multi objective fractional programming model

This study aimed to determine the optimal cropping pattern and the optimal amount of water usage emphasizing on sustainability of water resources and optimizing the economic and environmental factors in Fariman-Torbatjam plain. In the first section of this research, the status of sustainability of water resource were analyzed using the sustainability indices and calculation the water balance of underground water in wet, normal and dry water years. Considering that the study aimed to propose the optimal crop pattern by emphasizing on agricultural sustainability and water resource along with maximizing gross margin, the Multi Objective Programming Models like Multi Objective Fractional Programming must be employed. The defined goals of this model are maximizing sustainable indices which involve the ratio of gross margin to water resource usage, chemical fertilizers and pesticides. By implementation of the optimal cropping pattern, the usage of water, chemical fertilizers and chemical pesticides compared to the current crop pattern will decrease by 10, 5.11 and 12.52 percent respectively and gross margin will be increased by 0.6 percent. Also, sustainability index of water, chemical fertilizers and chemical pesticides compared to current cropping pattern, will be increased by 11.78, 6.02 and 15 percent. In order to achieve to the quantitative sustainability of water resources, the ratio of water usage in agricultural sector to renewable water was used. With the implementation of the proposed optimum model, the water consumption will be reduced by 10 percent yearly, then the amount of water usage in agricultural sector in sudied area will be decreaesd by 0.7 of renewable water in 8 years, and then the quantitative and qualitative of sustainability of water resources will be achieved.