Robust fractional programming approach for improving agricultural water-use efficiency under uncertainty

Water-use efficiency and uncertainty treatment are foci in the modeling of agricultural water management systems. To address these challenging issues, a robust fractional programming (RFP) method that coupled fractional programming with robust optimization was developed in this study to improve agricultural water-use efficiency under uncertainty. RFP improved upon the fractional programming by being able to tackle highly uncertain information without known distributions. It also extended the capability of the robust optimization method in addressing ratio optimal problems. To demonstrate its effectiveness and applicability, RFP was applied to a long-term agricultural water resources management problem in arid north-west China, where water scarcity and low water-use efficiency hindered local development. It generated benefit- and risk-explicit plans for crop pattern adjustments. Vegetables were recommended as the preferred crop. A number of scenarios combining different fluctuation and protection levels were analyzed and interpreted with practical implications. It was observed that higher water-use efficiency could be achieved through reducing parametric uncertainty and risk-aversion levels. Simulation experiments validated that the benefits claimed by the RFP model were sufficiently conservative and could be reliably achieved. The comparisons of RFP results against the baseline operations and those from two other alternatives demonstrated that, RFP could result in higher resource-use efficiency and controllable system-violation risks. The developed approach is also applicable to other optimization problems aiming at enhancing resource-use efficiency under uncertainty.