supply chain problem

arXiv: https://arxiv.org/abs/1906.06375 · HTML: https://mlsanity.com/paper/1906.06375/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2019.

## Built on by (most cited first, 2 of 2)

- [Reinforcement Learning for Multi-Objective Multi-Echelon Supply Chain Optimisation](https://mlsanity.com/paper/2507.19788/) (2025)
- [Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality](https://mlsanity.com/paper/2401.09556/) (2024)

## Abstract (arXiv)

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.