Robust energy optimization of irrigation allocation under water scarcity

Abstract

Energy-efficient irrigation allocation under water scarcity must account for yield preservation and parameter uncertainty. This study minimizes pumping electricity while retaining the yield-index floor achieved by proportional allocation over the same uncertainty set, and identifies the conditions for strict energy savings. A seasonal water–yield relationship, an upper bound on pumping electricity and budgeted uncertainty are combined in a linear robust model. A feasible reference policy establishes energy non-inferiority; a feasible-direction criterion characterizes strict improvement. In an entirely synthetic three-field example, a water limit of 131,250 m³ and Γ = 1.5 retain a robust index floor of 62.70% while reducing the electricity upper bound from 36,392.5 to 36,249.8 kWh, a 0.39% reduction. The nominal policy reduces this bound by 3.04% but violates the same robust floor by 1.30 percentage points. Across 24 additional generated systems, robust reductions range from 8.16% to 18.43%; the nominal policy violates the reference floor in every case. Results are checked against a separate vertex formulation, adversarial optimization and primal–dual agreement. The contribution is a transparent decision framework linking the comparator, uncertainty set and marginal conditions. Field effectiveness and calibrated risk guarantees remain unestablished.