Determine the Appropriate Patterns of Crops by Implementation Fuzzy Goal Programming Model based on Various Scenarios (Case Study: a Farm in North Khorasan Province)

Introduction Agricultural planning by fuzzy mathematical models has been one of the favorite topics for many researchers especially in Agriculture. The models can help the farmers to plan better and more realistic for their various decisions. Fuzzy goal programming (FGP) is a mathematical models for solving the multi objective problems. In this regard, the purpose of this study is to determine the appropriate patterns of crops by implementation fuzzy goal programming model. Materials and Methods This study is performed in a farm in North Khorasan province, shirvan. The fuzzy goal programming model has been used based on different scenarios. The Variables used in the model of this study are the area of cultivated land for crops of Wheat, Joe, lentils, peas and beans. The goals of the problem including water, task force, hours machines, poison, phosphate fertilizer, urea fertilizer, potash fertilizer, cash costs, and incomes. Restriction on land is the only crisp constraint in the problem. In particular, at first the model of the problem has been defined based on the fuzzy membership function. In the present study is used the Zimmermann method to build membership functions related to the cause of the problem. Then, using the concept of volatility, the model is converted to a goal programming problem with nine goal (water, work force, hours machines, poison, phosphate fertilizer, urea fertilizer, potash fertilizer, cash costs, and incomes). Next, based on different combinations of the goals, eight scenarios have been designed based on income, cost, production resources, income-cost, income-production resources, cost-production resources, income-cost-production resources with equal weights, and income-cost-production resources with different weights. The model of each of these scenarios, with nine goals and four crisp constraints, has been solved using vibration concept and by WinQSB software. Results Discussion Based on the maximum level of reaching the goals, different scenarios consist of income, cost, production resources, income-cost, income-production resources, cost-production resources, income-cost-production resources with equal weights, and income-cost-production resources with different weights have been prioritized and four crop patterns have been detected. In first pattern, three scenario consist of scenario 1 (income), scenario 4 (income-cost) and scenario 5 (income-production resources) have combined. The second pattern have made scenario 2 (cost). In third pattern, scenario 3 (production resources), scenario 6 (cost-production resources) and scenario 7 (income-cost-production resources with equal weights) have combined. The scenario 8 (income-cost-production resources with different weights) have situated in fourth pattern, too. For each of the patterns, the level of reaching the goals have been different. In order to determine the appropriate pattern of crop have used the levels of swing by Euclidean distance. The main difference between the outputs of these patterns in the pursuit of culture favorable to the cause of labor, urea, and the income, so that the highest aspiration to achieve the desired level of labor have been to cultivation patterns 2 and 3. The highest ideal of achieving the desired level of urea fertilizer have been 3, and the highest aspirations and achieve the desired level of income of the cropping pattern have been to 1. Finally, the appropriate pattern of crop have selected based on the minimum Euclidean distance among of four patterns. Finally, Pattern 4 based on scenario 8 (income-cost-production resources with different weights) with the minimum swing of the desired level of the goals have selected as appropriate pattern. Patterns 2, 3 and 1 situated in next priorities. Conclusion In agriculture Planning, always looking for different purposes, which may sometimes these objectives are in conflict with each other. Due to this, the goal programming is a technique that can be cultivated in order to achieve proper patterns in agricultural planning, taking into consideration the different objectives. Since we cant always say with certainty about the numbers of the desired level objectives so the absolute numbers of goal programming model results may be desirable to have or not to conform to actual conditions. To resolve this problem, fuzzy goal programming can be utilized where in addition to considering the appropriate level of ideals, fluctuations are defined for each of them. In this study, using fuzzy goal programming models crops on a farm scenario was finally, a model was identified. Indeed, the proposed method of this study can help farmers in decision makings for detecting crop patterns so that they can reach to reach to the right decisions based on the limitations, the available resources and the importance of the goals. We can offer farmers in the decision-making process regarding the appropriate cropping patterns based on different scenarios and considering the conditions encountered in the environment has helped many to the restrictions on the amount of available resources and the importance of goals or aspirations account Adopt decisions for growing crops.