Excessive extraction of aquifers to produce agricultural products is reduced the amount of water in groundwater sources, in the manner that this amount decreasing follows irreversible effects in various areas. In order to decreasing difficulties resulting from decrease in amount of aquifer deciding in considerable level is needed. This matter has made balancing of aquifers as one of the important factors in water resources management. In this study, in order to recovery of groundwater sources and implementing extraction reduction in country's aquifers, as one of the equilibrium projects, optimization the cultivation pattern with economical approach and investigation changes farmer's profit with exploitation reduction scenarios to 1%, 3% and 5% From two popular perspectives and analytical comparisons between them is done in 1395. For optimize the cropping pattern, two perspectives of changing the cropping pattern have been used by NLP method and reduction of cultivated subspecies, and using PMP optimization method. Results of using extraction reduction scenarios in Qazvin plain's aquifer, which has yearly deficiency to the value of 376 MCM showed that in the scenarios of groundwater extraction, the values of 21. 2, 63. 7 & 106. 6 MCM of extraction are reduced from the aquifer of the case study. Also, the results of the analysis of the two planning methods showed that the NLP optimization model, gaining more economical profits than the PMP model.

In this paper, we show a procedure for solving multilevel fractional PROGRAMMING problems in a large hierarchical decentralized organization using fuzzy goal PROGRAMMING approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal PROGRAMMING approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

The main objective of present study was to determine the optimum plan for integrated crop and livestock from farms. Data was collected from with mixed activities of cattle raising and crop production in Marvdasht region, Fars province, as well as from experts in the fields of agronomy and animal science.Then, a representative farm was selected and, using the multi period MATHEMATICAL PROGRAMMING method, optimum farm plan was developed. In the first year, irrigated wheat was not included in the pattern, due to shortage of capital. In the secound year, alittle irrigated wheat was included, but the area of maize (for feed) and forage crops was reduced. In the third year, farming and livestock activities arrived at an equilliburium in forms of capita level. The optimum areas for irrigated wheat, maize (for"grain), maize (for feedd) and alfa were achieved at, respectively 1,6.5 ,6.5 and 6 hectares. The optimum number of cattle, calves, and heifers, too, was optimized at 30, 20, 20 and 10 , respectively. The sensitivity analysis proved that the planned performance was hishly flexible, and remained constant against fluctuations in input and output prices.The results demonstrated the advantages of dynamic PROGRAMMING over the conventional linear PROGRAMMING technique in determining the optimum farm plans. Intergration of livestock and farming activites was found as one of the effective ways of increasing the return and reducing the risk of investment.

Due to increasing demand for the scarce available water throughout the world it is an extremely important matter, in water management, to make serious attempts in determining its true economic value. This paper discusses the optimal allocation of water to agriculture, the relatively true economic value of water as well as the cropping patterns for the Shirvan Barzo (SB) dam area in North Khorasan Province of Iran. The analysis is based on linear PROGRAMMING (LP) and on multi goal linear PROGRAMMING (MGLP) models for determining solutions that can maximize net return to farmers. In the study, the priority of goals is developmental, social, economical, and environmental respectively. The results indicated that optimizing the cropping patterns along with proper the allocation of irrigation water has yet substantial potential to increase the net return from agriculture. It has already decreased the applied water as much as 19 percent. The results show that the economic value of each unit of agricultural water is estimated to be between 107 to 1296 IRR×104 per cubic meter. This suggests managing the allocation of water based on optimal models and bring water prices close to its true economic value to motivate the farmers to economize in the applied water.

In this paper, a new class of nonconvex optimization problem is considered, namely  $(h,\varphi)$-$(b,F,\rho)$-convexity is defined for $(h,\varphi)$-differentiable MATHEMATICAL PROGRAMMING problem. The sufficiency of the so-called Karush-Kuhn-Tucker optimality conditions are established for the considered $(h,\varphi)$-differentiable MATHEMATICAL PROGRAMMING problem under (generalized) $(h,\varphi)$-$(b,F,\rho)$-convexity hypotheses. Further, the so-called  Mond-Weir $(h,\varphi)$-dual problem is defined for the considered $(h,\varphi)$-differentiable MATHEMATICAL PROGRAMMING problem and several duality theorems in the sense of Mond-Weir are derived under appropriate (generalized) $(h,\varphi)$-$(b,F,\rho)$-convex assumptions.

Transportation costs today are considered as one of the most important costs affecting the cost of goods and the final price of consumption for the customer, especially in supply chain management. Therefore, it is necessary to focus on transportation costs due to lower prices, and consequently increase customer satisfaction and increase the position of the industry among competitors. Given that the available resources (capacity of supply centers) are generally considered as the minimum capacity available in the model, generally to solve such models, first the fuzzy supply limit is definitively converted and then using methods. The existing solution is a crisp problem that unfortunately does not fit well with the nature of the uncertainty in the decision. Therefore, in this paper, in order to adapt to the real conditions, the supply constraint in the flexible fuzzy transportation model is studied. For this purpose, a fuzzy MATHEMATICAL PROGRAMMING approach to the transportation problem with flexible fuzzy constraints is proposed to obtain the most satisfactory solution. Finally, a numerical example for the proposed model and the proposed solution method is considered.

Transportation costs today are considered as one of the most important costs affecting the cost of goods and the final price of consumption for the customer, especially in supply chain management. Therefore, it is necessary to focus on transportation costs due to lower prices, and consequently increase customer satisfaction and increase the position of the industry among competitors. Given that the available resources (capacity of supply centers) are generally considered as the minimum capacity available in the model, generally to solve such models, first the fuzzy supply limit is definitively converted and then using methods. The existing solution is a crisp problem that unfortunately does not fit well with the nature of the uncertainty in the decision. Therefore, in this paper, in order to adapt to the real conditions, the supply constraint in the flexible fuzzy transportation model is studied. For this purpose, a fuzzy MATHEMATICAL PROGRAMMING approach to the transportation problem with flexible fuzzy constraints is proposed to obtain the most satisfactory solution. Finally, a numerical example for the proposed model and the proposed solution method is considered.

In this paper, we introduce a new MATHEMATICAL PROGRAMMING approach to estimate the parameters of fuzzy linear regression with crisp/fuzzy input and fuzzy output. The advantage of this approach is, both of dependent and independent variables are influenced on the objective function. Therefore, this model rectifies some problems about outliers. Also, in this paper we use possibility function in constraints. To compare the performance of the proposed approach with previous methods, three examples are presented.