Investigating the effects of management of irrigation water distribution on farmers' gross profit under uncertainty: A new positive mathematical programming model

The Middle Eastern countries along with Iran possess an arid to semi-arid climates. For this reason, they encounter many problems in water supply and distribution within different sectors, especially agriculture. Hence, it is necessary to achieve some strategies for optimal, efficient and fair use of water supplies and irrigation grids to manage water allocation and distribution for irrigation in agricultural sector to reduce water wastes. To this end, the present study mainly aims to formulate a model for optimal water distribution for irrigation under uncertain conditions and the impact of water redistribution on the gross profit of farmers. In this study, positive mathematical programming was used and for applying uncertainty in water transfer model, robust optimization method was utilized. A combination of these two methods led to invention of a robust positive mathematical programming (RPMP) model. Tajan Irrigation and Drainage Network in northern Iran was selected as a case study to evaluate the ability of the proposed model. The results showed that with the increase in the probability of deviation (p) of the available water constraint, area under cultivation of all the selected crops decreases, and this can reduce production ultimately declining farmers' gross profits. Also, as the probability level (p) increases, amount of water transfer from upstream to downstream of irrigation and drainage network increases. Thus, cultivation structure should be mitigated for farming crops in order to prevent from reduced profit for farmers. The results of Monte Carlo Simulation indicated that using results of RPMP model were reliable and it might noticeably contribute to changing cultivation pattern. •A Robust Positive Mathematical Programming (RPMP) model was designed for optimal distribution of irrigation water.•A real case study in Iran was used to evaluate the capability of the proposed model.•There was a significant trade-off between farmers' profits and the degree of conservatism.•Monte Carlo simulation results proved the reliability of the RPMP model.