Carbon emissions are the key factor of global warming. Nowadays, some countries have focused on reducing carbon emission. Carbon tax and cap policies are the key mechanism utilized in many countries to achieve this. Keeping this issue in mind, a sustainable economic production quantity (SEPQ) carbon tax and cap model has considered for a controllable carbon emissions rate by investing in green technology (GT) efforts under different with and without shortage situations. This study has three models; a) a sustainable economic production quantity carbon tax and cap model with no shortages; b) a sustainable economic production-quantity carbon tax and cap with partial backordering; and c) a sustainable economic production-quantity carbon tax and cap with full backordering with and without green technology investment. A solution methodology has been proposed for determining the optimal strategies of cycle time, green technology investment, and the fraction period length in positive inventory level. Several numerical examples have studied to validate the sustainable economic production quantity models. The results of this paper are a sustainable economic production quantity carbon tax and cap partial backlogging case has a better justifiable profit with the highest cycle time and the lowest value of the fraction length period as well as the lower green technology investment cost compared with other models. Finally, sensitivity analysis has provided with the managerial implication of the optimal feasible solution with respect to some key parameters. © 2020 Elsevier Ltd