Journal of Operational Research in its Applications
Year:2010 | Volume:6 | Issue:23|Papers Count:9

In this paper, we have extended some modifications of the classic Newton’s method for solving the systems of nonlinear equations. To these methods we have gotten the same convergence order in the nonlinear equations by convergence analysis. We have determined the efficiency index of methods and used the methods to solving the selected systems of nonlinear equations. Efficiency indexes rates and numerical tests verifying more usefulness of the five convergence order methods.

In this paper, perturbation technique and Lagrange expansion to solve the nonlinear algebriac equations is introduced. Also Some examples are provided to illustrate the simplicity and efficiency of the new proposed methods.

Ordinary differential equation (ODE) models play a relevant role in many application areas including biology. In this paper, we consider ODE related to bacterio phage growth. With adding stochastic parameters to model, we introduce a stochastic differential equation (SDE). The main aim of this paper is to analyze the effects of white and mixture noise in the stochastic model. We approximate this SDE with Euler-Maryamma (EM) method. Numerical simulations are in MATLAB programming.

In the framework of density functional theory, using exchange correlation potential with the LSDA+U method, the effect of excess titanium on PZT compounds have been calculated. Our results on electronic density of states shows that 3d bands of titanium atoms are in the edge of conduction bands then Ti atoms affects the value of band gap. The calculation shows that by increasing the amount of Ti atoms, the band gap slightly decreases.

The familiar multivariate process monitoring and control procedure is the Hotelling’s T2 control chart, a direct analog of the univariate shewhart  chart. But, its efficiency for detecting small to moderate shifts in the process mean is poor. To improve the power of chart, this paper presents the variable sampling intervals (VSI) scheme. It is assumed that the length of time the process remains in control has exponential distribution. The chart is modeled using Markov chains and is optimized using genetic algorithm optimization method. The results show that the T2 chart with variable ratio sampling scheme is quicker than the classical one in detecting almost all shifts in the process mean.

This paper presents a decision-making methodology based on a simple nonlinear programming model, which uses both quantitative and qualitative criteria, for evaluating facility layout design. A computer-aided layout-planning tool, Spiral, is adopted to facilitate the layout alternative design process as well as to collect quantitative. Analytic hierarchy process (AHP) is then applied to collect qualitative data related to quality and flexibility. A non-linear programming (NLP) model is proposed to solve the layout design problem by simultaneously considering both the quantitative and qualitative data. The purposed integrated procedure is applied to a real data.

The current paper deals with the problem of ranking of decision making units in data envelopment analysis. Toward this end, a procedure for generating one common set of weights is illustrated and these common weights will be used for ranking. A case of bank branches is presented to illustrate the applicability of the approach.

One of the most important problems in mathematical science is linear programming and its application. Interior point methods for solving these problems have been used since 1984. In this paper we have tried to analysis Zoutendijk idea in linear state. In fact, our algorithm starts from an absolute interior point in feasible region and moves across objective function gradient. When we arrive to a boundary, new direction is selected by some conditions. This process has been continued until arriving to stop condition.