Input-output dynamic model for optimal environmental pollution control

• Published in: Applied Mathematical Modelling Vol. 83; pp. 301 - 321
• Main Authors: Chen, Xin, Zhu, Yuanguo, Shen, Jiayu
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2020; Elsevier BV
• Subjects: Algorithms; Ammonia; Dynamic models; Environmental economy; Input-output analysis; Optimal control; Optimization; Pollution control; Random variables; Raw materials; Recurrence equations; Singular system; Wastewater treatment; Recurrence equations; Singular system; Input-output analysis; Optimal control; Environmental economy
• DOI: 10.1016/j.apm.2020.02.029
• ISSN: 0307-904X; 1088-8691

•A pollution control problem is introduced in uncertain random environments.•An equivalent mathematical programming for the problem is provided.•Algorithms are proposed for solving the mathematical programming.•The optimal distribution strategies of pollution control fund are obtained. This paper describes the allocation of a wastewater treatment fund within a region based on a dynamic input-output model. Considering the complexity of the input-output process, many indeterminate factors must be included in the model. For example, with the aging of machines, an unexpected loss will be caused by the retention of raw materials during an operation; this can be realistically considered as a random variable, because of the sufficiently large amount of historical data. By contrast, actions such as a temporary transfer or inexperienced operators can only be regard as uncertain variables, because of a lack of historical data. First, the pollution control model is formulated in an uncertain environment by including both human uncertainty and objective randomness. Second, an optimal control model subject to an uncertain random singular system is established; this model can be transformed into an equivalent optimization problem. To solve such a problem, recurrence equations are presented based on Bellman’s principle, and these were successfully applied to address the optimal control problem in two special cases. Moreover, two algorithms are formulated for solving the pollution control problem. Finally, the optimal distribution strategies of the pollution control fund used to control the emissions of COD and NH3-H, which are two indicators of wastewater in China, were obtained through the proposed algorithms.