A Fuzzy multi-objective programming approach to develop a green closed-loop supply chain network design problem under uncertainty: Modifications of imperialist competitive algorithm

The last decade has seen a numerous studies focusing on the closed-loop supply chain. Accordingly, the uncertainty conditions as well as the green emissions of facilities are still open issues. In this paper, a new fuzzy multi-objective programming approach is to present for a production-distribution model in order to develop a multi-product, multi-period and multi-level green closed-loop supply chain network problem, which this model is formulated as multi-objective mixed linear integer programming (MOMILP). In regards to offered fuzzy multi-objective model, three conflicting goals are exited, simultaneously. The objective functions are to minimizing the total cost, minimizing the gas emissions costs due to vehicle movements between centers, and maximizing the reliability of delivery demand due to the reliability of the suppliers. To get closer to real-world applications, the parameters of model are considered by fuzzy numbers. Another novelty of proposed model is in the solution methodology. To solve the model, this study not only uses a well-known Imperialist Competitive Algorithm (ICA) but a number of new modifications of ICA (MICA) also have been provided to address the proposed problem, which is to demonstrate the efficiency and performance of the proposed algorithm with other algorithms included: SA, ICA, ACO, GA, and PSO are compare. Finally, different analyses with a variety of problem complexity in different sizes are performed to assess the performance of algorithms as well as some sensitivity analyses on the efficiency of model are studied