List of Articles برنامه‌ریزی خطی

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  1 - A revisit of a mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers
  A. Ebrahimnejad
  In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP More

  In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi–objective linear programming (MOLP) problem with crisp constraints and then a lexicographic ordering method is used for solving the resulting MOLP problem. However, this approach cannot be used for finding the fuzzy optimal solution of FFLP problems with inequality constraints. The aim of this study is to point out and correct some errors in the definitions, notations operations and fuzzy ordering of the current approach for solving FFLP problems with fuzzy inequality constraints. Hence, a modified approach to obtain the fuzzy optimal solution of the FFLP problems with inequality constraints is proposed. Finally, several numerical examples are presented to illustrate the proposed approach. Manuscript profile
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  2 - A New Method for Solving the Fully Interval Bilevel Linear Programming Problem with Equal Constraints
  seyyedeh farkhondeh tayebnasab farhad hamidi mehdi allahdadi
  Most research on bilevel linear programming problem is focused on its deterministic form, in which the coefficients and decision variables in the objective functions and constraints are assumed to be crisp. In fact, due to inaccurate information, it is difficult to know More

  Most research on bilevel linear programming problem is focused on its deterministic form, in which the coefficients and decision variables in the objective functions and constraints are assumed to be crisp. In fact, due to inaccurate information, it is difficult to know exactly values of coefficients that used to construct a bilevel model. The interval set theory is suitable for describing and solving uncertainty and inaccuracy in these decision-making issues. For this reason, interval bilevel linear programming problem, in which the coefficients in both objective functions and constraints are interval, is an attractive subject. In this paper, we consider a type of interval bilevel linear programming problem full , in which all the coefficients in both objective functions and constraints are interval. The purpose of this paper is to present a new method for solving fully interval bilevel linear programming problem with equality constraints. By providing numerical examples, the implementation of this method is expressed. economics and in the problems that we have certain, converting to interval programming a, is studied problems simply Manuscript profile
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  3 - Estimating the Solution of the Best-Worst Method Non-Linear Programming Model by solving the Mixed Integer Linear Programming Model Solutions
  Mohammad Reza Dehghani Mehdi Abbasi
  The Best-Worst Method (BWM) is one of the latest methods in Multiple Attribute Decision Making (MADM) problems. The mentioned method determines the optimal solution by forming and solving a Non-Linear Programming Model (NLPM). In respect to the difficulties of solving t More

  The Best-Worst Method (BWM) is one of the latest methods in Multiple Attribute Decision Making (MADM) problems. The mentioned method determines the optimal solution by forming and solving a Non-Linear Programming Model (NLPM). In respect to the difficulties of solving the relevant NLPM, some attempts have been made to provide Linear Programming Models (LPM) or Equivalent Mixed Linear Programming Models. But there are some deficiencies in each of the proposed models. In this paper, by removing the mentioned deficiencies, an algorithm was proposed to estimate the solution of BWM NLPM with an acceptable error by forming and solving Mixed Integer Linear Programming Models (MILPMs). In the suggested algorithm, first, the equivalent model of NLPM (ENLPM) was formed. Then by Piecewise Linear Approximation (PLA) using the SOS2 method, the non-linear sentences of ENLPM were approximated and the first MILP model was formed and solved. If the error of solution is not acceptable, improving the PLA of the ENLPM nonlinear sentences, the forming of new MILPMs, and its solving continues until a solution with acceptable error obtained. To investigate the reliability of the algorithm, a new method for generating samples was proposed. Then using this method, 128 samples with three and five attributes were generated. The results of implementing the proposed algorithm to solve generated samples showed the performance and efficiency of the proposed algorithm. In this regard by forming and solving a maximum of three MILPMs of the samples, an estimation of the solution with 1% error was obtained. Manuscript profile
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  4 - A New Approach to Solve Fully Fuzzy Linear Programming with Trapezoidal Numbers Using Conversion Functions
  S.H. Nasseri
  Recently, fuzzy linear programming problems have been considered by many. In the literature of fuzzy linear programming several models are offered and therefore some various methods have been suggested to solve these problems. One of the most important of these problems More

  Recently, fuzzy linear programming problems have been considered by many. In the literature of fuzzy linear programming several models are offered and therefore some various methods have been suggested to solve these problems. One of the most important of these problems that recently has been considered; are Fully Fuzzy Linear Programming (FFLP), which all coefficients and variables of the problem are the same kind of fuzzy numbers. One of most common of them is the model in which all fuzzy parameters are discussed by triangle numbers. In this paper, we first define a fully fuzzy linear programming with trapezoidal numbers and then suggest a new method based on reducing the original problem to the problem with triangle number. Specially, a conversion function for converting two trapezoidal and triangular numbers to each other is offered. Finally, the mentioned method is illustrated by a numerical example. Manuscript profile
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  5 - A bi-level linear programming problem for computing the nadir point in MOLP
  J. Vakili H. Dehghani
  Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the More

  Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a convex set which is a convex optimization problem‎, ‎but the problem of computing ‎the nadir point in MOLP is equivalent to solving a nonconvex optimization‎problem whose solving is very hard in the general case‎. ‎‎In this paper‎, ‎a bi-level linear programming problem is presented for obtaining the nadirpoint in MOLP problems which can be used in general to optimize a ‎linear function on the nondominated set‎, ‎as well‎. Then‎, ‎as one of the solution methods of this problem‎, ‎a‎mixed-integer linear programming problem is presented which obtains ‎the exact nadir values in one stage‎. Manuscript profile
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  6 - The Calculation of the output price vectorby applying reverse linear programming: The novel approach in DEA
  S. Sadri M. Rostamy-Malkhalifeh
  In the today’s world wherein every routine is based on economic factors, there is no doubt that theoretical sciences are driven by their capabilities and affordances in terms of economy. As a mathematical tool, data envelopment analysis (DEA) is provided to econom More

  In the today’s world wherein every routine is based on economic factors, there is no doubt that theoretical sciences are driven by their capabilities and affordances in terms of economy. As a mathematical tool, data envelopment analysis (DEA) is provided to economics, so that one can investigate associated costs, prices and revenues of economic units. Data Envelopment Analysis (DEA) is a linear programming technique used for measuring the relative efficiency of decision making units based on input and output data. One of the applications of this technique is calculation of revenue efficiency. Methods of revenue efficiency calculation in DEA are generally presented for obtaining maximum revenue from output selling, these methods are not sufficiently efficient for evaluation of all system including network systems due to ignoring the internal structure of units and their middle products. Therefore, in this article, in addition to introduction of inverse linear programming in DEA and its application in calculating revenue efficiency, a new method is presented which considers the network structure of units, the ability to determine the optimal price and appropriate costs for efficiency of the unit. The proposed numerical examples demonstrated the superiority of the proposed methods over the traditional data envelopment analyses. Manuscript profile
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  7 - Portfolio selection by Using Multi Attribute Decision Making based on grey relational analysis and linear programming
  A. Asghar Anvari Rostami Mahdis Taghavi M. Ebrahim Aghababaei
  One of the most important challenges in the stock market for investors is selecting Portfolio. This study by considering the financial ratios as evaluating indicators tries to determine appropriate model for investment decisions in stocks. In this study, the combination More

  One of the most important challenges in the stock market for investors is selecting Portfolio. This study by considering the financial ratios as evaluating indicators tries to determine appropriate model for investment decisions in stocks. In this study, the combination of respectively models, linear regression, multi attribute decision making and linear programming were used to forecast the future of financial ratio trends, ranking companies and asset allocation. In the first step of study, after selecting 17 financial ratios and indicators as variables of the hybrid model, their values from the first quarter of 2007 to the first quarter of 2015 was calculated for companies included in the sample. Then by using the moving average with exogenous inputs and Auto Regressive Moving Average with exogenous input, these variables were predicted for the studied period (second quarter 2015). In the next step, we used Shannon entropy to determine the weight of indexes and the grey relational analysis for ranking companies. Finally, by using a linear programming model, a model was developed to select the optimal portfolio. According to this model, a portfolio of stocks formed and by using the Sharp ratio, its performance was compared with the overall index and the top 50 index. The results showed that the hybrid model has had a better performance than the overall index and the top 50 index, in the period of the study. Manuscript profile
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  8 - Application of Simplex method and Mitigation Concept in Participatory Environmental Impact Assessment (Case study: Compost Plants and Landfill Alternatives in Golestan Province)
  Samaneh Deziani Abdolrasoul Salmanmahiny
  10.22034/jest.2017.10733
  Background and Objective: Environmental impact assessment studies are one of the proper means of ensuring a sustainable development. Determining limitations and mitigation procedures for the negative effects compose the main core of the EIA procedure, in case the sugges More

  Background and Objective: Environmental impact assessment studies are one of the proper means of ensuring a sustainable development. Determining limitations and mitigation procedures for the negative effects compose the main core of the EIA procedure, in case the suggested development has been allowed. In this study, impact assessment has been applied for five suggested compost and landfill sites in Golestan Province of Iran. Method: In this study, considering the associated costs, linear programming has been applied to rank the proposed landfill and compost plant sites. For this purpose, GIS data has been used and the optimum site selection process has been implemented. The site has been determined so as to minimize the likely impacts. Findings: The results show that by using linear programming, site 1 on the eastern part with a slight difference to others, and site 5 in the west,ern part with the least goal function value are the best. The most effective parameters for the sites 1 to 4 is underground water pollution, and for site 5 is loss of valuable land. However, at the site 5, the impact on the neighboring no-hunting area is more important than underground water pollution, considering costs and the required time for mitigation efforts. Conclusion: Using the minimum and maximum levels of mitigation levels shows that increase of mitigation can reduce pollution, and vice versa. Sensitivity analysis confirms the accuracy of this method. Manuscript profile
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  9 - رهیافتی جدید برای حل مسئله برنامه‌ریزی خطی دو ترازه تماما فازی
  S. F. Tayebnasab F. Hamidi M. Allahdadi
  در این مقاله، یک نوع از مسئله برنامه‌ریزی خطی دو ترازه تماما فازی را که در آن تمام ضرایب و متغیرهای تصمیم‌گیری در هر دو تابع هدف و قید ‌ها به عنوان اعداد فازی مثلثی بیان شده‌اند در نظر می­گیریم. به منظور بدست آوردن جواب بهینه­ی فازی، رهیافت کارامد جدیدی  بر More

  در این مقاله، یک نوع از مسئله برنامه‌ریزی خطی دو ترازه تماما فازی را که در آن تمام ضرایب و متغیرهای تصمیم‌گیری در هر دو تابع هدف و قید ‌ها به عنوان اعداد فازی مثلثی بیان شده‌اند در نظر می­گیریم. به منظور بدست آوردن جواب بهینه­ی فازی، رهیافت کارامد جدیدی  برای مسئله­ی برنامه ریزی خطی دوترازه­ی تماما فازی با پارامترها و متغیرهای فازی ارایه شده است. این رهیافت بر اساس برنامه ریزی دوترازه­ی قطعی می‌باشد. در نهایت، مثال‌های عددی برای نشان دادن قابلیت پیاده‌سازی روش‌های مورد نظر ارائه گردیده است. Manuscript profile
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  10 - Optimal utilization of Reservoir by using of linear programming model (Case study: Dorudzan dam)
  Hassan Torabi reza dehghani Ahmad Godarzi
  Optimal utilization of multi-purpose reservoirs is one of the complex and sometimes non-linear issues in multi-objective optimization. One of the appropriate decision-making ways for optimal utilization of the water resources was the modeling of optimization problems of More

  Optimal utilization of multi-purpose reservoirs is one of the complex and sometimes non-linear issues in multi-objective optimization. One of the appropriate decision-making ways for optimal utilization of the water resources was the modeling of optimization problems of utilization from dam reservoir by using of different mathematical methods. In this study was evaluated, the current status of utilization and providing of optimum utilization and appropriate policy for the dam reservoir. For this purpose was used linear programming model and optimization of utilization of intended reservoir dam model. Evaporation simulation of the system were performed by using imput flow. The results showed that the existing policy of reservoir utilization, only in the raining pick months is capable of demand meeting, while low-water months are critical use-months. Also, the value of reservoir saving by using of linear programming model at SQ method estimated in about 23% more than the existing reservoir utilization method. In conclusion, the result showed that using of linear programming model can be effective in optimal utilization of reservoir dams. Which inturn helps to facilitate the development and implementation of water resources management strategies. Manuscript profile
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  11 - Mathematical modeling and solution method of Milkran logistics in Saipa ‎Group's inbound supply chain under consideration of order time windows, ‎return cost of empty pallets and in-vehicle loading restrictions
  Masoum Najafian Ali Husseinzadeh Kashan Davood Mohammaditabar ALiakbar Akbari
  10.30495/imj.2022.688760
  In the Milkran logistics system, vehicles are sent to collect orders from suppliers and deliver them to ‎assembly lines, according to pre-planned routes. In this way, the vehicle goes to the location of ‎several suppliers to pick up orders and then is sent to on More

  In the Milkran logistics system, vehicles are sent to collect orders from suppliers and deliver them to ‎assembly lines, according to pre-planned routes. In this way, the vehicle goes to the location of ‎several suppliers to pick up orders and then is sent to one or more destinations for delivery. In this ‎logistics system, cargoes are aggregated within the vehicle and through various nodes in the logistics ‎network. This paper introduces a mixed integer linear programming model for the Milkran logistics ‎problem that takes into account considerations such as three-dimensional loading of the order ‎pallets into vehicles, 50% higher cost for returning empty pallets, order timewindows, and ‎heterogeneous fleets. Given the nature of the problem, an algorithm based on grouping evolutionary ‎strategy is introduced that uses heuristic methods to ensure vehicles’ loading and routing feasibility. ‎The effectiveness of the introduced mathematical model and meta-heuristic algorithm is measured ‎using data collected from Saipa Automotive Group. The computational results show that Milkran ‎Logistics has the ability to reduce costs by 24.5% (on average), compared to the direct shipping ‎strategy pursued by Saipa.‎ Manuscript profile
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  12 - Optimization of Fuller Experimental Formula Regional Coefficients by Linear Programming and Genetic Algorithm in unguaged watersheds with Spatial Data
  Ebrahim Yousefi Mobarhan Ebrahim karimi sanghchini behroz arasto Ali Asghar Hashemi
  One of the methods used for calculating flood peak discharge in non-statistical watersheds is experimental methods. One of the empirical methods used in this study is the Fuller method which has advantages over other empirical methods for different flood periods. In thi More

  One of the methods used for calculating flood peak discharge in non-statistical watersheds is experimental methods. One of the empirical methods used in this study is the Fuller method which has advantages over other empirical methods for different flood periods. In this research, we have compared the linear programming optimization techniques and genetic algorithm in optimizing the fuller experimental formula coefficients in Excel and MATLAB respectively for selected watersheds of the region. For this purpose, the statistics of maximum 24-hour discharge of 9 stations in West Azarbaijan province with a statistical period of 21 years were studied. Comparison of the results showed the superiority of the genetic algorithm method and then linear programming. The results also show that the use of smart search methods improves the performance of conventional methods significantly. For this purpose, the statistics of maximum 24-hour discharge of 9 stations in West Azarbaijan province with a statistical period of 21 years were studied. Comparison of the results showed the superiority of the genetic algorithm method and then linear programming. The results also show that the use of smart search methods improves the performance of conventional methods significantly. For this purpose, the statistics of maximum 24-hour discharge of 9 stations in West Azarbaijan province with a statistical period of 21 years were studied. Comparison of the results showed the superiority of the genetic algorithm method and then linear programming. The results also show that the use of smart search methods improves the performance of conventional methods significantly. Manuscript profile
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  13 - Bi-Level Energy Management Optimization in Multi-Area Smart Grids
  Mohammad Ali Hormozi Bahman Bahmani Firoozi Taher Niknam
  Optimal energy management in multi area smart grids will increase social welfare, reduce economic costs and environmental pollution. Power management solutions for smart grids include issues such as economical distribution of load, suitable load management, optimized ch More

  Optimal energy management in multi area smart grids will increase social welfare, reduce economic costs and environmental pollution. Power management solutions for smart grids include issues such as economical distribution of load, suitable load management, optimized charging and discharging of energy storages, and the availability of renewable resources considering limitation of power exchange in different area, all of which are issues in an intelligent grid, that in this paper has been considered. This paper presents a bi-level mixed integer quadratic programming (MIQP) model for energy management in multi-are smart grids with the aim of reducing economic costs and environmental pollution and increasing social welfare by considering energy storage systems, load management and Renewable resources are presented. In this paper presents a bi-level approach that the upper level is formulated to minimization economic cost and pollution of resource and lower level is presented to maximization social welfare in the form of Karush–Kuhn–Tucker (KKT) conditions. The simulation is implemented in MATLAB with Gurobi solver that the results show that the proposed bi-level model is also an efficient way to optimize energy in multi-area smart grids compared to Pareto front and Weight methods. Manuscript profile
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  14 - Bi-Level Optimization Model for Coordinated Management of Integrated Transmission and Distribution Systems
  Roozbeh Tamizkar Mahmoud Samiei Moghaddam Azita Azarfar Mohamad Hosseini Abardeh Mojtaba Vahedi
  In this paper, a bi-level optimization model is proposed for the coordinated management of integrated transmission and distribution networks. The problem of the security-constrained unit commitment as an upper-level problem to reduce operating costs, startup/shutdown co More

  In this paper, a bi-level optimization model is proposed for the coordinated management of integrated transmission and distribution networks. The problem of the security-constrained unit commitment as an upper-level problem to reduce operating costs, startup/shutdown costs, and no-load along with load shedding as a mixed integer linear programming model and the problem of optimal operation in independent distribution networks by considering renewable and non-renewable resources along with charging stations for electric vehicles as a lower-level problem to reduce the costs of purchasing power from the upstream network and reduce the costs of power outages. The resources and charging power of electric vehicle charging stations are considered a linear model. To solve the bi-level problem, the proposed lower-level model is modeled as Karush-Kahn-Tucker optimality conditions. Several different networks have been considered for validating the model and the proposed method, and the results obtained from the simulation prove the efficiency of the model and the proposed method in considering the coordinated operation of intelligent transmission and distribution networks. To show the superiority of the proposed method over other algorithms for solving multilevel models, the proposed method has been compared with decomposition algorithms, and the results show the superiority of the proposed method in terms of execution time and faster convergence. Manuscript profile
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  15 - Optimal Allocation of Water Using Fuzzy Programming Models
  Morteza Molaei Javad Hosseinzad Firouzy
  To achieve goals such as economic growth, food security and sustainability of scarce resources, including water resources depends more than ever to correct use of these resources.‌ Climatic  More

  To achieve goals such as economic growth, food security and sustainability of scarce resources, including water resources depends more than ever to correct use of these resources.‌ Climatic characteristics of our country, wasting too much water in various uses, especially its low efficiency in the agricultural sector, unwillingness of private sector in investment in water resources development and inappropriate patterns of the crop pattern at one hand, and Scarcity of water resources on the other hand has led the optimal allocation of water to be of interest and importance. Accordingly, the aim of this study is to estimate the real value (shadow price) of water and determine the optimal cropping pattern with regard to products that are more efficient in using of water. For this purpose Fuzzy linear programming model used and the results are compared with exact linear programming model. Results for lands under coverage of Alavian dam show that the real price of water by using both models is identical and equal to 198 Rials per cubic meter, but profits per unit of water consumed in the fuzzy model is much more definite pattern.            Manuscript profile
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  16 - Optimal Portfolio Diversification Strategy Using WCVaR Risk Criteria and Its Comparison with Monte Carlo Method
  Mohammad reza Haddadi seyed parviz jalili kamju sara goodarzi dahrizi
  Choosing an optimal portfolio is one of the main goals of financial management. The initial strategy is to zero the risk of non-systematic risk by diversification in the optimal portfolio. In this research, WCVaR applied model and linear programming method for stock mar More

  Choosing an optimal portfolio is one of the main goals of financial management. The initial strategy is to zero the risk of non-systematic risk by diversification in the optimal portfolio. In this research, WCVaR applied model and linear programming method for stock market risk measurement and selection of a weight optimized portfolio were used. WCVaR is one of the newest risk measurements and covers the defects of the VaR and CVaR models. This research 11-year period information (1387 -1397) was used from actual data of 10 different companies accepted in Tehran Stock Exchange. This research uses data from ten companies accepted in TESM during the period of 1397-1387. The results of model estimation using the linear programming method in Matlab software showed that changing the benchmark optimization would lead to a change in the weight of the basket stock and change the strategy of diversification in the optimal portfolio. The results of estimating the model using the linear programming method showed that changing the optimization criterion will lead to a change in the stock weight of the portfolio and a change in the diversification strategy in the optimal stock portfolio. Among the 44 baskets with different weights, the most optimal Manuscript profile
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  17 - ارائه مدل برنامه ریزی خطی بر مبنای
  زهرا امیرحسینی معصومه قبادی
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  18 - مدل برنامه‌ریزی خطی فازی برای ﻣﺴﺌﻠﻪ اﻧﺘﺨﺎب ﺳﺒﺪ ﺳﻬﺎم بهینه
  مقصود امیری مهسا محبوب قدسی
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  19 - Comparing Three Methods of Linear, Goal and Fuzzy Programming in Optimal Combination of Resources and Consumption in Agriculture Bank
  Seyed Mohammad Reza Hosseinipour Simin Mohseni Masoud Jafari Moghaddam
  The aim of this study is to present a mathematical model according to mathematical programming models also to weave the agriculture bank and in the year of 2016 which is the best year of combination of loans and deposits that while customer satisfaction, the most profit More

  The aim of this study is to present a mathematical model according to mathematical programming models also to weave the agriculture bank and in the year of 2016 which is the best year of combination of loans and deposits that while customer satisfaction, the most profitable for banks are to be followed. In this research, the sample size is equal to the statistical population and including all branches of Agricultural Bank of Kerman province. Also the model is estimated by using of 3 programming methods: linear, goal and fuzzy. Some soft wares like Excel and Win QSB were used for analyzing this data. Due to the results, linear and goal programming are more allocation and the proceeds of the grant increased by using linear and goal programming than fuzzy programming and the bank current allocation. The results suggest that using linear and goal programming can help the managers for allocating resources so that higher yields will be achieved. Manuscript profile