مجله پژوهش های نوین در ریاضی
پیاپی 1 (Spring 2015)

The inverse kinematics problem of a two degree of freedom (2DOF) planar robot arms is solved using Adomian’s decomposition method (ADM), after converting to a system of two nonlinear algebraic equations. The advantage of the method is that it gives the solutions as functions of the desired position of the end effecter and the length of the arms. The accuracy of the solutions can be increased up to desired order. The solutions haven’t any singularity. The problem must be solved once for any structure and the results can be used for any path and finally, the method is fast and simple to understand.

This study designs optimal systems for the centralized structures in data envelopment analysis (DEA). It assumes that a collection of decision making units (DMUs) with a master decision maker and a certain budget for them is available and introduces an optimal system for each DMU by maximizing their total revenue. A nmerical example is used to illustrate the proposed model.

Data envelopment analysis (DEA) is a mathematical programming method for calculating efficiency of decision making units (DMU). In calculating the efficiency score of units through DEA we may come up with some efficient units. But the question is among these efficient units which of them is better. As we know, it is possible to rank inefficient units through efficiency score; however, for ranking efficient units it is not helpful and other methods should be developed in these regards. To obviate this problem there have been so many attempts in the literature which have their pros and cons. Cross-efficiency method was first introduced by Sexon et al. for ranking efficient units. The major problem of this method is alternative optimal solutions in each model which must be solved for each DMU. Another problem of this method is dependency of obtained solutions on the solution obtained by other units. Another method which has widely been used is super efficiency, presented by Anderson and Petersen. There are several flaws in their suggested method. Infeasibility, instability, dependency of the model on the input and output orientation and non-zero slack variables are the weaknesses of this method which may occur in specific problems. This article is an attempt to present a method which does not have the aforementioned problems and can be utilized to calculate the rank of extreme efficient units through using the Hit or Miss Monte Carlo method. At the end of the article some examples are made in order to show the efficiency of the presented method.

Project scheduling is the part of project management that deals with determining when in time to start (and finish) which activities and with the allocation of scarce resources to the project activities. In practice, virtually all project managers are confronted with resource scarceness. In such cases, the Resource-Constrained Project Scheduling Problem (RCPSP) arises. This optimization problem has become popular over the last few decades because of its practical relevance to various industrial and research fields. Numerous procedures have been developed in the literature for finding either optimal or heuristic solutions for the RCPSP. Resource constrained project scheduling problem under stochastic circumstances have been considered in recent decades where uncertainty is modeled by means of activities’ duration. In this research we study an extension of basic stochastic RCPSP in which availability of resources is not predefined. Activities follow preempt-resume mode in case of any disruption due to resource infeasibility. A solution for this variant of RCPSP is defined in three steps by utilizing heuristic procedures for creating initial schedule, adding time and resource buffers in order to yield proactive schedule and applying reactive policies to encounter with unhandled breakdowns. Computational experiments depict that proposed combined procedure achieve significant performance gains over the use of each method separately.

The stochastic data envelopment analysis (SDEA) was developed considering the value of inputs and outputs as random variables. Therefore, statistical distributions play an important role in this regard. The skew-normal (SN) distribution is a family of probability density functions that is frequently used in practical situations. In this paper, we assume that the input and output variables are skew-normally distributed. With introducing asymmetric error structure for random variables of SN distribution, a stochastic BCC model is provided. The proposed model includes BCC model assuming a normal distribution of data as well. Finally, the proposed model is used in a numerical example.

In this research a discipline for grading of country’s student dormitory will be designed. The major goal of classification is to promote the quality of student dormitories, and results of this grading in addition of creating a healthy competitive space between universities for promotion, will have important consequence of equating the rental money of dormitories proportionate with dormitories grade. Also with respect to appendix policies of article 44 of constitutional law and 5th program of development sentences, ministry of science, research and technology shall give welfare services to nongovernmental companies. So existing of such systems for grading of dormitories, will obviously invigorate the supervising dimension of ministry of science, student welfare fund and universities on given dormitories. Although there are several evaluation methods for universities and centers for higher education, but no method for grading of dormitories in international level has been reported up to now. Therefore in this paper, with different beneficiaries corporation, important dimensions and measures for grading of dormitories has been determined and with help of designed system, student dormitories are classifying to four classes.