The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called Push-and-Pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The Push Phase develops a basic variabl...

The Random-Facet algorithm is a randomized variant of the simplex method which is known to solve any linear program with n variables and m constraints using an expected number of pivot steps which is subexponential in both n and m. This is the theoretically fastest simplex algorithm known to date if m ≈ n; it provably beats most of the classical deterministic variants which require exp(Ω(n)) pi...

— We identify the best root node strategy for the approximation of the time-indexed bound in min-sum scheduling by sorting through various options that involve the primal simplex, dual simplex, and barrier methods for linear programming, the network simplex method for network ow problems, and DantzigWolfe decomposition and column generation. Note to Practitioners— Min-sum scheduling problems ar...

The problem of determining a maximum-weight marking in a marked graph is mathematically dual to the transshipment problem of operations research. The special structure of the transshipment problem facilitates efficient implementation of the simplex method of linear programming, for solving such problems. In this paper, we first show that the maximum-weight marking problem possesses as much stru...

We consider the Nelder and Mead Simplex Method for the optimization of stochastic simulation models. Existing and new adaptive extensions of the Nelder and Mead simplex method designed to improve the accuracy and consistency of the observed best point are studied. We compare the performance of the extensions on a small microsimulation model, as well as on ve test functions. We found that gradua...

A Simplex Elements Stochastic Collocation (SESC) method is introduced for robust and efficient propagation of uncertainty through computational models. The presented non– intrusive Uncertainty Quantification (UQ) method is based on adaptive grid refinement of a simplex elements discretization in probability space. The approach is equally robust as Monte Carlo (MC) simulation in terms of the Ext...

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for...

Herpetic keratitis which is resulted from herpes simplex virus type I, is considered the most common cause of corneal blindness that needs being diagnosed and treated in order to prevent irreversible eye effects. The best method to diagnose it is molecular method which has high sensitivity and exclusivity. The current study was done on 25 eye samples collected from patients referred to the Feyz...