JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2017 | Volume:3 | Issue:9|Papers Count:10

Supply chain management is essential for the success of firms and customer satisfaction. In addition, a suitable performance evaluation system is vital to the effective management of the supply chain.Due to the importance of cost management in the supply chain, an approach based on Data Envelopment Analysis (DEA) is proposed in the current study for evaluating the cost efficiency of closed-loop supply chains while dual-role factors and undesirable outputs exist. DEA is a beneficial mathematical programming method for evaluating and analyzing the relative efficiency of decision maker units with multiple inputs and outputs. Indeed, in this study, the cost efficiency scores of supply chains with three components, supplier, manufacturer and repair and recycling, as well as forward and reverse flows are measured using DEA technique. The assumption of weak disposability on undesirable outputs is considered. Also, a case study is provided to illustrate and to analyze the proposed method. The results show a correct identification of the role of the factors and the incorporation of the undesirable and reversible factors in supply chain systems play the important role in the correct calculation of the cost efficiency in each of components and whole supply chain.Moreover, in the introduced method, the overall cost efficiency can be represented as the weighted sum of the cost efficiency of components.

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a functionf that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives off at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear combination for 5th degree polynomials linear space and same approach develops to introduce 5th degree fuzzy piecewise Hermite interpolation polynomials.At first, construction method along with an example has presented for 5 th degree fuzzy Hermite interpolation. Because of the introduced method applies for interpolation of first order Generalized Hukuhara differentiable functions so during an example cubic fuzzy Hermite interpolation polynomial compares with fuzzy Hermite polynomial and we explain the superiority of the presented piecewise method next in the end we provide 5th degree fuzzy piecewise Hermite interpolation polynomial. Using such interpolant shows that the smoothness condition improves for interpolation polynomial core when successive degree of fuzzy piecewise Hermite interpolation polynomial comes up from three to five.

In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy.The main advantage of this approximation method is its flexibility and simple applicability.

In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations.The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [1], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability.

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some papers such as [7, 11]. By the above concepts we can generalize some theorems which was proved by other authors, especially Darbo’s fixed point theorem. The space of our solution contains of all convergence sequences with a finite limit, such that with suitable norm is a Banach space. To reach our subject, we prove some theorems by using measure of non-compactness and Meir-Keeler condensing operators to generalize some theorems which are created by some authors. For validity and application of our proposed theorems, we prove existence of solution for infinite system of second order differential equations with boundary conditions.

The Vehicle Routing Problem (VRP), a famous problem of operation research, holds a central place in combinatorial optimization problems. In this problem, a fleet vehicles with Q capacity start to move from depot and return after servicing to customers in which visit only ones each customer and load more than its capacity not at all. The objective is to minimize the number of used vehicles and total distance traversed. This paper presents an application of Imperialist Competitive Algorithm (ICA)) in VRP. Unlike other evolutionary optimization algorithms, ICA is inspired from a socio political process, the competition among imperialists and colonies. Comparison between this method and famous meta-heuristic algorithms shows the effectiveness of the proposed approach.Computational experience with two groups of instances involving from 50 to 200 confirms that proposed algorithm is competitive in compared to the famous meta-heuristic algorithms in terms of the quality of generated solutions. In addition, this algorithm finds closely the best known solutions (BKS) for most of the instances.

In this paper, using shearlet frames, we present a numerical method for solving the wave equation.We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

In this paper, the improved -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained further solutions comparing this method with other methods. These solutions might play important role in engineering and physics fields. Being concise and straightforward, the method are applied for such problems. In addition, by using Matlab, some graphical simulations were done to see the behavior of these solutions.

Using Metaheuristics models and Evolutionary Algorithms for solving portfolio problem has been considered in recent years. In this study, by using particles swarm optimization and tabu search algorithms weoptimized two-sided risk measures r a,p (R). A standard exact penalty function transforms the considered portfolio selection problem into an equivalent unconstrained minimization problem. And in finally the historical data from s& p100 from years 2007 through 2009 is used as model input andthen the model was solved and these algorithms were compared.

In this paper we investigate similar triangles which are not congruent but have two pair congruent sides. We show that greatest lower bound of values for similarity ratio of such triangles is golden ratio. For right triangles, we prove that the supremum of values for similarity ratio is the square root of the golden ratio.