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Interval-Parameter Robust Minimax-regret Programming and Its Application to Energy and Environmental Systems Planning

Abstract In this study, an interval-parameter robust minimax-regret programming method is developed and applied to the planning of energy and environmental systems. Methods of robust programming, interval-parameter programming, and minimax-regret analysis are incorporated within a general optimization framework to enhance the robustness of the optimization effort. The interval-parameter robust minimax-regret programming can deal with uncertainties expressed as discrete intervals, fuzzy sets, and random variables. It can also be used for analyzing multiple scenarios associated with different system costs and risk levels. In its solution process, the fuzzy decision space is delimited into a more robust one through dimensional enlargement of the original fuzzy constraints; moreover, an interval-element cost matrix can be transformed into an interval-element regret matrix, such that the decision makers can identify desired alternatives based on the inexact minimax regret criterion. The developed method has been applied to a case study of energy and environmental systems planning under uncertainty. The results indicate that reasonable solutions have been generated.