Among the carbon regulation policy schemes, the cap-and-trade has received more attention because of its efficiency and flexibility. Two primary challenges with the cap-and trade scheme are determining the correct cap and carbon trading price in the carbon market. This paper presents a bi-level model to investigate these two challenges in the cap-and-trade scheme formed between multiple supply chains and the government. At the first level, the government minimizes the cap in such a way that the costs of the supply chains do not rise too much. At the second level, the supply chains minimize their costs according to their cap and trade the dedicated allowances. An exact and a heuristic method are developed to solve the bi-level model. The computational results on a set of randomly generated instances show the effectiveness of the presented heuristic. Sensitivity analysis demonstrates that the government should choose proper amounts of caps to balance costs and environmental benefits.

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