Inexact Multistage Stochastic Quadratic Programming Method for Planning Water Resources Systems under Uncertainty

An inexact multistage stochastic quadratic programming (IMQP) method was developed for supporting water resources management under uncertainty. The IMQP method improves upon the existing multistage programming and inexact quadratic programming approaches, and can directly tackle uncertainties presented as interval numbers and probability distributions within a multistage context. Moreover, it can accommodate real-time dynamics of system uncertainties based on a complete set of scenarios; it can also deal with non-linearities in the objective function to reflect the effects of marginal utility on system benefits and costs. Because penalties are exercised with recourse against any infeasibility, the IMQP can support the analysis of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The developed method was applied to the planning of water resources management in the Heshui River Basin, China. The results are useful for generating decision alternatives that correspond to various system conditions and for water resources managers.