مجله پژوهش های نوین در ریاضی
پیاپی 11 (پاییز 1396)

Two stages DEA models are used in many fields of management and industry. One of the concepts that has attracted the attention of researchers in the theory of production is the concept of ranking the units with a two-stage network. A unit ranking can provide useful information to decision makers (DMUs) about optimal decision making activities. This concept defines the superiority of a unit in terms of efficiency and effectiveness on other units. The calculation of the efficiency of the units in the two-stage DEA network was performed, and the efficiency of the two-stage unit could be a suitable criterion for ranking one unit. But the main problem is the time when some efficient units all rank as one. So far, there is no linear model for solving this problem.The purpose of this research is to provide a model for ranking of effecient units using the common weight method in a two-stage DEA network.

Cross efficiency is one of the useful methods for ranking of decision making units (DMUs) in data envelopment analysis (DEA). Since the optimal solutions of inputs and outputs weights are not unique so the selection of them are not simple and the ranks of DMUs can be changed by the difference weights. Thus, in this paper, we introduce a method for ranking of DMUs which does not have a unique problem. In the real life, the outputs can be shown as desirable and undesirable outputs. So it is important to provide models for the ranking of DMUs in present of desirable and undesirable outputs. The classic DEA models deals with certain data. But, in the real word, all data are not necessarily certain. For solve of this problem, we present a new method that compute the ranks of all DMUs by uncertain data and calculate the lower and upper bounds for the ranks of DMUs. Finally, the results of a simple example are given.

Nowadays, managing a supply chain is turned to be one of the fundamentals of business process. In doing so, investigating and analyzing each and every of the processes and selecting the best of each process is an important challenge for strategic managers. In this paper Data Envelopment Analysis (DEA) technique is used and a model is provided for selecting the best suppliers with flexible inputs and outputs. Here, suppliers according to the different requirements of the next stage can be flexible for providing the already forecasting alterations. As an instance, transporting one of the flexible outputs can be considered which can be sent from the earth, sea, or the air. This has the direct effect on the selection of the best suppliers and according to this selection the new chain will be selected in accordance to the requirements of the whole chain. In this paper, according to DEA models and the binary algorithm, a new model will be presented for suppliers.

Data envelopment analysis (DEA) is a mathematical method to evaluate the performance of decision-making units (DMU). In the performance evaluation of an organization based on the classical theory of DEA, input and output data are assumed to be deterministic, while in the real world, the observed values of the inputs and outputs data are mainly fuzzy and random. A normal distribution is a continuous distribution which is extremely important in statistics because of its behavior.It is assumed in most cases that fuzzy random data are normally distributed, while such an assumption may not hold in practice. Therefore, using the normal distribution leads to erroneous conclusions. In the present study, we investigated DEA fuzzy random model under condition of probability -possibility, in the presence of a skew-normal distribution.In other words, this method embraced the previous methods in a specific state. Finally, a set of numerical example is presented to demonstrate the efficacy of procedure and algorithm.

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds of nonpositive curvature states that a homogeneous Riemannian manifold of nonpositive curvature is diffeomorphic to ...

Determining the type of returns to scale (RTS) and identifying stability region for RTS of evaluating unit are appropriate abilities for forecasting the future the unit when its size is changed. This paper aims to introduce RTS sustainability of frontier decision making units (DMUs) in data envelopment analysis (DEA). Based on the importance of RTS in relation to decisions of managers, different methods have been proposed to define RTS and determine the type RTS. Research on RTS led to a more general categorize for the type of RTS, named left RTS (L-RTS) and right RTS (R-RTS). All of the methods in evaluating L-RTS and R-RTS have presented parametric programming problems which are non-linear programs, naturally. In tis situation, researchers are facing the challenge to determine the value of parameters. In order to survey this limitation, the present paper suggests linear programming problems. Moreover, the proposed models with minor changes are appropriate tools for determining the RTS sustainability for evaluating unit.

Computation of the Schrodinger equation energy levels is very important in physics. For example we can use these levels to calculate the absorption coefficient and light refraction in a material as well as calculation of the interband and intersubband transition energies. Density of states of the system can also be obtained by using the energy levels. Thereafter we can determine that the system is dielectric, semiconductor or metal. There are different methods to calculate the energy levels and each of them has some advantages and some disadvantages. The asymptotic iteration method, genetic algorithm, numerov method, neural networks, transfer matrix etc. are some of them. However calculation of the energy levels by using the Sinc method has less been studied.
In this paper we consider the Sinc collocation method to calculate these energy levels. We approximate the unknown function by Sinc functions and convert the problem to the eigenvalue problem by collocation method. In sequel numerical examples are included to compare the accurately of our method with finite difference method. The results demonstrate the accuracy of our method to comparison the other methods. All computations were carried out using Maple on a personal.

Data Envelopment Analysis (DEA) as a non–parametric method is used to measure relative performance of organizational units. The aim of this paper is to develop a new model to evaluate the efficiency of a general two-stage network structures proposed by Li et al. (2012) for measuring the performance of Decision Making Units (DMUs). In addition, this paper expands the work of Li et al. (2012) and improves the heuristic search procedure to estimate the optimal solutions of non-linear centralized models. In order to evaluate the proposed model of this study, it has been applied to a case of regional Research and Development (R&D) system related to 30 provincial level regions in China. The experimental results compared with method developed by Li et al. (2012) show that the proposed method is efficient and has much lower computational complexity.

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring . It is shown that Gorenstein homological dimensions of an -RΓ module M with respect to a semi-dualizing module, are equal over R and RΓ .

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A-stability and L-stability, they are not suitable for the numerical solution of special classes of problems arising from different research areas, for example the mathematical models of celestial objects which are Hamiltonian systems. Since the solution of such problems has special geometric property such as symplecticity and usually reversibility. Therefore, it is natural to search for numerical methods that share this property. It is the purpose of this paper to design high order symplectic and symmetric methods. Efficiency and accuracy of the constructed methods are confirmed by implementing on well-known Hamiltonian problems of the motions of celestial objects.