Stochastic order-based optimal design of a surface reservoir–irrigation district system

Abstract

This paper explores the effects of streamflow uncertainty and the type of stochastic order, which is used for comparing stochastic variables, on optimal design of a reservoir multi-crop irrigation district system. Four nonlinear mathematical programs with an economic objective function including deterministic, stochastic-EXP with expected value order, stochastic-SD with stochastic dominance (SD) order, and stochastic-EGCL with expected gain-confidence limit (EGCL) order were developed. Afterwards, the approaches of successive linear programming (SLP) and PSO–MC, which combines particle swarm optimization (PSO) algorithm and Monte Carlo simulation (MC), to solve the programs were selected. Hajiarab Irrigation District located in Ghazvin Province of Iran was used as a case study and the results obtained from using different programs and solution approaches were analyzed and compared. Among the solution approaches, SLP could not solve the programs other than the deterministic one while PSO–MC could find at least good solutions, if not the global optima, for all the programs. Among the main decision variables, the stochastic programs resulted in a reduced size of irrigation district compared with that obtained by the deterministic program. Moreover, the programs using stochastic orders other than a simple expected value converged at solutions different from the solution reached by the expected value-based program.