Carbon emissions have been known as a substantial part of the environmental burden in the manufacturing industry. As an emerging topic on controlling carbon emissions, green and sustainable manufacturing requires not only cost efficiency but also environmental friendliness. Facing the problem, this paper introduces environmental constraints (i.e., carbon emission constraints) into a capacitated multi-level production planning problem. When minimizing total costs by scheduling production for a number of items over the planning horizon, we make decisions on setup periods, time-phased production and inventory for all items over the planning horizon with no violation on limits of carbon emissions. We apply a lower and upper bound guided nested partitions method to solve the problem and compare the method with a commercial solver. Computational results indicate that the proposed sustainable lot sizing model can reduce carbon emissions, and the optimization method is computationally tractable and is able to obtain better results under the same computational resources.