A design of a circular closed-loop agri-food supply chain network-A case study of the soybean industry

In recent years, there has been an irresistible need for the agri-food industry to prioritize the development of efficient supply chain systems considering circular economy concepts. Agri-food products are critical to sus-taining human life, as they provide essential nutrients required for maintaining bodily functions. Producing the appropriate quantity of agri-food products to match the potential demand is crucial for efficient supply to in-dustries and markets. In addition, the principles of the circular economy can be employed to effectively utilize or reintroduce agri-food waste back into the network. This work formulates a novel mixed-integer linear pro-gramming model to propose a closed-loop agri-food supply chain network design for the soybean industry under sustainability and circular economy terms. The multi-objective network struggles to manage the total net profit while monitoring CO2 emissions and the satisfaction of customers within the network. Given the NP-hard nature of the network, the solution approach embraces a set of conventional and hybrid metaheuristics to surmount its complexity effectively. To this end, four multi-objective optimizers and three hybrid algorithms are utilized. Hence, the model's compatibility with real conditions is investigated using fifteen practical tests. The results of interval plots and the hybrid multi-criteria decision-making techniques emphasize that optimizers can solve all sizes of problems. However, MOGWO is better suited for addressing small-size problems, whereas MOHHSA is highly effective for tackling problems of medium and large sizes.