The issues of carbon emission and global warming have increasingly aroused worldwide attention in recent years. Despite huge progresses in carbon abatement, few research studies have reported on the impacts of carbon emission reduction mechanisms on manufacturing optimisation, which often leads to decisions of environmentally unsustainable operations and misestimation of performance. This paper attempts to explore carbon management under the carbon emission trading mechanism for optimisation of lot sizing production planning in stochastic make-to-order manufacturing with the objective to maximise shareholder wealth. We are concerned not only about the economic benefits of investors, but also about the environmental impacts associated with production planning. Numerical experiments illustrate the significant influences of carbon emission trading, pricing, and caps on the dynamic decisions of the lot sizing policy. The result highlights the critical roles of carbon management in production planning for achieving both environmental and economic benefits. It also provides managerial insights into operations management to help mitigate environmental deterioration arising from carbon emission, as well as improve shareholder wealth. 
Stochastic lot sizing manufacturing under the ETS system for maximisation of shareholder wealth