In this paper, we consider a joint optimal decision on lot size and carbon reduction investment under direct shipment strategy. We first provide mathematical models with three types of carbon emission constraints, carbon cap, carbon tax, and carbon cap-and-trade. With optimal solutions that are derived in a closed-form, we show that joint optimal lot size and reduction investment under direct shipment can lead to reduce the amount of carbon emissions with the smaller total cost. In addition, we compare the effects of three carbon emission constraints on the reduction of carbon emission and total costs.