International Journal of Industrial Mathematics
Volume:4 Issue: 3, Summer 2012

Separable programming deals with such nonlinear programming problem in which the objective function as well as constraints are separable. For solving Separable Nonlinear Programming Problem (SNPP) is reduced first to Linear Programming Problem (LPP) by approximating each separable function by a piecewise linear function and than usual graphical, simplex method applied. A new form of Gauss elimination technique for inequalities has been proposed for solving a Separable Nonlinear Programming Problem. The technique is useful than the earlier existing methods because it takes least time and calculations involve in are also simple. The same has been illustrated by a numerical example of SNPP.

This paper is focused on the investigation of heat transfer characteristics of mixed convection flow of water at 4◦C along a continuously moving vertical non-isothermal, nonconducting plate in the presence of a transverse magnetic field. The governing equations of continuity, momentum and energy for this boundary-layer flow are transformed into self-similar ordinary differential equations using the similarity transformation technique. The resulting coupled and non-linear ordinary differential equations are solved using the fourth-order Runge-Kutta method along with the shooting technique. The fluid flow and heat transfer characteristics are discussed and presented graphically. The values of the skin-friction coefficient and the Nusselt number at the plate surface are obtained for various values of the physical parameters and presented in tabular form and the physical aspects of these results are discussed.

Outliers are considered as a set of data that distinctly stands out from the rest of that data. Accepting or rejecting the outliers depends on various factors. The objective of this paper is to explain the accepting or rejecting conditions of outliers. Studying the congestion of the outlier units is one of the which through which the acceptance or rejection conditions can be figure out. In this method, it is first needed to identify the outliers that have congestion and then decide about the accepting or rejecting them. Discussions are presented following some examples to obtain higher level of underestimating of the proposed method. In addition, the return to scale of outliers are determined and discussed by using some examples.

In this paper, we propose a bounded DEA based model to measure the overall risk of failure modes. In the proposed model risk is measured within the range of an interval, whose performance is definitely superior to any one. The risks, obtained from bounded DEA models, turn out to be all intervals and are referred to as interval risk, which combine the best and the worst relative risk in a reasonable manner to give an overall assessment of performances for all failure modes. Assessor’s preference information on input and output weights is also incorporated into bounded DEA models reasonably and conveniently. A practical example is provided to compare the proposed model with those in the literature.

The importance as well as the difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middle-point and the spread of each -cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each -cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions.

In this paper, a new approach to the numerical solution of Volterra- Fredholm integral equations by using expansion method based on the composition of the inverse and direct discrete fuzzy transforms (shortly F-transforms) in combination with the collocation technique is proposed. First, the unknown function is approximated by using the composition of the inverse and direct discrete F-transforms based on the fuzzy partition, then the Volterra- Fredholm integral equation is reduced to the linear system of equations. Moreover, the convergence theorem for the proposed method is given in terms of the modulus of continuity. Finally, illustrative examples are included to show the accuracy and the efficiency of the proposed method.

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.