Mean-variance analysis of sustainable newsvendor problems with stochastic demand under cap-and-trade policy

(Communicated by Jie Sun)

This paper studies the single-product single-period newsvendor problem with sustainability investment, where the manufacturer determines its optimal production quantity and sustainability level under cap-and-trade policy. Specifically, the proposed model addresses the trade-off between the expected profit and its variance under the mean-variance framework. The demand under consideration is stochastic and dependent on the sustainability level. By taking into account two different forms of the underlying demand, that is, additive and multiplicative, we prove the existence and uniqueness of the optimal solution of the corresponding optimization models under some mild conditions. Further, we conduct sensitivity analysis on the optimal expected profit and its variance with respect to the risk-averse. Preliminary numerical experiments are conducted to illustrate the theoretical results and managerial insights.

This work is dedicated to Prof Fukushima to honor his outstanding contributions in optimization on his 75th birthday.