A bi-level model for a closed-loop agricultural supply chain considering biogas and compost

In today’s competitive marketplace, to increase customer satisfaction and profitability, supply chain management has become more prominent. Therefore, thorough planning and designing the supply chain by seeing all levels and units are essential to growing the efficiency of the entire supply chain. In the present study, an eight-echelon network is designed for a closed-loop agricultural supply chain. These eight echelons are consisting of suppliers, farms, distribution centers (DCs), customers, recycling depots, biogas centers, compost production centers, and biogas applicants. To design the agricultural logistics network, a bi-level programming mathematical model is presented. The first objective seeks to minimize total costs of the upper-level which consist of shipping costs, construction costs, production costs, inventory holding costs, and buying costs. Besides, the second objective attempts to maximize total profits of the lower-level using subtraction of incomes from the costs which the total income is calculated by selling manufactured biogas and compost to its applicants. Since the bi-level programming problems are part of the NP-hard class and due to the computational complexity of the problems, the meta-heuristic algorithms are utilized to solve the formulated problem. To this end, two meta-heuristics consisted of Genetic Algorithm (GA) and Stochastic Fractal Search (SFS) are employed. Moreover, two hybrid metaheuristics created from these algorithms which include GA-SFS and SFS-GA are suggested to search for more appropriate solutions. Finally, various comparisons and analyses are performed to evaluate the model’s performance and the capabilities of the solution methods and the results showed the superiority of SFS-GA over other methods. Also, the results imply that considering biogas and compost can not only prevent environmental pollution, but also lead to profitability and the production of new products. Therefore, using this plan in countries that have agricultural products and also do not produce fossil fuels can be more attractive and practical.