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Search Results: 1 - 10 of 9239 matches for " Linear Programming "
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A New Approach for Solving Linear Fractional Programming Problems with Duality Concept  [PDF]
Farhana Ahmed Simi, Md. Shahjalal Talukder
Open Journal of Optimization (OJOp) , 2017, DOI: 10.4236/ojop.2017.61001
Abstract: Most of the current methods for solving linear fractional programming (LFP) problems depend on the simplex type method. In this paper, we present a new approach for solving linear fractional programming problem in which the objective function is a linear fractional function, while constraint functions are in the form of linear inequalities. This approach does not depend on the simplex type method. Here first we transform this LFP problem into linear programming (LP) problem and hence solve this problem algebraically using the concept of duality. Two simple examples to illustrate our algorithm are given. And also we compare this approach with other available methods for solving LFP problems.
The Sliding Gradient Algorithm for Linear Programming  [PDF]
Hochung Liu, Peizhuang Wang
American Journal of Operations Research (AJOR) , 2018, DOI: 10.4236/ajor.2018.82009
Abstract: The existence of strongly polynomial algorithm for linear programming (LP) has been widely sought after for decades. Recently, a new approach called Gravity Sliding algorithm [1] has emerged. It is a gradient descending method whereby the descending trajectory slides along the inner surfaces of a polyhedron until it reaches the optimal point. In R3, a water droplet pulled by gravitational force traces the shortest path to descend to the lowest point. As the Gravity Sliding algorithm emulates the water droplet trajectory, it exhibits strongly polynomial behavior in R3. We believe that it could be a strongly polynomial algorithm for linear programming in Rn too. In fact, our algorithm can solve the Klee-Minty deformed cube problem in only two iterations, irrespective of the dimension of the cube. The core of gravity sliding algorithm is how to calculate the projection of the gravity vector g onto the intersection of a group of facets, which is disclosed in the same paper [1]. In this paper, we introduce a more efficient method to compute the gradient projections on complementary facets, and rename it the Sliding Gradient algorithm under the new projection calculation.
A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm  [PDF]
Sumon Kumar Saha, Md. Rezwan Hossain, Md. Kutub Uddin, Rabindra Nath Mondal
Open Journal of Optimization (OJOp) , 2015, DOI: 10.4236/ojop.2015.43010
Abstract: In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if β is negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.
Application of Linear Programming Algorithm in the Optimization of Financial Portfolio of Golden Guinea Breweries Plc, Nigeria  [PDF]
Emmanuel Nwabueze Ekwonwune, Dominic Chukwuemeka Edebatu
Open Journal of Modelling and Simulation (OJMSi) , 2016, DOI: 10.4236/ojmsi.2016.43008
Abstract: In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.
Application of Simplex Method in the Radiotherapy Treatment  [PDF]
Thais R. Salvador, Silvia M. S. Carvalho, Mayk V. Coelho
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.717177
Abstract: This work presents an application of the Simplex Method for solving an optimal planning problem for cancer treatment by radiotherapy. Linear Programming can aid the optimal planning for radiation therapy, where the concern is to apply a high enough radiation in the tumor while saving significantly healthy regions or critical organs.
Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application  [PDF]
Farhana Akond Pramy, Md. Ainul Islam
Open Journal of Optimization (OJOp) , 2017, DOI: 10.4236/ojop.2017.64011
Abstract: In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.
An Application of Determining the Best Tax Ratios by Goal Programming
Ahmet ?ahiner,H. Seda Ak?n,Bahri Türen
Sel?uk Journal of Applied Mathematics , 2010,
Abstract: Numerous procedures are used to solve multiple criteria decision-making problems. Among these the most frequently used procedure is goal programming, which is also the selected procedure for this study. It will be used to calculate the best tax ratios for the city of Isparta, a daily problem.
An Alternative Approach for Solving Bi-Level Programming Problems  [PDF]
Rashmi Birla, Vijay K. Agarwal, Idrees A. Khan, Vishnu Narayan Mishra
American Journal of Operations Research (AJOR) , 2017, DOI: 10.4236/ajor.2017.73016
Abstract: An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.
A New Approach for a Class of Optimal Control Problems of Volterra Integral Equations  [PDF]
Mohammad Hadi Noori Skandari, Hamid Reza Erfanian, Ali Vahidian Kamyad
Intelligent Control and Automation (ICA) , 2011, DOI: 10.4236/ica.2011.22014
Abstract: In this paper, we propose a new approach for a class of optimal control problems governed by Volterra integral equations which is based on linear combination property of intervals. We convert the nonlinear terms in constraints of problem to the corresponding linear terms. Discretization method is also applied to convert the new problems to the discrete-time problem. In addition, some numerical examples are presented to illustrate the effectiveness of the proposed approach.
Evaluating the Performance of Iranian Football Teams Utilizing Linear Programming  [PDF]
Mehrzad Hamidi, Hamidi Sajadi, Jahangir Soleimani-Damaneh
American Journal of Operations Research (AJOR) , 2011, DOI: 10.4236/ajor.2011.12010
Abstract: In this paper, we utilize Data Envelopment Analysis (DEA), which is a linear programming-based technique, for evaluating the performance of the teams which operate in the Iranian primer football league. We use Analytical Hierarchy Process (AHP) technique for aggregating the sub-factors which involve in input-output factors, and then DEA is used for calculating the efficiency measures. Also, AHP is used to construct some weight restrictions for increasing the discrimination power of the used DEA model. For calculating the efficiency measures, input-oriented weight-restricted BCC model is utilized.
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