Tiered transferable pollutant pricing for cooperative control of air quality to alleviate cross-regional air pollution in China

Cross-regional air pollution is a widespread concern worldwide. This problem is particularly acute in China, where it has caused a substantial public health crisis. We consider the problem of determining tiered transferable pollution price control for air quality based on a piecewise transfer cost. Under tiered pricing, the more pollution that is transferred, the higher the transfer cost per pollution unit that must be paid. The tiered transferable pollutant pricing (TTPP) control problem is first formulated as a bi-level mathematical program model in which the upper level consists of China's Ministry of Environmental Protection, which controls air pollution using a tiered transferable pollution price, and the lower level is represented by a group of administrative regions that aim to relieve pollution with respect to their generalized costs, including reduction and transfer costs. Based on optimal conditions, the TTPP control problem is theoretically reformulated as the minima of a solution set for a sequence of equations. Each equation sequence is structured such that all of its components are optimal reactions of the lower-level regions. Then, we apply a bisection-based algorithm to solve the sequence of equations. Finally, we use the pollutant SO2 control problem in the Beijing-Tianjin-Hebei delta as a numerical example to provide insight into the model and performance of the algorithm. The results reveal that all regions in that delta can benefit from the tiered transfer pricing scheme, which also implies that the scheme has potential for practical application.