This paper introduces three novel techniques for updating the invertible representation of the basis matrix when solving practical sparse linear programming (LP) problems using a high performance implementation of the dual revised simplex method, being of particular value when suboptimization is used. Two are variants of the product form update and the other permits multiple Forrest-Tomlin upda...

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic ...

The simplex method has been used to optimise the inulinase production by Aspergillus niger strain 13/36 with respect to 5 components of the medium. The extracellular enzyme activity was almost 80 U/mL, and over 1.6-fold higher than the results obtained by the classical »one-factor-at-a-time« method. The greatest advantage of the simplex method is that the optimum factor levels were determined i...

We first introduce matrix concepts in linear programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for linear programming, simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficienci...

Abstract In this paper we have investigated a fuzzy linear programming problem with fuzzy quantities which are LR triangular fuzzy numbers. The given linear programming problem is rearranged according to the satisfactory level of constraints using breaking point method. By considering the constraints, the arranged problem has been investigated for all optimal solutions connected with satisf...

The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underest...

This study is devoted to address the notion of duality in Fully Intuitionistic Fuzzy Linear Programming Problems (FIFLP). The problem is addressed by using a revised simplex method with the Gaussian elimination process in fully intuitionistic fuzzy environment. Intuitionistic Fuzzy Trapezoidal Numbers (IFTrpN), along with the basic arithmetic techniques defined on them help in solving the (FIFL...

G eorge Dantzig, in describing the " Origins of the Simplex Method, " 1 noted that it was the availability of early digital computers that supported and invited the development of LP models to solve real-world problems. He agreed that invention is sometimes the mother of necessity. Moreover, he commented that he initially rejected the simplex method because it seemed intuitively more attractive...

This paper proposes a hybrid computational method (DIPS method) which works as a simplex method for solving a standard form linear program, and, simultaneously, as an interior point method for solving its dual. The DIPS method generates a sequence of primal basic feasible solutions and a sequence of dual interior feasible solutions interdependently. Along the sequences, the duality gap decrease...

background and aims: considering difficulties in usual laboratory methods in detection of viral infections, improved dna-based diagnostic techniques are more reliable. loop mediated isothermal amplification method (lamp) is a nucleic acid amplification method that amplifies dna using six primers which has been developed to diagnose viruses as a rapid and high efficiency test. in this study, the...