A new algorithm for solving linear programming problems (original) (raw)
Related papers
An efficient search direction for linear programming problems
Computers & Operations Research, 2002
In this paper, we present an auxiliary algorithm, in terms of the speed of obtaining the optimal solution, that is e!ective in helping the simplex method for commencing a better initial basic feasible solution. The idea of choosing a direction towards an optimal point presented in this paper is new and easily implemented. From our experiments, the algorithm will release a corner point of the feasible region within few iterative steps, independent of the starting point. The computational results show that after the auxiliary algorithm is adopted as phase I process, the simplex method consistently reduce the number of required iterations by about 40%.
New Approach for Simplex Method to Solve Linear Programming Problem
2015
The simplex method is most popular method for solving Linear Programs. In today's life the simplex algorithm of linear programming has greatest influence on the development and practice of science and engineering technology. In this paper, an alternative method for simplex method is introduced. This method is easy to solve linear programming problem (LPP). It is powerful method to reduce number of iterations and save valuable time.
Practical application of simplex method for solving linear programming problems
BALKAN JOURNAL OF APPLIED MATHEMATICS AND INFORMATICS, 2018
In this paper we consider application of linear programming in solving optimization problems with constraints. We used the simplex method for finding a maximum of an objective function. This method is applied to a real example. We used the “linprog” function in MatLab for problem solving. We have shown, how to apply simplex method on a real world problem, and to solve it using linear programming. Finally we investigate the complexity of the method via variation of the computer time versus the number of control variables.
In this chapter, we present a systematic procedure for solving linear programs. This procedure, called the simplex method, proceeds by moving from one feasible solution to another, at each step improving the value of the objective function. Moreover, the method terminates after a finite number of such transitions.
On Interior-Point Methods and Simplex Method in Linear Programming
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
In this paper we treat numerical computation methods for linear programming. Started from the analysis of the efficiency and defficiency of the simplex procedure, we present new possibilities offered by the interior-point methods, which appears from practical necessity, from the need of efficient means of solving large-scale problems. We realise the implementation in Java of the Karmarkar's method.
A New Method Combining Interior and Exterior Approaches for Linear Programming
Journal of Mathematics and System Science, 2015
In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.
A new approach to linear programming
SIGMAP bulletin, 1973
This is a preliminary report on a new method which is able to solve the standard LP problem. subject to MiN Z = <C,X> Ax=b where A is a M-BY-N MATRIX Aa 0 in a number of operations which is bounded by a polynomial in M and N. The fundamental idea of this algorithm is to select one column vector of A after the other in such a way that we can be sure that they belong to the final basis. After M steps the final solution is obtained. Hence, we do not have to follow a path through a sequence of vertices like in the Simplex method. V. Klee has shown that there are problems for which the height of the underlying polytope is fantastically large and therefore they are unsolvable using the Simplex algorithm in any of its forms, from a practical viewpoint. Also, Zadeh presented real problems of this class. All these inconveniences are avoided with the new algorithm.
iaeme
Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimise their use of planes and staff. NASA has been using them for many years to optimize their use of limited resources. Oil companies use them to optimise their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In this paper, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for its optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the productmix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this paper is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit which still touches the feasible region.