Journal of Operational Research in its Applications
Year:2007 | Volume:4 | Issue:13|Papers Count:9

In this paper we apply neural network method for solving generalized assignment problem. This problem is the generalization of the well-known assignment problem that can be formulated as a zero-one integer programming problem. For solving this problem applying neural network method, first we transform it to a nonlinear programming problem, then we use two types of neural network structure one based on penalty function and the other augmented lagrangean multiplier method and compare them with each other. It will be noticed that neural network based on penalty function method is not appropriate to combinatorial optimization problems because it reaches an infeasible solution or gets stuck in a nonoptimal feasible solution while neural network based on augmented lagrangean multiplier method can alleviate this problem to some extent.

In this article, we try to use statistical experiment in data envelopment analysis to obtain more accurate analytical DEA models, and use cluster sampling in this operation. Also we have examined the models for 35 branchs of commerical banks in different monthes and the results show that the models work well.

Today, in the real world, many quantitative and qualitative factors like the quality, price, flexibility and efficiency of the delivery process should be considered in decision making problems. Therefore, linguistic variables can be expressed in trapezoidal or triangular fuzzy numbers are used to assess the rating of each alternative and the weight of each criterion. Hence, the aim of this paper is to extend the TOPSIS method to decision-making problems with fuzzy data to find appropriate alternative under vague and ambiguous environment with team of decision making. According to the concept of the TOPSIS method in group multiple criteria decision making (GMCDM) problem, an index of closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distance to the both fuzzy ideal solution and fuzzy anti-ideal solution based on approach of ranking of the fuzzy numbers simultaneously. Finally, an example is given to highlight the procedure of the proposed method.

QFD is one of the efficient tools in quality management which has a widespread application in various industries in order to improve product quality. It is also utilized as one of the quality engineering procedures for incorporating customer demands into products to increase satisfaction. The significance of the customer demands has an ambiguous value, however, as ranking the demands only importance factor is taken into consideration. At the present paper in addition to quantifying the language terms through fuzzy logic and identifying key factors with the aid of satisfaction-importance matrix, a method for determination of the priorities of the customer demands in quality house matrix through phase logic, considering the combination effect of the importance and demands satisfaction, is represented. a case study is also introduced for the products of a tire plant.

In this paper we prove completely the several main inertia theorems which using in computing of inertia of a matrix then present a new proof for the main inertia theore .At the end section we obtain the inertia of several matrices with using the Main inertia theorem and author’s innovation method.

In this paper additive perturbations of all data in the Charnes-Cooper-Rhodes (CCR) model preserving efficiency of an efficient Decision Making Unit (DMU) are considered first. Sufficient conditions for an efficient DMU to preserve its efficiency after additive perturbations of all data are given. These result are applied to 10 bank branches of a commercial bank of iran using 3 inputs and producing 2 outputs are considered. For each DMU, efficient according to the additive model, a region of efficiency is obtained. In that region inputs and outputs of the corresponding efficient DMU can be changed and its efficiency is preserved.

After successful applications of fuzzy logic in the controller systems this logic has been applied in many other fields such as simulation, artificial intelligence, management, operations research and etc. In the real world, many applied problems are modeled as mathematical programming problems and it may be necessary to formulate these models with uncertainty. Many problems of these kinds are linear programming with fuzzy parameters. The concept of fuzzy mathematical programming on general level was first proposed by Tanaka et al. in 1974 in the framework of the fuzzy decision of Bellman and Zadeh. Afterwards, many authors considered various types of the fuzzy linear programming (FLP) problems and proposed several approaches for solving these problems. These methods are related to the type of fuzzy linear programming and hence there is not a general method for solving these problems. Nevertheless, some methods use the concept of comparison of fuzzy numbers for solving fuzzy linear programming problems. In effect, most convenient methods are based on the concept of comparison of fuzzy numbers by use of ranking functions. In the other words, usually in such methods authors define a crisp model which is equivalent to the FLP problem and then use optimal solution of the model as the optimal solution of the FLP problem. In this paper, based on the some fundamental concepts of linear programming we present some concepts and definitions of fuzzy linear programming such as fuzzy feasible solution, fuzzy basic feasible solution, fuzzy optimal solution and non-degenerated solution and optimality conditions in fuzzy environments. Moreover, we state fuzzy simplex algorithms that recently proposed by Mahdavi-Amiri and Nasseri. And also we give a two phase method for solving linear programming problems with fuzzy numbers. Some new examples are given to illustrate the mentioned methods.

In this paper our aim to know the ability of students and chose the correct way for education of mathematics for them. Also, verify the relation between mind, ingenious and education of mathematics.