Designing and solving a bi-level model for rice supply chain using the evolutionary algorithms

•A bi-level mathematical model is firstly formulated for the rice supply chain.•Two-hybrid and a modified metaheuristic algorithms are developed.•A real-life applied example is provided.•Results of numerical experiments demonstrate the efficiency of the modified algorithm. According to the recent gigantic development in the agricultural section, Agricultural Supply Chain (ASC) management has attracted both researchers and agronomic practitioners. In this regard, rice as one of the important agricultural products is generally cultivated by rural farmers in small farmlands. Due to the high demand, high price, type of products, and also wide geographic range of production and consumption, the rice supply chain has special characteristics in ASC. In this regard, this paper not only firstly considers rice supply chain and but also proposes a bi-level optimization model for rice supply chain. The proposed model aims to minimize total cost with respect to the two decision makers' opinions. Since, the bi-level programming is NP-hard, to solve the proposed model, two well-known meta-heuristic algorithms including Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) along with two hybrid algorithms (PSO-GA and GA-PSO) and a modified algorithm (GPA) are utilized. In order to fill the literature gaps and to get closer to real-world applications, an applicable example in Iran is studied. Based on the results and managerial insights, the GPA is chosen as the best method and its allocated value of the variable are reported. The results show that the proposed model and solution methods are valid, practical, and effective. Also, in order to provide an insight to the functionality of the model and the results of the case, some sensitivity analyses on the major model parameters such as the demand are provided.