Interval-parameter robust optimization for environmental management under uncertainty

In this study, an interval-parameter robust optimization (IPRO) method is developed through incorporating techniques of interval-parameter programming and robust optimization within a two-stage stochastic programming framework. The IPRO improves upon the two-stage stochastic programming methods by allowing uncertainties presented as both intervals and random variables to be handled in the optimization system. Moreover, in the modeling formulation, penalties are exercised with the recourse against any infeasibility, and robustness measures are introduced to examine the variability of the second-stage costs that are above the expected level. The IPRO is generally suitable for risk-aversive planners under high-variability conditions. The developed method is applied to a case of long-term waste management under uncertainty. Interval solutions under different robustness levels have been generated. They cannot only be used for analyzing various policy scenarios that are related to different levels of economic penalties when the pre-regulated waste allocation allowances are violated, but also help decision makers to analyze the interrelationships between the penalties and their variabilities.