<p>Modern businesses are now focusing on minimizing their carbon footprints as a crucial part of the sustainability transition. This study develops a vendor–buyer inventory system in which the vendor aims to reduce emissions through investment in green technologies. Green technology investments increase costs. To lower the total system cost, the vendor motivates the buyer to purchase larger quantities by offering a multi-level price break policy and delivers the product through multiple unequal shipments. The model incorporates emissions generated during the manufacturing of goods, warehousing process and logistics activities to ensure environmental sustainability. Furthermore, a progressive carbon tax scheme is considered, and it has proven to be more effective in balancing the trade-off between cost and emissions than a flat tax rate. This model also addresses the randomness of demand during lead time. It initially assumes that demand during lead time follows a normal distribution and then examines the system without specifying any probability distribution. A solution methodology is proposed to minimize the overall system cost. Finally, the developed model is validated through numerical examples. The numerical results indicate that the unequal shipment policy and green investments significantly reduce both the total cost and the emissions. We can also conclude that a progressive carbon taxation offers greater flexibility in achieving sustainability goals.</p>