Distributionally robust newsvendor problem with partial demand information under carbon emission regulations

Abstract

Carbon emission schemes are widely adopted and implemented in practice to control greenhouse gas emissions. However, a firm restricted by carbon emission schemes with only partial demand information may face greater challenges. In this paper, we investigate an ordering and pricing newsvendor problem with partial demand information, which considers carbon emissions generated from the processes of ordering and disposing of the excess inventory. We propose three distributionally robust models to maximize the worst-case profit under different carbon emission regulations: carbon tax, cap-and-trade and carbon cap, respectively. We derive the implicit solution under the carbon tax scheme and design heuristic algorithms based on Lagrangian relaxation under the cap-and-trade and carbon cap regulations. Numerical analysis indicates: (i) all three regulations are effective in reducing carbon emissions; (ii) the implementation of carbon schemes leads to higher optimal pricing and lower optimal ordering quantity, both carbon tax and carbon cap regulations will always lead to lower profit, while the retailer may benefit from the cap-and-trade regulation by selling out the carbon credit; (iii) the proposed approach performs well under different distribution specific scenarios.