Governments all over the world adopted different forms of progressive carbon taxation strategies (for example concave, convex and linear for respectively Swedish, French, and Canadian government). These progressive strategies provide companies with different degrees of flexibility to adapt their decisions to the new environmental regulations and reduce their carbon emissions without compromising their profit. However, no existing work has compared the impact of each progressive legislation on the optimal decisions of the supply chain, its profit, and its environmental performances. In this paper, we contribute to the literature by developing four multi-period technology selection models under different forms of progressive carbon taxes. We analytically determine the optimal strategic investment timing decision under each taxation strategy. We then develop a carbon tax assessment method using multi-criteria analysis techniques to compare the efficiency of each carbon taxation form in reducing carbon emission and maximising the Supply Chain (SC) profit. We prove that the earliest green investment decision and the decision of not investing in green depend on the target carbon tax rather than the taxation form. We show that government decision about the suitable taxation form should be based on the performance of the available green technologies.