A Loss-Averse Newsvendor with Cap-and-Trade Carbon Emissions Regulation

This study aims to provide an optimization model for operational efficiency in individual firms with cap-and-trade carbon emissions regulation. In addition, this study assumes that customers’ demand takes a probability distribution. Under this circumstance, our intention is to draw theoretical and policy implications for carbon emissions regulation by setting and analyzing newsvendor models in which the decision maker is loss-averse for her risk preference. Then, we formulate two loss-averse newsvendor models where we use a “kinked” piecewise linear and concave utility function. More specifically, we show that our objective functions are concave to derive the existence and uniqueness of the optimal solution. After then, through a comparative static analysis, we conduct a sensitivity analysis of how the model parameters affect the optimal solution. Then, the analytical results can be summarized as follows. First, in a lost-sale model, loss aversion significantly affects the optimal policy of newsvendors’ decision-making with cap-and-trade regulations. Second, in a stockout penalty cost model, the inclusion of cap-and-trade regulation terms and shortage penalty costs adds more structural complexity in the optimal solution. Thus, the directions of the impacts are mixed and the impacts on the optimal solutions are not monotone, especially with cap-and-trade terms. All these analytical results show big differences between the existing risk-neutral and our loss-averse models, which are confirmed by numerical experiments.