Double-sided stochastic chance-constrained linear fractional programming model for managing irrigation water under uncertainty

A double-sided stochastic chance-constrained linear fractional programming (DSCLFP) model is developed for managing irrigation water under uncertainty. The model is developed by incorporating double-sided stochastic chance-constrained programming (DSCCP) into a linear fractional programming (LFP) optimization framework. It can address ratio optimization problems with double-sided randomness (i.e. both left-hand and right-hand sides). More importantly, it also improves upon the existing stochastic chance-constrained programming for handing random uncertainties in the left-hand and right-hand sides of constraints simultaneously. A non-equivalent but sufficient linearization form of the DSCLFP is provided and proved, which will greatly reduce the computational burden. Then, the model is applied to a case study in Yingke Irrigation District (YID) in the middle reaches of the Heihe River Basin, northwest China. Four confidence levels (e.g. αi = 0.85, 0.90, 0.95 and 0.99) are provided to examine and compare the results. The objective function values are slightly decreased from 5.284 Yuan/m3 to 5.276 Yuan/m3 when αi level is raised from 0.85 to 0.99. The results from the DSCLFP can identify desired irrigation water allocation plans under the objective function of maximizing water productivity under different confidence levels. Therefore, the results can provide tradeoffs among water productivity, confidence level and constraint-violation risk level. Moreover, comparisons with double-sided stochastic chance-constrained linear programming (DSCLP) model and deterministic model are introduced to highlight advantages and feasibility of the developed model. Therefore, these results can provide decision-support for managers in arid areas.