Designing a sustainable supply chain network integrated with vehicle routing: A comparison of hybrid swarm intelligence metaheuristics

Recently, a growing concern with sustainability has become a consideration in business operations. However, there is a lack of mathematical models that quantify environmental effects and, in particular, social impacts of supply chains because of the inherently subjective nature of these aspects. To fill this gap, this paper models a distribution network in which the triple bottom lines of sustainability are captured. Different impacts of the network on the stakeholders, including company owners, workers, consumers and society, are considered as whole. In the current model, a multi-product vehicle routing problem with time windows (MPVRPTW) as an operational decision is integrated with strategic decisions related to the network design. To solve this model, three hybrid swarm intelligence techniques (particle swarm optimization (PSO), electromagnetism mechanism algorithm (EMA), and artificial bee colony (ABC)) are proposed, and each is hybridized with variable neighborhood search (VNS) are proposed. Because metaheuristic methods are sensitive to input parameters, response surface methodology (RSM) with the multi-objective decision making (MODM) approach is applied for tuning the parameters. The proposed approaches are compared with the hybrid of genetic algorithm (GA) and VNS as the benchmark algorithm. A fair comparison is conducted by employing six metrics to evaluate the quality of the Pareto frontier obtained by the algorithms on the test problems. According to the results, the predominance of EMA is enhanced by VNS local search.