Water resources management under multi‐parameter interactions: A factorial multi‐stage stochastic programming approach

The paper proposes a factorial multi‐stage stochastic programming (FMSP) approach to support water resources management under uncertainty. This approach was developed based on the conventional inexact multi‐stage stochastic programming method. Five alternative inexact multi‐stage stochastic programming algorithms in addition to the conventional algorithm were introduced and bundled to offer multiple decision options that reflect decision makers' perspectives and the complexities in system uncertainties. More importantly, factorial analysis, a multivariate inference method, was introduced into the modeling framework to analyze the potential interrelationships among a variety of uncertain parameters and their impacts on system performance. The proposed approach was applied to a water resources management case. The desired water‐allocation schemes were obtained to assist in maximizing the total net benefit of the system. Multiple uncertain parameters and their interactions were examined, and those that had significant influences on system performance were identified. For example, the medium flow in the third planning period was the system objective's most influential factor. Any variation of this factor would significantly influence the acquisition of the total net benefit in the community. The significant interactions were also identified, such as the interaction between the agricultural sector's penalty and the medium flow in the third planning period. Through the analysis of multi‐parameter interactions, the interrelationships among the uncertain parameters could be further revealed.