This study proposes a sustainable closed-loop supply chain under uncertainty to create a response to the COVID-19 pandemic. In this paper, a novel stochastic optimization model integrating strategic and tactical decision-making is presented for the sustainable closed-loop supply chain network design problem. This paper for the first time implements the concept of sustainable closed-loop supply chain for the application of ventilators using a stochastic optimization model. To make the problem more realistic, most of the parameters are considered to be uncertain along with the normal probability distribution. Since the proposed model is more complex than majority of previous studies, a hybrid whale optimization algorithm as an enhanced metaheuristic is proposed to solve the proposed model. The efficiency of the proposed model is tested in an Iranian medical ventilator production and distribution network in the case of the COVID-19 pandemic. The results confirm the performance of the proposed algorithm in comparison with two other similar algorithms based on different multi-objective criteria. To show the impact of sustainability dimensions and COVID-19 pandemic for our proposed model, some sensitivity analyses are done. Generally, the findings confirm the performance of the proposed sustainable closed-loop supply chain for the pandemic cases like COVID-19. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-16077-6.

Multi-criterion decision-making models are widely used in supplier selection problems. This study contributes to a green supplier selection problem considering the green manufacturing, green transportation, and green procurement. This study contributes to reverse logistics, eco-design, reusing, recycling, and remanufacturing with their high impact on the industries. In addition to the logistics costs and transportation costs, the carbon emissions are considered. With regard to the game theory, this paper uses a cooperative green supplier selection model. If transportation requirements of two or more companies are combined, it will help manufacturers to have less emissions with lower cost. After creating the optimization model to consider the uncertainty, this cooperative game theory model is established in a fuzzy environment. In this regard, a fuzzy rule-based (FRB) system is deployed and the set of fuzzy IF–THEN rules is considered. The proposed FRB model is contributed for the first time in the area of green supplier selection problem. Finally, some sensitivity analyses are conducted in a numerical example to evaluate the proposed model. With regard to the findings, although the cost of CO 2 emission of horizontal cooperation is increased, the cost saving of companies is increased. It means our total cost is optimal in a logistic network using the cooperative game theory. The results also indicate that horizontal cooperation in logistic network causes less cost and benefits for each company. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-17015-2.

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.

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