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Aggravating global warming has heightened the imminent need by the world to step up forceful efforts on curbing emission of greenhouse gases. Although manufacturing is a major resource of carbon emission, few research works have studied the impacts of carbon constraints on manufacturing, leading to environmentally unsustainable production strategies and operations. This paper incorporates carbon emission management into production planning for make-to-order (MTO) manufacturing. This paper proposes a model that solves lot-sizing problems to maximise profits under carbon emission caps. The model adopts stochastic interarrival times for customer orders to enhance the practicality of the results for real-world manufacturing. Numerical experiments show that reducing carbon emission undercuts short-term profits of a company. However, it is conducive to the company’s market image as being socially responsible which would attract more customers who concern about environmental protection. Hence, reducing carbon emission in manufacturing is beneficial to long-term profitability and sustainability. The results provide managerial insights into manufacture operations for balancing profitability and carbon control.