Adjustable Robust Optimization for Multi-Period Water Allocation in Droughts under Uncertainty

Abstract

Optimal, rational water resource allocation can go some way to overcoming water deficiencies; however, its achievement is complex due to conflicting hierarchies and uncertainties, such as water availability (WA) and water demand (WD). This study developed a robust water withdrawal scheme for arid and semi-arid regions that balanced the trade-offs between the sub-areas and water use participants, ensured sustainable regional system development, and guaranteed robust solutions for future uncertainties. A bi-level affinely adjustable robust counterpart (AARC) programming framework was developed, in which the regional authority as the leader allocates water to the sub-areas to maximize the intra- and intergenerational equity, and the sub-areas as the followers allocate water to their respective water departments to maximize their economic benefits and minimize water shortages. This method used affine functions between the decision variables (water allocation amount) and the uncertain parameters (WA, WD) to deal with the computationally intractable (NP-hard) robust counterpart for the multi-period water resources management. To illustrate the applicability and feasibility of this framework, a case study from Neijiang, China, is given. This model can assist regional authorities develop more robust water resource allocation solutions for multi-period planning responses to uncertain water deficiencies.