A meta-heuristic-based algorithm for designing multi-objective multi-echelon supply chain network

Recently, practitioners and researchers have concentrated on the use of meta-heuristics in the design of multi-objective supply chain networks. The number of publications in this field reflects this interest. The purpose of this paper is to propose a novel metaheuristic approach for designing supply chain network problems in the case of multi-objective supply chains. The proposed algorithm hybridizes three meta-heuristic approaches; simulated annealing, tabu search, and variable neighborhood algorithms. The proposed algorithm is also combined with a linear programming approach. The purpose of hybridization is to aggregate the approaches in order to benefit from the advantages of these solution algorithms. The features of these algorithms are investigated in this paper for the first time. The most useful characteristics of each algorithm are then utilized for developing the new algorithm. The performance of the proposed algorithm is compared with an exact algorithm, simulated annealing, and tabu search algorithms. The results indicated that the proposed algorithm is comparable to the exact in the case of small and medium-sized supply chain problems. The findings revealed that the proposed algorithm takes on an average of 6.3 min to solve small and medium problems, while the exact algorithm takes 412 min. Moreover, the proposed algorithm outperforms other algorithms with a mean ideal distance (MID) of 13,606,871, a percent of domination (POD) of 0.84, and a computational time of 15.64 min compared to the tabu search algorithm's MID of 15,574,523, a POD of 0.55, and a computational time of 21.46 min. The simulated annealing algorithm, on the other hand, achieved an average MID of 18,145,931, a POD of 0.40, and a computational time of 30 min. Furthermore, the findings showed that the proposed algorithm is capable of solving complex and large supply chain problems in a reasonable time when exact approaches fail.