A multi objective mathematical modeling for crop planning problem under Z-number uncertainty

Agriculture is considered as one of the main sources of wealth in the economy. Because of its significant role in providing food, social welfare and economic growth, developing countries should keep it at the forefront of their economic plans to overcome the economic crisis. Management and planning of agricultural water resources are strategically vital. In this research, both cropping and import aspects of the products have been considered. The aim of this research is to study of land capability and existed resources for agriculture production so that it improves the economic and social conditions of the farmers in country. In this study, the data are collected from documented reports of the ministry of agricultural Jihad and the Iranian National Irrigation and Drainage Committee. A comprehensive mathematical model is presented that it aims to reduce the amount of water consumed, increase the production of strategic products, and consider the social factors such as the employment of local laborers. In fact, it is possible to determine how much water can be allocated and which product should be cropped so that both water resource management, and profitability is being guaranteed for farmers. Generally speaking, the nature of decision-making in the real world is uncertain, and finding a solution without regard to this issue will make the decision unrealistic. Fuzzy decision approach can be applied to tackle uncertainty in many problems, but this approach has its practical limitations, and in some circumstances, it may not be able to model the uncertainty accurately. Accordingly, we use a new concept of uncertainty which is called as the Z-number. To optimize multiple objectives, an interactive approach has been applied. The proposed mathematical model is linear one and is solved by Cplex software. In the country, there are no agricultural cropping patterns based on regional needs, the status of water resources and exports. This matter not only leads to the loss of water resources, but also have a significant impact on farmers' productivity losses and without a specific program, there may be a sharp price fluctuation of agricultural products in markets. Considering the strategic aspects of some agricultural products such as wheat, alfalfa and barley in the presented study, the production rate of these products is higher than other ones. Results show that the products will not be planted in 22% area of the land, and this is because the limitation of resources for planting or the import may be cost-effectiveness rather than planting. The results show that in the proposed model, the strategic importance of agricultural products directly effects on the amount of production of them. According to the statistics of the Ministry of Agriculture in 2014, 61.18% of the total agricultural products are covered in this research. The obtained results show that decision making based on the Z-number approach provides a conservatism solution rather than fuzzy and deterministic approaches.