a facility location problem in a green closed-loop supply chain network design by considering defective products

This paper proposes a bi-objective model for a green closed-loop supply chain network design. four levels for forward and five levels for reverse flow were considered, including plants, distribution centers, online retailers, traditional retailers and customers for forward flow and customers, collecting centers, disposal centers, repair centers and plants for the reverse flow. the objectives are minimizing the ghg emission and maximizing profit by considering defective products and a second market for these products. also, online retailers were considered alongside with traditional ones, since the covid-19 pandemic has led to increase in the amount of online shopping. gams software and the lpmetric technique were used to solve the model in the small and medium sizes. however, for the large size, we used grasshopper optimization algorithm (goa) as a meta-heuristic approach since solving the large size problem with gams is a complicated and time-consuming process. we provided numerical and computational results to prove the efficiency and feasibility of the presented model. finally, the managerial insights and future works were provided.