A set of calibrated metaheuristics to address a closed-loop supply chain network design problem under uncertainty

Abstract

Nowadays, there is a great deal of interest in developing supply chain networks with the goal of optimisation. This paper addresses a new stochastic optimisation model by using a two-stage stochastic programming for a closed-loop supply chain network design problem. To control the uncertainty circumstances of manufacturing of products, customers’ demand, prices of products and its returned rates, the financial risk is considered as a distinguished objective function to find a robust solution. To address the developed model, a new recent nature-inspired algorithm, namely, Whale Optimisation Algorithm (WOA) and also Particle Swarm Optimisation (PSO) as a popular method in swarm intelligence algorithms are utilised in this study. In addition to this development, Genetic Algorithm (GA) and Simulated Annealing (SA) as the well-known metaheuristics used repeatedly among the literature are employed to have a comprehensive comparison. In order to be faired, a popular method for calibration called Response Surface Method (RSM) is applied to tune the algorithms’ parameters. Finally, some evaluation metrics to assess the Pareto optimal fronts of algorithms’ quality are considered to conduct a comparative study using statistical analyses and some sensitivity analyses are performed through an industrial example.