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1

S. Mohan, S. Mohan, and Dr S. Sekar Dr. S. Sekar. "Linear Programming Problem with Homogeneous Constraints." Indian Journal of Applied Research 4, no. 3 (2011): 298–307. http://dx.doi.org/10.15373/2249555x/mar2014/90.

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2

D, Sempavazhaam, Jothi K, and Kamali S. Nandhini A. Princy Rebekah J. "A Study on Linear Programming Problem." International Journal of Trend in Scientific Research and Development Volume-3, Issue-2 (2019): 903–4. http://dx.doi.org/10.31142/ijtsrd21539.

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3

Mahjoub Mohammed Hussein, Elfarazdag. "Application of Linear Programming (Transportation Problem)." International Journal of Science and Research (IJSR) 12, no. 3 (2023): 452–54. http://dx.doi.org/10.21275/sr21222020051.

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4

Gebreanenya, Haftom. "Integer Linear Programming Problem in Messebo Cement Factory." International journal of Emerging Trends in Science and Technology 03, no. 12 (2016): 4858–65. http://dx.doi.org/10.18535/ijetst/v3i12.10.

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5

Hussian, Abdel-Nasser, Mai Mohamed, Mohamed Abdel-Baset, and Florentin Smarandache. "Neutrosophic Linear Programming Problem." Mathematical Sciences Letters 6, no. 3 (2017): 319–24. http://dx.doi.org/10.18576/msl/060315.

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6

Ahuja, R. K. "Minimax linear programming problem." Operations Research Letters 4, no. 3 (1985): 131–34. http://dx.doi.org/10.1016/0167-6377(85)90017-3.

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7

Princy Flora, M. "Solving Fuzzy Linear Programming as Multi Objective Linear Programming Problem." Asian Journal of Science and Applied Technology 5, no. 1 (2016): 28–32. http://dx.doi.org/10.51983/ajsat-2016.5.1.2545.

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The constraints and the objective function of the fuzzy linear programming problem are converted into the multi-objective optimization problem (i.e.,) into an equivalent crisp linear problem.Finally, the multi-objective linear programming problem is converted into the weighted linear programming problem to show that they are independent of weights and obtained the complete optimal solution.
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8

Stetsyuk, P., O. Lykhovyd, and A. Suprun. "On Linear and Quadratic Two-Stage Transportation Problem." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 5–14. http://dx.doi.org/10.34229/2707-451x.20.4.1.

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Introduction. When formulating the classical two-stage transportation problem, it is assumed that the product is transported from suppliers to consumers through intermediate points. Intermediary firms and various kinds of storage facilities (warehouses) can act as intermediate points. The article discusses two mathematical models for two-stage transportation problem (linear programming problem and quadratic programming problem) and a fairly universal way to solve them using modern software. It uses the description of the problem in the modeling language AMPL (A Mathematical Programming Language) and depends on which of the known programs is chosen to solve the problem of linear or quadratic programming. The purpose of the article is to propose the use of AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems, to formulate a mathematical model of a quadratic programming two-stage transportation problem and to investigate its properties. Results. The properties of two variants of a two-stage transportation problem are described: a linear programming problem and a quadratic programming problem. An AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems is given. The results of the calculation using Gurobi program for a linear programming two-stage transportation problem, which has many solutions, are presented and analyzed. A quadratic programming two-stage transportation problem was formulated and conditions were found under which it has unique solution. Conclusions. The developed AMPL-code for a linear programming two-stage transportation problem and its modification for a quadratic programming two-stage transportation problem can be used to solve various logistics transportation problems using modern software for solving mathematical programming problems. The developed AMPL code can be easily adapted to take into account the lower and upper bounds for the quantity of products transported from suppliers to intermediate points and from intermediate points to consumers. Keywords: transportation problem, linear programming problem, AMPL modeling language, Gurobi program, quadratic programming problem.
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9

Ka, Pratik, S. Suma, and Vishwas B R. "Solving Linear Programming Problems Using AMPL Modeling LanguageSolving Linear Programming Problems Using AMPL Modeling Language." International Journal of Research and Review 9, no. 11 (2022): 66–69. http://dx.doi.org/10.52403/ijrr.20221110.

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Optimization problems arise in many contexts. A modelling language like AMPL makes it easier to experiment with formulations and use the right solvers to address the resultant optimization issues. Variables, objectives, constraints, sets of possible parameters, and notations that resemble well-known mathematical notation can all be stated using AMPL. The AMPL command language enables computation and display of data regarding the specifics of a problem and the solutions provided by solvers. It also enables the modification of problem formulations and the resolution of problem chains. Both continuous and discrete optimization issues are addressed by AMPL. In this paper, AMPL is used to solve different optimization problems such as Wyndor Glass problem, Transportation and Assignment problem and Purchase Planning problem. Keywords: Optimization, AMPL, Wyndor Glass Problem, Transportation and Assignment Problem, Purchase Planning Problem
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10

ZANGIABADI, M., and H. R. MALEKI. "A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE." Asia-Pacific Journal of Operational Research 24, no. 04 (2007): 557–73. http://dx.doi.org/10.1142/s0217595907001395.

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In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.
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11

Toloo, Mehdi. "An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach." Mathematics 9, no. 14 (2021): 1586. http://dx.doi.org/10.3390/math9141586.

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Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.
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12

Someshwar, Siddi* Dr. Y. Raghunatha Reddy. "SOLUTION OF INTEGER LINEAR PROGRAMMING PROBLEMS WITH TRIANGULAR FUZZY NUMBERS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 3 (2017): 325–28. https://doi.org/10.5281/zenodo.400958.

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Fuzzy Integer Linear Programming problem is an application of fuzzy set theory in linear decision problems and most of these problems are related to linear programming with fuzzy variables. In this paper, we proposed a method for Integer linear programming problems with fuzzy variables. Two numerical examples were illustrated with the help of the proposed method. This method is a simple tool for the best solution to a variety of Integer linear programming problems.
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13

Calvete, Herminia I., and Carmen Galé. "The bilevel linear/linear fractional programming problem." European Journal of Operational Research 114, no. 1 (1999): 188–97. http://dx.doi.org/10.1016/s0377-2217(98)00078-2.

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14

Mathur, K., S. Bansal, and M. C. Puri. "Bicriteria bottleneck linear programming problem." Optimization 28, no. 2 (1993): 165–70. http://dx.doi.org/10.1080/02331939308843911.

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15

Ahuja, Ravindra K. "The balanced linear programming problem." European Journal of Operational Research 101, no. 1 (1997): 29–38. http://dx.doi.org/10.1016/s0377-2217(96)00142-7.

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16

Vicente, L., G. Savard, and J. Judice. "Discrete linear bilevel programming problem." Journal of Optimization Theory and Applications 89, no. 3 (1996): 597–614. http://dx.doi.org/10.1007/bf02275351.

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17

Saif, Nagib M. A., and Gerhard-Wilhelm Weber. "Inverse Linear Goal Programming Problem." Thamar University Journal of Natural & Applied Sciences 3, no. 3 (2023): 67–76. http://dx.doi.org/10.59167/tujnas.v3i3.1284.

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This paper considers the inverse linear goal programming problem of multi-objective function in case the change in coefficient of the objective function. 
 Let denote the set of feasible solutions points of linear goal programming problem of a multi-objective function, and let be the positive and negative deviation variables of the maximum and minimum goals respectively, be a specified cost vector, be given feasible solution vector, and be given tow vectors denoted the feasible positive deviation and the feasible negative deviation points of the max or min goals, respectively.
 The inverse linear goal programming problem of multi-objective function is as follows:
 Consider the change of the cost vectors as less as possible such that the vectors feasible solution becomes an optimal solution of LGP of multi-objective function under the new cost vectors and is minimal, where is some selected -norm. 
 In this paper, we consider the inverse version ILGP of LGMP. under the -norm where the objective is to minimize , with denoting the index set of variables . We show that the inverse version of the considered under -norm reduces to solving a problem for the same kind; that is, an inverse multi-objective assignment problem reduces to an assignment problem.
 
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18

Gorelik, Victor, and Tatiana Zolotova. "Linear-quadratic programming and its application to data correction of improper linear programming problems." Open Computer Science 10, no. 1 (2020): 48–55. http://dx.doi.org/10.1515/comp-2020-0005.

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AbstractThe problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.
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19

Moshirvaziri, Khosrow, Mahyar A. Amouzegar, and Stephen E. Jacobsen. "Test problem construction for linear bilevel programming problems." Journal of Global Optimization 8, no. 3 (1996): 235–43. http://dx.doi.org/10.1007/bf00121267.

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20

Sinha, S. B., A. Biswas, and M. P. Biswal. "Linear Programming Approach to Solve Geometric Programming Problem." Journal of Information and Optimization Sciences 10, no. 1 (1989): 165–67. http://dx.doi.org/10.1080/02522667.1989.10698959.

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21

MUKHACHIOVA, E. A., and V. A. ZALGALLER. "LINEAR PROGRAMMING CUTTING PROBLEMS." International Journal of Software Engineering and Knowledge Engineering 03, no. 04 (1993): 463–76. http://dx.doi.org/10.1142/s0218194093000240.

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Different optimal cutting problems are considered in this paper. Among them are cutting forming problems (closed packing problems) and problems of cutting totality planning with intensities of their application. For solving these planning problems, linear or integer programming is used. Furthermore, different cutting technological and organizational situations are considered. Different optimal criteria and a compromise solution choice procedure are presented. All the statements are illustrated by numerical examples from a guillotine cutting area. The possibility of linear cutting approximation for a non-guillotine (closed packing) cutting stock problem is shown. Rectangular packing algorithms based on this approximation can be built. These algorithms form the basis of special software. Their characteristics are presented in the conclusion of the paper.
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22

Yakubova, U., N. Mirkhodjaeva, and N. Parpieva. "Some Notes on Linear Programming Problems." Bulletin of Science and Practice 10, no. 3 (2024): 36–43. http://dx.doi.org/10.33619/2414-2948/100/03.

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The paper considers such problems of linear programming as the problem of using raw materials, the problem of composing a diet. The basic definitions, theorems, algorithm and solution of the linear programming problem by the graphical method are given.
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23

Jyoti, Arora, and Sharma Surbhi. "Solving Trapezoidal Fuzzy Linear Programming Problem using Modified Big-M." Journal of Applied Mathematics and Statistical Analysis 4, no. 3 (2023): 1–5. https://doi.org/10.5281/zenodo.10165868.

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<i>The fuzzy logic and fuzzy numbers have been applied in many areas of Mathematical Programming. Optimization under uncertainty is one of the most important problem in Mathematical Programming.&nbsp;This paper proposes a Modified Big M method to solve fully fuzzy Trapezoidal linear programming problem with fuzzy decision variables and fuzzy parameters.&nbsp;</i>
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24

Sempavazhaam, D., K. Jothi, and S. |. Nandhini A. |. Princy Rebekah J. Kamali. "A Study on Linear Programming Problem." International Journal of Trend in Scientific Research and Development 3, no. 2 (2019): 903–4. https://doi.org/10.31142/ijtsrd21539.

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Green supply chain management GSCM is about incorporating the environmental idea in every stage of a supply chain. It has The LPP is the simplest way to calculate the profit and loss of a management. The important application of LPP is cost reduction in various business fields. It is also used to solve many diverse combination problems. LPP is more adaptive and flexible to analyze solution in various problems. Here we have discussed about the revenue and income of a hotel using LPP. The problem is solved using simplex method. The simplex method is easy to find the solution to the problem. Sempavazhaam D | Jothi K | Kamali S | Nandhini A | Princy Rebekah J &quot;A Study on Linear Programming Problem&quot; Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21539.pdf
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25

Sharma, Anuradha. "Reformulation of bilevel linear fractional/linear programming problem into a mixed integer programming problem via complementarity problem." International Journal of Computing Science and Mathematics 15, no. 4 (2022): 359. http://dx.doi.org/10.1504/ijcsm.2022.10050770.

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26

Sharma, Anuradha. "Reformulation of bilevel linear fractional/linear programming problem into a mixed integer programming problem via complementarity problem." International Journal of Computing Science and Mathematics 15, no. 4 (2022): 359. http://dx.doi.org/10.1504/ijcsm.2022.125903.

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27

Majeed, Amir Sabir, and Fadhil Salman Abed. "A Proposed Method to Solve Quadratic Fractional Programming Problem by Converting to Double Linear Programming." Journal of Zankoy Sulaimani - Part A 19, no. 1 (2016): 239–49. http://dx.doi.org/10.17656/jzs.10602.

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28

Surapati, Pramanik*. "NEUTROSOPHIC LINEAR GOAL PROGRAMMING." Global Journal of Engineering Science and Research Management 3, no. 7 (2016): 1–11. https://doi.org/10.5281/zenodo.57367.

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This paper proposes the framework of neutrosophic linear goal programming (NGP) approach for solving multi objective optimization problems involving uncertainty and indeterminacy. In the proposed approach, the degree of membership (acceptance), indeterminacy and falsity (rejection) of the objectives are simultaneously considered. Three neutrosophic linear goal programming models have been proposed. The drawbacks of the existing neutrosophic optimization models have been addressed and new direction of research in neutrosophic optimization problem has been proposed. The essence of the proposed approach is that it is capable of dealing with indeterminacy and falsity simultaneously.
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29

Kostyukova, O. I., and T. V. Tchemisova. "Generalized problem of linear copositive programming." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 3 (2019): 299–308. http://dx.doi.org/10.29235/1561-2430-2019-55-3-299-308.

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We consider a special class of optimization problems where the objective function is linear w.r.t. decision variable х and the constraints are linear w.r.t. х and quadratic w.r.t. index t defined in a given cone. The problems of this class can be considered as a generalization of semi-definite and copositive programming problems. For these problems, we formulate an equivalent semi-infinite problem and define a set of immobile indices that is either empty or a union of a finite number of convex bounded polyhedra. We have studied properties of the feasible sets of the problems under consideration and use them to obtain new efficient optimality conditions for generalized copositive problems. These conditions are CQ-free and have the form of criteria.
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30

Usenik, Janez. "FUZZY DYNAMIC LINEAR PROGRAMMING IN ENERGY SUPPLY PLANNING." Journal of Energy Technology 4, no. 4 (2024): 45–62. https://doi.org/10.18690/jet.4.4.45-62.2011.

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Linear programming is an important field of optimisation. Many practical problems can be expressed as linear programming problems and be solved with a simplex method. When all data in a linear program are determined and quantities are known in advance, the simplex algorithm, i.e. the simplex method, is explicit. However, in special cases the coefficients in the linear programming problem can be a) fuzzy numbers or b) functions of time with specific requests. In this manner, we have either fuzzy linear programming in the first situation or continuous dynamic linear programming in the second. The synthesis of both methods is a fuzzy dynamic linear programming problem, which is explored in this article and represents a new method in the theory of linear programming problems. Following the theory, we have some different procedures for solving an energy supply planning problem, Fabijan, Predin, [1], Usenik, [2]. One rational possibility is to define the mathematical model as a problem of fuzzy dynamic linear programming and solve it with the new simplex procedure. In this article, the simplex method for this possibility is proposed. At the end of the article, a numerical example is shown.
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31

Kunwar, R., and H. P. Sapkota. "An Introduction to Linear Programming Problems with Some Real-Life Applications." European Journal of Mathematics and Statistics 3, no. 2 (2022): 21–27. http://dx.doi.org/10.24018/ejmath.2022.3.2.108.

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Linear programming is a mathematical tool for optimizing an outcome through a mathematical model. In recent times different mathematical models are extensively used in the planning of different real-life applications such as agriculture, management, business, industry, transportation, telecommunication, engineering, and so on. It is mainly used to make the real-life situation easier, more comfortable, and more economic, and to get optimum achievement from the limited resources. This paper has tried to shed light on the basic information about linear programming problems and some real-life applications. It presents the general introduction of the linear programming problem, historical overview, meaning and definition of a linear programming problem, assumptions of a linear programming problem, component of a linear programming problem, and characteristics of a linear programming problem, and some highlights of some real-life applications.
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32

CALVETE, HERMINIA I., and CARMEN GALÉ. "A PENALTY METHOD FOR SOLVING BILEVEL LINEAR FRACTIONAL/LINEAR PROGRAMMING PROBLEMS." Asia-Pacific Journal of Operational Research 21, no. 02 (2004): 207–24. http://dx.doi.org/10.1142/s0217595904000205.

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Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.
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33

Cheng, Haifang, Weilai Huang, and Jianhu Cai. "Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/726296.

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In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.
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34

BUCKLEY, JAMES J., THOMAS FEURING, and YOICHI HAYASHI. "MULTI-OBJECTIVE FULLY FUZZIFIED LINEAR PROGAMMING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 05 (2001): 605–21. http://dx.doi.org/10.1142/s0218488501001083.

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In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.
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35

Albayrak, Inci, Mustafa Sivri, and Gizem Temelcan. "A Solution Algorithm for Interval Transportation Problems via Time-Cost Tradeoff." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 2 (2018): 7691–701. http://dx.doi.org/10.24297/jam.v14i2.7417.

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In this paper, an algorithm for solving interval time-cost tradeoff transportation problemsis presented. In this problem, all the demands are defined as intervalto determine more realistic duration and cost. Mathematical methods can be used to convert the time-cost tradeoff problems to linear programming, integer programming, dynamic programming, goal programming or multi-objective linear programming problems for determining the optimum duration and cost. Using this approach, the algorithm is developed converting interval time-cost tradeoff transportation problem to the linear programming problem by taking into consideration of decision maker (DM).
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36

Mitu, Afsana Akter, and M. Babul Hasan. "Application of Stochastic Programming in Agricultural and Newsvendor Problems and It's Application in Real Life." Dhaka University Journal of Science 72, no. 1 (2024): 30–45. http://dx.doi.org/10.3329/dujs.v72i1.71183.

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The study of making the best decision under risk management in a variety of areas of our lives is known as Stochastic Programming. We will go through two-stage Stochastic Linear Programming approaches for a variety of real-world choice issues, as well as how to solve them. We will achieve this by constructing stochastic linear programming models based on real-world situations like the well-known Farmer's situation and News Vendors problems. The influence of pricing, Stochastic Integer Linear Programming problem, second stage Stochastic Integer Linear Programming problem, first stage Stochastic Binary Linear Programming problem, risk aversion problem, and continuous function for random variables based on two-stage SLP with the aid of Farmer's problem will all be examined. We will address the Newsvendor’s problem with Deterministic Equivalent Stochastic Linear Programming, an extension of Deterministic Stochastic Linear Programming for risk aversion with a high number of decision variables and restrictions, utilizing the two-stage Stochastic Linear Programming approach once more. Hand calculation is a challenging way to acquire the solution to the problems. As a result, we will use the programming language AMPL to design computer solutions for tackling both farmer and newsvendor difficulties. We will also utilize MATLAB to create graphs for the farmer's problem's continuous function. Dhaka Univ. J. Sci. 72(1): 30-45, 2024 (January)
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37

H, Nethravathi. "Formulation of Investment Problem Using Linear Programming Problem." International Journal for Research in Applied Science and Engineering Technology 6, no. 4 (2018): 3635–38. http://dx.doi.org/10.22214/ijraset.2018.4604.

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38

Bhatia, D., and Pankaj Gupta. "Generallized Linear Complementarity Problem and Multiobjective Programming Problem." Optimization 46, no. 2 (1999): 199–214. http://dx.doi.org/10.1080/02331939908844452.

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39

Broughan, Kevin, and Nan Zhu. "An Integer Programming Problem with a Linear Programming Solution." American Mathematical Monthly 107, no. 5 (2000): 444. http://dx.doi.org/10.2307/2695300.

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40

Broughan, Kevin, and Nan Zhu. "An Integer Programming Problem with a Linear Programming Solution." American Mathematical Monthly 107, no. 5 (2000): 444–46. http://dx.doi.org/10.1080/00029890.2000.12005218.

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41

Hasan, Md Mohedul, and Md Rajib Arefin. "Application of Linear Programming in Scheduling Problem." Dhaka University Journal of Science 65, no. 2 (2017): 145–50. http://dx.doi.org/10.3329/dujs.v65i2.54526.

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Scheduling problem is a great concern for several institutions. Larger organizations have to maintain proper scheduling of their employees to ensure good service. This type of problems can be solved using linear programming (LP) as a useful tool. In this paper, we study the application LP to the scheduling problem. We mainly present four different scheduling problems and formulate them using LP. Finally, we solve them using MATHEMATICA v9 software.&#x0D; Dhaka Univ. J. Sci. 65(2): 145-150, 2017 (July)
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42

Kabiraj, Arpita, Prasun Kumar Nayak, and Swapan Raha. "Solving Intuitionistic Fuzzy Linear Programming Problem." International Journal of Intelligence Science 09, no. 01 (2019): 44–58. http://dx.doi.org/10.4236/ijis.2019.91003.

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43

Verma, Vanita. "Constrained integer linear fractional programming problem." Optimization 21, no. 5 (1990): 749–57. http://dx.doi.org/10.1080/02331939008843602.

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44

Amirkhanova, G. A., A. I. Golikov, and Yu G. Evtushenko. "On an inverse linear programming problem." Proceedings of the Steklov Institute of Mathematics 295, S1 (2016): 21–27. http://dx.doi.org/10.1134/s0081543816090030.

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45

Bogdan, Marcel. "Multiple solutions in linear programming problem." Procedia Manufacturing 22 (2018): 1063–68. http://dx.doi.org/10.1016/j.promfg.2018.03.151.

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46

Pradhan, Avik, and M. P. Biswal. "Multi-choice probabilistic linear programming problem." OPSEARCH 54, no. 1 (2016): 122–42. http://dx.doi.org/10.1007/s12597-016-0272-7.

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Júdice, J. J., and A. Faustino. "The Linear-Quadratic Bilevel Programming Problem." INFOR: Information Systems and Operational Research 32, no. 2 (1994): 87–98. http://dx.doi.org/10.1080/03155986.1994.11732240.

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Stancu-Minasian, I. M., R. Caballero, E. Cerdá, and M. M. Muñoz. "The stochastic bottleneck linear programming problem." Top 7, no. 1 (1999): 123–43. http://dx.doi.org/10.1007/bf02564715.

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Das, Bimal Chandra. "A Comparative Study of the Methods of Solving Non-Linear Programming Problem." DIU Journal of Science & Technology 4, no. 1 (2024): 18–34. https://doi.org/10.5281/zenodo.13691009.

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Abstract:
The work present in this paper is based on a comparative study of the methods of solving Non-linear programming (NLP) problem. We know that Kuhn-Tucker condition method is an efficient method of solving Non-linear programming problem. By using Kuhn-Tucker conditions the quadratic programming (QP) problem reduced to form of Linear programming(LP) problem, so practically simplex type algorithm can be used to solve the quadratic programming problem (Wolfe&rsquo;s Algorithm).We have arranged the materials of this paper in following way. Fist we discuss about non-linear programming problems. In second step we discuss Kuhn- Tucker condition method of solving NLP problems. Finally we compare the solution obtained by Kuhn- Tucker condition method with other methods. For problem so consider we use MATLAB programming to graph the constraints for obtaining feasible region. Also we plot the objective functions for determining optimum points and compare the solution thus obtained with exact solutions.
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Haftom, Gebreanenya. "INTEGER LINEAR PROGRAMMING PROBLEM IN MESSEBO CEMENT FACTORY." Journal of Progressive Research in Mathematics 9, no. 2 (2016): 1350–60. https://doi.org/10.5281/zenodo.3980464.

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To solve integer linear programming problem is very difficult than to solve linear programming problem. In this paper we are going to see the formulation of integer linear programming problem and one of its solution techniques called Branch and Bound method. This paper also contains a real world problem of integer linear programming problem on Messebo Cement Factory (Mekelle, Tigray, Ethiopia) solved using the Branch and Bound method.
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