Design and planning of waste transfer stations, treatment facilities, and landfills are essential components of municipal solid waste management. The source separation process reduces waste separation costs and improves the quality of recycled products by preventing the generation of mixed waste and assisting the waste recycling process. The purpose of this paper is to present a multi-period, multi-objective model for designing an integrated and sustainable supply chain network for municipal solid waste management that considers source separation and employs a reward-penalty mechanism. The objective functions include minimizing the system's total cost, greenhouse gas emissions, and adverse environmental impacts on residential areas. The proposed model is illustrated through a case study in Kermanshah, Iran. Three scenarios including the optimal solution of the proposed model considering the landfill location as a decision variable, the optimal solution of the proposed model with the current landfill location fixed, and the existing waste management system are introduced and compared. The results indicate that when the proposed system is used instead of the previous two scenarios, waste management costs are reduced by 12.4% and 66.6%, greenhouse gas emissions are reduced by 0.5%, and increased by 3.3%. Environmental impacts are increased by 16.5% and reduced by 8.9%, respectively. Finally, a sensitivity analysis is conducted to determine the effect of varying the waste impurity percentage on supply chain performance, as source separation is believed to reduce system costs.