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

## TL;DR

This paper introduces a novel Lagrangian-based heuristic, $AugMathLagr$, for solving complex multi-objective sustainable supply chain problems, demonstrating competitive and outstanding performance through extensive testing and case studies.

## Contribution

The paper presents a new Lagrangian matheuristic method, $AugMathLagr$, specifically designed for multi-objective sustainable supply chain optimization problems.

## Key findings

- $AugMathLagr$ outperforms existing methods in artificial instance tests.
- The method shows superior results in a real-world case study.
- Computational experiments validate the efficiency and competitiveness of $AugMathLagr$.

## Abstract

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 $AugMathLagr$.