Inexact Two-Stage Stochastic Robust Optimization Model for Water Resources Management Under Uncertainty

An inexact two-stage stochastic robust programming model (ITSRP) was developed in this study for dealing with water resources allocation problems under uncertainty. ITSRP was formulated based on integration of interval linear programming (ILP), stochastic robust optimization (SRO), and two-stage stochastic programming (TSP) techniques. It could deal with uncertainties expressed as not only probability distributions but also discrete intervals, and could facilitate analyses of the policy scenarios that are associated with economic penalties when the predefined policies were violated. Moreover, the variability measure about the second-stage penalty costs was incorporated into the objective function, such that the trade-off between system economy and stability could be evaluated. The developed model was applied to a hypothetical case of water resources management system. Results demonstrated that the ITSRP model could help decision makers generate stable and balanced water resources allocation patterns, gain in-depth insights into effects of the uncertainties, and analyze trade-offs between system economy and stability.