A numerical solution for the air pollution control problem in 3D1

Abstract

This paper studies the minimization of the cost of an air pollution control problem in a three-dimensional region where there exists several sources of pollution. Since the control area has an infinite set of points, the proposed model was formulated using semi-infinite programming (SIP). The problem was solved by using a version of Volkov–Zavriev’s (1997) stochastic outer approximations method, which consists of an active search for relevant constraints based in quasi-optimal functions. The concentration of the contaminant at each point in the region is obtained from a Gaussian model. Three cases were analyzed taking into account the Colombian standard for sulfur dioxide. The hypothesis that polluting sources should not be established within cities was supported. Lastly, results indicate that solutions that cost the least allow the harmful effects caused by sources in a control area to be estimated.

Keywords

• Semi-infinite programming
• stochastic programming
• air pollution control
• numerical solution
• three-dimensional region (3D)