Inventory management in supply chains with consideration of Logistics, green investment and different carbon emissions policies

•It is an integrated inventory model for supply chains considering carbon emissions.•Carbon emissions from production, transportation, and storage are all considered.•Carbon taxation, limited carbon emissions, and cap and trade are considered.•The optimal number of shipments, transportation lot size are determined.•The optimal amount of investment in green technologies are also determined. This study investigates the effects that carbon policies and green technologies may have on the integrated inventory of a two-echelon supply chain with consideration of carbon emissions during the processes of product production, transportation, and storage. The three carbon emissions policies: limited total carbon emissions, carbon taxation, and cap-and-trade, are considered in the study. The proposed model can assist firms in determining their corresponding optimal production quantity, delivery quantity, and green investment amount with an aim of minimizing the costs under different carbon emissions policies. Moreover, this study also provides practical implications for the government to make appropriate policies and regulations in balancing the trade-off between environmental protection and economic growth. Finally, the results indicate that firms adopting the carbon tax policy would prefer to invest in a relatively efficient green technology. With regard to the sources of carbon emissions, the effects of unit carbon emissions during production and unit distance of transportation are the most dramatic, and the cap limit has greater effects than the carbon emissions reduction factor of the green technology. Besides, the government should set the limit of carbon emissions within a reasonable range under the cap-and-trade policy to avoid suppliers overly trading their quotas of carbon emissions.