A fuzzy-stochastic robust programming model for regional air quality management under uncertainty

This paper proposes a hybrid fuzzy-stochastic robust programming (FSRP) method and applies it to a case study of regional air quality management. As an extension of the existing fuzzy-robust programming and chance-constrained programming methods, FSRP can explicitly address complexities and uncertainties without unrealistic simplifications. Parameters in the FSRP model can be expressed as PDFs and/or membership functions, such that robustness of the optimization process can be enhanced. In its solution process, the FSRP model is converted to a deterministic version through transforming m imprecise constraints into 2 km precise inclusive constraints that correspond to k alpha-cut levels (under each given significance level). Results of the case study indicate that FSRP is applicable to problems that involve a variety of uncertainties. Air pollution control invariably involves a number of processes with socio-economic and environmental implications. These processes are associated with extensive uncertainties due to their complex, interactive, dynamic, and multiobjective features. Through the FSRP modeling study, useful solutions for planning regional air quality management practices have been generated. They reflect complex trade-offs between environmental and economic considerations. Willingness to pay higher operating costs will guarantee meeting environmental objectives; however, a desire to reduce the costs will run the risk of potentially violating the emission and/or ambient-air-quality standards.