International Journal of Industrial Mathematics
Volume:8 Issue: 3, Summer 2016

With the huge global and wide range of attention placed upon quality, promoting and optimize the reliability of the products during the design process has turned out to be a high priority. In this study, the researcher have adopted one of the existing models in the reliability science and propose a bi-objective model for redundancy allocation in the series-parallel systems in accordance with the redundancy policy- given that failure rate depends on the number of the active elements. The objective behind the proposed model is to maximize the reliability and to minimize the total cost of the system. Internal connection cost, which is the most common parameter in electronic systems, put in this model in order to simulate the real-world conditions. As the proposed model is an NP-Hard one(for getting results), the researcher adopted a Non-dominated Sorting Genetic Algorithm (NSGA II) after optimizing its operators’ rate by using Response Surface Methodology (RSM)ý.ý

ýýIn this articleý, ýa new method is introduced to give approximate solution to Van der Pol equationý. ýThe proposed method is based on the combination of two different methodsý, ýthe spectral Adomian decomposition method (SADM) and piecewise methodý, ýcalled the piecewise Adomian decomposition method (PSADM)ý. ýThe numerical results obtained from the proposed method show that this method is an effectiveý, accurate and powerful tool for solving Van der Pol equation andý, ýthe comparison show that the proposed technique is in good agreement with the numerical results obtained using Runge-Kutta methodý. ýThe advantage of piecewise spectral Adomian decomposition method over piecewise Adomian decomposition method is that it does not need to calculate complex integralsý. ýAnother merit of this method is thatý, ýunlike the spectral methodý, ýit does not require the solution of any linear or nonlinear system of equationsý. Furthermoreý, ýthe proposed method is easy to implement and computationally very ýattractive.

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-ýsubgroups.ý

In this paper, linear Data Envelopment Analysis models are used to estimate Markowitz efficient frontier. Conventional DEA models assume non-negative values for inputs and outputs. however, variance is the only variable in these models that takes non-negative values. Therefore, negative data models which the risk of the assets had been used as an input and expected return was the output are utilized . At the beginning variance was considered as a risk measure. However, both theories and practices indicate that variance is not a good measure of risk. Then value at risk is introduced as new risk measure. In this paper,we should prove that with increasing sample size, the frontiers of the linear models with both variance and value at risk , as risk measure, gradually approximate the frontiers of the mean-variance and mean-value at risk models and non-linear model with negative data. Finally, we present a numerical example with variance and value at risk that obtained via historical simulation and variance-covariance method as risk measures to demonstrate the usefulness and effectiveness of our ýclaim.ý

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and Block-Pulse functions which are orthonormal and have compact support on $[0, 1]$. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and efficiency of the proposed ýmethod.ý

It is well known that in operations researchý, ýdegeneracy can cause a cycle in a networký ýsimplex algorithm which can be prevented by maintaining strongý ýfeasible bases in each pivotý. ýAlsoý, ýin a network consists of n arcsý ýand m nodesý, ýnot considering any new conditions on the enteringý ývariableý, ýthe upper bound of consecutive degenerate pivots is equalý $\left( ý\begin{array}{c}ý ýn-m \\ý ýk \\ý ý\end{array}ý ý\right)$ý ýwhere $k$ is the number of degenerate arcs in the basisý. ýAsý ýwell asý, ýthe network simplex algorithm may stall if it goes throughý ýsome long consecutive degenerate pivotý. ýThrough conditions such asý ý(LRC) and (LRS) upon entering variable rulesý, ýthis upper bound caný ýbe reduced to $mn$ and $m^2$ respectivelyý. ýIn this current paper weý first suggest a new algorithm for anti--stalling in which a newý ýcondition is provided to the entering variable and then show thatý ýthrough this algorithm there are at most $k$ consecutive degenerate ýpivots.ý

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method \cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. The solutions obtained are compared with Adomian decomposition method and iterative method used in \cite{35 } and Adams method \cite{36}.

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also presented.

Selecting the most suitable robot among their wide range of specifications and capabilities is an important issue to perform the hazardous and repetitive jobs . Companies should take into consideration powerful group decision-making (GDM) methods to evaluate the candidates or potential robots versus the selected attributes (criteria) . In this study , a new GDM method is proposed by utilizing the complex proportional assessment method under interval-valued hesitant fuzzy (IVHF)-environment . In the proposed method , a group of experts is established to evaluate the candidates or alternatives among the conflicted attributes . In addition , experts assign their preferences and judgments about the rating of alternatives and the relative importance of each attribute by linguistic terms which are converted to interval-valued hesitant fuzzy elements (IVHFEs) . Also , the attributes’ weights and experts’ weights are applied in procedure of the proposed interval-valued hesitant fuzzy group decision-making (IVHF-GDM) method . Hence , the experts’ opinions about the relative importance of each attribute are considered in determination of attributes’ weights . Thus , we propose a hybrid maximizing deviation method under uncertainty . Finally , an illustrative example is presented to show the feasibility of the proposed IVHF-GDM method and also the obtained ranking results are compared with a recent method from the literature .

Malmquist Productivity Index (MPI) is a numeric index that is of great importance in measuring productivity and its changes. In recent years, tools like DEA have been utilized for determining MPI. In the present paper, some models are recommended for calculating MPI when there are just ratio data available. Then, using DEA and DEA-R, some models are proposed under the constant returns to scale (CRS) technology and based on value efficiency (VE) in order to calculate MPI when there is just a ratio of the output to the input data (and vice versa). Finally, in an applied study on 30 welfare service companies under CRS technology, the progress and/or regression of companies are determined in DEA and DEA- R.

One of the major problems in Data Envelopment Analysis (DEA) is to determine the projection of inefficient Decision Making Units (DMUs) into the efficient frontier. In conventional DEA models, inputs and outputs of inefficient DMUs alter arbitrarily for reaching to the efficient frontier. Nevertheless, sometimes the ability of DMUs is defined and restricted. Moreover, there are situations in the real world applications that limited resources exist. Therefore, in these cases inputs and outputs cannot vary irrationally. Actually, there are pre-specified alteration levels of inputs and outputs. For this purpose, the current study proposes DEA-based models, radial and non-radial models, to evaluate the relative efficiency of DMUs with restricted input and output variables. Furthermore, non-radial super-efficiency models are extended for ranking efficient DMUs. An example from the banking sector is used to illustrate the proposed approach.

The problem of two-phase MHD boundary layer flow, heat and mass transfer over a stretching sheet with fluid-particle suspension and thermal radiation has been studied. The effect of mass transfer in dusty fluid over a stretching sheet is considered for the first time. The governing equations are reduced to a set of non-linear ordinary differential equations under suitable similarity transformations. The transformed equations are then solved numerically. The influence of various physical parameters such as magnetic parameter, fluid-particle interaction parameters, Prandtl number, Eckert number and thermal radiation parameter on velocity, temperature and concentration of both fluid and particle phase is analyzed. The numerical results of the present investigation were compared with previously published results and found to be an excellent agreement. It is found that, the momentum, thermal and solute boundary layer thickness of both fluid and dust phase are reduced for higher values of mass concentration of suspended dust particles.

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example \cite{darabi1,TS}), but these methods have been done for fuzzy problems with triangular fuzzy initial value. Therefore by extending the r-cut solutions of the original problem we will obviate this deficiency. The presented idea is based on: if a second order fuzzy differential equation satisfy the Lipschitz condition then the initial value problem has a unique solution on a specific interval, therefore our main purpose is to present a method to find an interval on which the solution is valid.

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet''s methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of the fractional order differentiation are obtained. Then we propose the Haar-wavelet operational matrix method to achieve the Haar-wavelet time response output solution of fractional order linear systems where a fractional derivative is defined in the Caputo sense. Using collocation points, we have a Sylvester equation which can be solve by Block Krylov subspace methods. So we have analyzed the errors. The method has been tested by a numerical example. Since wavelet representations of a vector function can be more accurate and take less computer time, they are often more useful.

This paper proposes a multi-supplier multi-product inventory model in which the suppliers have unlimited production capacity, allow delayed payment, and offer either an all-unit or incremental discount. The retailer can delay payment until after they have sold all the units of the purchased product. The retailer’s warehouse is limited, but the surplus can be stored in a rented warehouse at a higher holding cost. The demand over a finite planning horizon is known. This model aims to choose the best set of suppliers and also seeks to determine the economic order quantity allocated to each supplier. The model will be formulated as a mixed integer and nonlinear programming model which is NP-hard and will be solved by using genetic algorithm (GA), simulated annealing (SA) algorithm, and vibration damping optimization (VDO) algorithm. Finally, the performance of the algorithms will be compared.