A screening technique for joint chance-constrained programming for air-quality management

This technical note presents a screening technique for using chance-constrained programming to achieve overall system (i.e., joint) reliability when there is statistical dependence between constraints representing an ambient air-quality requirement at different geographical locations. The technique is intended to determine whether the full analysis of row interdependence, which requires more intensive programming and larger computational effort, is warranted, by examining a possible spectrum of solutions at three extreme cases of row dependence. The technique is illustrated for airborne particulate emissions control, in which the overall cost of controlling particulate emissions from two electrostatic precipitators is minimized in a manner that maintains ground-level particulate concentration at all receptors with a prescribed reliability. In accordance with the theory presented here, such screening is achieved by setting the required reliability values of individual constraints according to assumptions of complete codependence, zero codependence, and complete negative codependence. In application, these reliability values represent the probability of achieving the ambient concentration standard at several receptor locations. The results of the screening technique are compared to those of two more computationally intensive methods for achieving overall system reliability. It is found that, for a given example, the screening technique brackets the results of those full-analysis methods for row dependence, as expected.