Data-driven distributionally robust supplier selection and order allocation problems considering carbon emissions

Under the constraints of uncertainty and carbon emission policies, reasonable and flexible supplier selection and order allocation can minimize the total cost, which is of great significance to the supply chain. We study sustainable supplier selection and order allocation problems with multiple periods, multiple suppliers, and multiple products under a carbon cap-and-trade policy. We exploit distributionally robust versions of supplier selection and order allocation problems with an explicit distributional uncertainty set and derive computationally tractable reformulations of the distributionally robust optimization model with chance constraints by cone duality theory and conditional value-at-risk measure. Numerical experiments show that the proposed distributionally robust optimization models with nice computational tractability and probability guarantees are superior to the existing distributionally robust chance-constrained optimization models in terms of cost and risk aversion. Relevant management insights on different carbon emission regulations and the application of distributionally robust optimization models are provided for policymakers and enterprises' decision-makers based on the derived results.