Designing a sustainable closed-loop supply chain network of face masks during the COVID-19 pandemic: Pareto-based algorithms

Abstract

This study develops a novel mathematical model to design a sustainable mask Closed-Loop Supply Chain Network (CLSCN) during the COVID-19 outbreak for the first time. A multi-objective Mixed-Integer Linear Programming (MILP) model is proposed to address the locational, supply, production, distribution, collection, quarantine, recycling, reuse, and disposal decisions within a multi-period multi-echelon multi-product supply chain. Additionally, sustainable development is studied in terms of minimizing the total cost, total pollution and total human risk at the same time. Since the CLSCN design is an NP-hard problem, Multi-Objective Grey Wolf Optimization (MOGWO) algorithm and Non-Dominated Sorting Genetic Algorithm II (NSGA-II) are implemented to solve the proposed model and to find Pareto optimal solutions. Since Meta-heuristic algorithms are sensitive to their input parameters, the Taguchi design method is applied to tune and control the parameters. Then, a comparison is performed using four assessment metrics including Max-Spread, Spread of Non-Dominance Solution (SNS), Number of Pareto Solutions (NPS), and Mean Ideal Distance (MID). Additionally, a statistical test is employed to evaluate the quality of the obtained Pareto frontier by the presented algorithms. The obtained results reveal that the MOGWO algorithm is more reliable to tackle the problem such that it is about 25% superior to NSGA-II in terms of the dispersion of Pareto solutions and about 2% superior in terms of the solution quality. To validate the proposed mathematical model and testing its applicability, a real case study in Tehran/Iran is investigated as well as a set of sensitivity analyses on important parameters. Finally, the practical implications are discussed and useful managerial insights are given.