IFTCIP: An Integrated Optimization Model for Environmental Management under Uncertainty

In this study, an interval-fuzzy two-stage chance-constrained integer programming (IFTCIP) method is developed for supporting environmental management under uncertainty. The IFTCIP improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within a general mixed integer linear programming framework. It has advantages in uncertainty reflection, policy investigation, risk assessment, and capacity-expansion analysis in comparison to the other optimization methods. Moreover, it can help examine the risk of violating system constraints and the associated consequences. The developed method is applied to the planning for facility expansion and waste-flow allocation within a municipal solid waste management system. Violations of capacity constraints are allowed under a range of significance levels, which reflects tradeoffs between the system cost and the constraint-violation risk. The results indicate that reasonable solutions for both binary and continuous variables have been generated under different risk levels. They are useful for generating desired decision alternatives with minimized system cost and constraint-violation risk under various environmental, economic, and system-reliability conditions. Generally, willingness to take a higher risk of constraint violation will guarantee a lower system cost; a strong desire to acquire a lower risk will run into a higher system cost.