An inexact optimization model associated with two robust programming approaches for water resources management

In this study, an interval fuzzy-robust two-stage stochastic-robust programming (IFRTSRP) model is developed for water resources management under uncertainty. The developed IFRTSRP model incorporates two-stage stochastic programming (TSP), fuzzy robust programming (FRP), interval linear programming (ILP), and stochastic robust optimization (SRO) within a general optimization framework. The IFRTSRP model can not only deal with uncertainties presented as probability distributions, fuzzy membership functions, discrete interval numbers, and their combinations, but also provide an effective linkage between the pre-regulated water resources management policies and the associated economic implications. The IFRTSRP model can also enhance the robustness for the optimization process by delimiting the uncertain decision space through dimensional enlargement of the original fuzzy constraints. Moreover, the IFRTSRP model can evaluate the trade-offs between system economy and stability by incorporating the variability measures on penalty costs into the objective function. The IFRTSRP model is applied to a hypothetical case study of water resources management. The results indicate that reasonable solutions would be generated under different levels of λ and/or ω (non-negative weight coefficients); moreover, a higher net system benefit would correspond to lower system stability and higher system failure risk. Thus, the modeling results can be used for generating decision alternatives and thus help the managers to identify desired water allocation policies based on the reasonable consideration of system economy, system stability, and system failure risk.