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Adoption of carbon regulation mechanisms facilitates an evolution toward green and sustainable supply chains followed by an increased complexity. Through the development and usage of a multi-choice goal programming model solved by an improved algorithm, this article investigates sustainability strategies for carbon regulations mechanisms. We first propose a sustainable logistics model that considers assorted vehicle types and gas emissions involved with product transportation. We then construct a bi-objective model that minimizes total cost as the first objective function and follows environmental considerations in the second one. With our novel robust-heuristic optimization approach, we seek to support the decision-makers in comparison and selection of carbon emission policies in supply chains in complex settings with assorted vehicle types, demand and economic uncertainty. We deploy our model in a case-study to evaluate and analyse two carbon reduction policies, i.e., carbon-tax and cap-and-trade policies. The results demonstrate that our robust-heuristic methodology can efficiently deal with demand and economic uncertainty, especially in large-scale problems. Our findings suggest that governmental incentives for a cap-and-trade policy would be more effective for supply chains in lowering pollution by investing in cleaner technologies and adopting greener practices.