Newsvendor’s optimal decisions under stochastic demand and cap-and-trade regulation

Cap-and-trade regulation (CTR) is universally considered as one of the most environmentally friendly approaches to reducing carbon emission. In this paper, the newsvendor with a warranty service is regarded as the benchmark model firstly. Then, we study extended models about the newsvendor’s carbon footprint under CTR in the carbon trading market. Specifically, the carbon footprint exists in the four stages: production, sale, residual disposal, and return warranty service. And we adopt low-carbon technologies to improve the carbon footprint. Thirdly, we derive the newsvendor’s optimal production quantity, emission abatement level, and the expected profit. Interestingly, improving the carbon footprint in the sale and return warranty stages leads to a sharply higher profit in the carbon trading market. Finally, results and discussion are addressed in detail by numerical examples. We discover that optimal production quantity with an improved carbon footprint is larger than that with an original carbon footprint and earns more. Besides, the warranty service cost is negatively related to both the newsvendor’s optimal production quantity and profit. In the carbon trading market, the newsvendor is supposed to improve carbon footprint by carbon reduction investment. Besides, carbon quotas provided by the government do no affect the optimal production quantity but affects the profit of carbon trade.