This research considers both cost and environmental protection to design a multi-objective optimization model.  With multi-period customer demands, the model can solve a multi-plant resource allocation and production planning problem by focusing the decisions on supplier selection, facility selection, production batches, transportation mode selection, and distribution of the materials and commodities of a green supply network.  In this paper, four transportation modes—namely, road, rail, air, and sea—have their corresponding transportation time, cost, and CO₂ emissions.  Based on multiple planning periods, this research calculates the minimal total cost and total CO₂ emissions based on production and transportation capacity.  Using numerical analyses, the results show that, when the budget is sufficient, only production capabilities with α = 1.5 and 2.0 are beneficial for improving environmental protection; carbon dioxide emissions of both production capacities are not significant differences.  Furthermore, when the production batch size increases, total cost increases.  Regarding transportation capacity, the results show that, when the budget is sufficient, increasing transportation quantity limits will be slightly beneficial for improving environmental protection.