Government regulations and responsible customers’ behavior are key drivers for businesses to adopt respectful management strategies towards the environment and reduce the overall carbon emissions of their supply chains.Under a strict carbon emissions legislation and the increased awareness of customers about carbon emissions issues, companies are now pushed to improve their environmental performance to achieve better profits. Thus, they need to make optimal decisions within their Supply Chain Management to reduce the carbon emissions that are generated from their various activities.In this context, we identify the issue of the low carbon supply chain management. In this thesis, our objective is first to study this problem and to identify its key drivers. We then aim to review the literature and to study how quantitative models have addressed this problem and its related constraints. We therefore develop new models of low carbon supply design problems under the carbon tax legislation, which is recognized to be one of the relevant applied carbon legislations. In our proposed models, we particularly emphasize on the features of this carbon regulation that have been ignored within the literature. We first study strategic decisions of the company taking into consideration the non-homogeneous carbon tax scheme between countries. We then, study the investment decision of the company under a progressive carbon tax strategy. Through analytical and numerical analyses, we study the impact of such carbon legislations schemes on strategic decisions of the company and its performances. We aim to provide companies with a decision support tool to help them make optimal strategic decisions under this carbon legislation. We also provide recommendations to governments, as to which carbon tax legislations are the most efficient. Finally, we initiate the development of stochastic models to study the strategic investment problem in such an environmental context. We first consider a random customer demand, and then a dynamic and ...