In recent years, the stability development in supply chain management has changed to a significant challenge and problem by increasing pressure on the functions of factories through excessive pressures from customers, the government, and non-governmental organizations, and also increasing social and environmental awareness. Considering the globalization of supply chain, location-routing is considered as the most challenging problem. The selection of routes in delivering pleas to customers can have a direct influence on environmental contaminants resulting from fossil fuels in machines. Also the best place to establish or to make the facilities active can influence the social desired goal in a direct way. In the present study, location-routing is considered having four levels (provider, producer, distribution center, and customer). It is tried to find the optimal place of facilities, materials and product transport, technology selection, capacity levels, and efficient routes of facilities, so that minimization of the expenses, adverse environmental effects, and maximization of social desirability have been considered and optimized. The method of contemporary epsilon constraint by GAMS software with Cplex solver is used to solve the model.
