A two-stage programming approach for water resources management under randomness and fuzziness

In this study, a fuzzy stochastic two-stage programming (FSTP) approach is developed for water resources management under uncertainty. The concept of fuzzy random variable expressed as parameters’ uncertainties with both stochastic and fuzzy characteristics was used in the method. FSTP has advantages in uncertainty reflection and policy analysis. FSTP integrates the fuzzy robust programming, chance-constrained programming and two-stage stochastic programming (TSP) within a general optimization framework. FSTP can incorporate pre-regulated water resources management policies directly into its optimization process. Thus, various policy scenarios with different economic penalties (when the promised amounts are not delivered) can be analyzed. FSTP is applied to a water resources management system with three users. The results indicate that reasonable solutions were generated, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and different levels of constraint-violation probability. The developed FSTP was also compared with TSP to exhibit its advantages in dealing with multiple forms of uncertainties.