The distributionally robust newsvendor problem with dual sourcing under carbon tax and cap-and-trade regulations

Both carbon tax and cap-and-trade regulations as carbon emissions reduction schemes are widely adopted and implemented in practice. Based on the dual sourcing newsvendor framework, this paper proposes two distributionally robust newsvendor models under those two carbon regulations. The optimal order quantity and carbon emissions of each model are derived by using a maximin expected profit method, and comparisons of the profits between the models with and without carbon emission regulations are provided. It is observed that the carbon tax regulation will lead to a lower profit while adjusting the value of carbon cap leads to comparable profits between the model under cap-and-trade regulation and that without carbon emission consideration. Finally, several numerical examples are presented to illustrate the analytical results and the models developed herein.