Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations

Cap-and-trade and carbon tax are two emission regulations widely used to curb the carbon emissions generated from firms. Based on economic order quantity (EOQ) model, this paper examines the production lot-sizing issues of a firm under these two regulations, respectively. The optimal lot-size and emissions under the two regulations are achieved. We then investigate the impacts of production and regulation parameters on the optimal lot-size and emissions. Furthermore, we compare the firm's optimal carbon emissions under the two regulations. It is found that under the cap-and-trade regulation, the firm's decisions of the optimal emissions as well as permits trading depend on the differentiated permits trading prices. If setup incurs the same cost as holding incurs per unit of generated emissions, both regulations always lead to the same optimal emissions (which is also equal to that without emission regulation). Otherwise, neither regulation always leads to lower emissions than the other does.