An Inexact Two-Stage Quadratic Program for Water Resources Planning

Abstract

An inexact two-stage stochastic quadratic programming (ITQP) model is developed for water resources management under uncertainty. The model is a hybrid of inexact quadratic programming and two-stage stochastic programming. It can deal with the uncertainties presented as both probabilities and intervals. Moreover, it can deal with nonlinearities in objective function to reflect the effects of marginal utility on the benefit and cost components. Using quadratic form in the objective function rather than linear one, the ITQP can minimize the unfair competition of water resources among multiple users under uncertain water conditions. In the modeling formulation, penalties are imposed when policies expressed as the promised water supply targets are violated. In its solution process, the ITQP model is transformed into two deterministic submodels based on an interactive algorithm and a derivative algorithm, which correspond to the lower and upper bounds of the desired objective. Interval solutions, which are feasible and stable in the given decision space, can then be obtained by solving the two submodels sequentially. The developed method is then applied to a case study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with maximized system benefit and minimized system-failure risk.

Keywords: decision making, inexact optimization, quadratic programming, two-stage stochastic, water resources