Optimal sizing of irrigation delivery systems using a two-stage stochastic programming approach

In arid areas where the available water is limited and randomly changing with time, the surface irrigation might still be the best option due to economic and other considerations. Hence, the irrigation delivery system should be sized in such a way that the allocation of available surface water to different crops at any time yields maximum possible revenues. This can be ultimately achieved with the aid of a two-stage optimal formulation combining the present design stage with the future operational conditions. This work applies two stochastic mathematical techniques to determine the optimal sizes of a hypothetical surface irrigation delivery system subjected to varying deficit levels of available water and considering the uncertainties associated with the available water and the crop revenues. Canal sizes represented the first-stage decisions while the future water allocations were made in the second stage. The Regularized Stochastic Decomposition approach solved the case of stochastic available water present at the right hand side, while the L-Shaped method solved the case of stochastic second-objective coefficients associated with the crop selling prices. The L-Shaped method was also used to consider the problem of uncertain parameters in both the right hand side and the second-objective coefficients. The problem was investigated by considering a system of nine irrigation canals and six farms grown with different crops during a season of two distinctive irrigation periods. Results obtained from the stochastic formulation were compared with the corresponding ones obtained from an equivalent deterministic formulation. The comparison showed that the effect of parameter uncertainties on canal sizes and associated revenues increases with the increasing levels of deficit in water supply.