Abstract
Supply Chain Networks Distribution (SCND) topology aims to find the best position and size for facilities to ensure optimal products flow based on the Matheuristic approach (i.e. decomposition meta-heuristics). This problem is a multi-objective function designed to reduce the transported costs and associated delivery times. The Matheuristic presents a brilliant hybridize between the meta-heuristics steps and mathematical procedures in solving large-size problems with the slightest deviation empty set. This paper proposed an ant colony-based algorithm evolved by mathematical procedures called Mat-ACO, compared with SA "simulated annealing" and CA "Camel algorithm." The authors deduced that the mathematical solution is limited as the instances grow, significantly if increased than 600 network hotspots. The Mat-ACO, SA, and CA results are close to counterparts obtained by LINGO, with a difference of 2.03%, 2.49%, and 3.75%, respectively, and continue to extract results from more than 1350 network hotspots. The main contribution is to find the optimum tuning parameters, which will reduce the deviation from the exact solution. This paper reveals that no feasible solution can catch the LINGO at large-size problems. At the same time, the CA is superior to SA in the large problem sizes, while Mat-ACO still presents preferred solutions in minimum time. The proposed methodology is classified as a closed-loop network strategy that targets green management.