As we move to a more carbon-constrained world, business will ultimately have to meet customer needs in a way that reduces the carbon footprint of products across the supply chain to minimize carbon emissions and mitigate climate change. The various activities contributing to carbon emissions in a supply chain are transportation, ordering and holding of inventory. This research work develops a mixed-integer nonlinear programing (MINLP) model that considers the scenario of supply chain with multiple periods, multiple products, and multiple suppliers. The model assumes that the demand is deterministic, the buyer has a limited storage space in each period, the buyer is responsible for the transportation cost, a supplier-dependent ordering cost applies for each period in which an order is placed on a supplier and inventory shortage is permissible.  The model provides an optimal decision regarding what products to order, in what quantities, with which suppliers, and in which periods to minimize the overall supply chain cost as well as associated cost of carbon emissions. For evaluating the carbon emissions, four different carbon regulating policies i.e., carbon cap-and-trade, strict cap, carbon offset and carbon tax on emissions, have been considered. The proposed MINLP has been validated using a randomly generated data set.