Inexact Multistage Fuzzy-Stochastic Programming Model for Water Resources Management

In this study, an inexact multistage fuzzy-stochastic programming (IMFSP) model was developed for water resources management under uncertainty. In the IMFSP model, the uncertainties existing in the objective functions, and the constraints’ left side and right side are expressed as fuzzy sets so that the uncertainties can be directly communicated into the optimization process and various water allocation schemes can be obtained under different $\alpha$-cut levels at a plurality of periods regardless of the shapes of their membership functions. The IMFSP model can not only generate the most possible, lower and upper bound values for all possible decision schemes but it can also provide information about the degrees of membership of the decision variables between the lower and upper bound values. Meanwhile, the scenario-based multistage stochastic programming was incorporated in the IMFSP model to adequately reflect the dynamic variations and uncertain information of the water resources system. Therefore, the IMFSP model offers significant improvements over existing multistage stochastic programming models for water resources management with respect to the capacity of tackling various uncertainties and their interrelationships. Additionally, a simple hypothetical case for water resources management was provided for demonstrating applicability of the IMFSP model to support decision making within multiple scenarios during many time periods under uncertainty. In general, the proposed IMFSP has only been demonstrated and tested on a hypothetical example. Future research can be directed toward expanding/testing it on more complex real-world problems.