مجله پژوهش های نوین در ریاضی
پیاپی 14 (تابستان 1397)

The time - cost tradeoff problem is one of the most critical issues in the project scheduling field and so far, a lot of research has been done with a variety of quantitative and qualitative approaches on this subject. In this research, we intend to provide a two - objective mathematical model which balances crash and delay for activities. So that it provides the right tools for decision makers to decide on the scheduling of activities, with considering available facilities and time available, to complete the project. In the proposed mathematical model, it is attempting to use the assumptions such as the nonlinear cost function as well as the time value of money so that the problem conditions will be as close as possible to the real environment. At the end, we solve the mathematical model presented in this paper using the Multi Objective Particle Swarm Optimization (MOPSO) algorithm and the impact of the crash and delay for activities in the final non-dominated solutions is investigated.

So far, many types of location models have been developed to find optimal spatial patterns according to different spatial metrics such as cost, coverage and availability. The initial focus of these models is on the location availability of service providers and demand estimates, and some of these models are within the framework of multi-objective programming models. After the advent of science of data envelopment analysis, some researchers have considered the efficiency of selected facilities as one of the target functions in locational issues and provide solutions. In this paper, we present a multi-objective programming model by integrating a joint weights estimation model and location model. The resulting model, unlike the former models, is characterized by a single run of efficiently selected centers from several potential centers. The proposed model is investigated by a numerical example, and the results show the contradiction between location and performance functions.

Logistics Network Design includes network configuration decisions having long-standing influences on other tactical and operational decisions. Recently, regarding environmental issues and customer awareness and global warming closed-loop supply chain network design is taken into consideration. The proposed network for the integrated forward and reverse logistics is developed by formulating a cyclic logistics network problem which decisions for selecting the places of manufactories, distribution centers, dismantlers and disposal centers with the respective operating units were supported with the maximizing the profit. Moreover, the palaces of suppliers and customer zone are predefined in this model. Therefore, this paper presents a mixed integer quadratic programing for a dynamic multi-period multi-products closed-loop logistics network. The possibility of opening and closing of each facility at each period and expanding the capacities of facilities is the main feature of the proposed model. After model formulation, the credibility and the performance evaluation are investigated by numerical examples.

In this paper a multi - objective linear fractional programming problem with the fuzzy variables and vector of fuzzy resources is studied and an algorithm based on a parametric approach is proposed. The proposed solving procedure is based on the parametric approach to find the solution, which provides the decision maker with more complete information in line with reality. The simplicity of the proposed method is one of the advantages of the presented algorithm, which allows the decision maker to better understand the solving procedure. Moreover, a numerical example is presented to illustrate the proposed method.

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get compactness results for the group. SIN-groups are also compact with irreducible representations that have admissible vectors. Study of this part of harmonic analysis results in the study of the properties of the rajhman algebra , AR-groups, and SIN-groups. Given that with an admissible algorithm, an isometry of the Hilbert space is displayed in L ^ 2 (G), and this is necessary to look at the corresponding representation assubrepresentation of λ_G. Examining the properties of the subrepresentation of λ_G of the consequences of the admissible vector's existence. One of the important issues in the harmonic analysis is the writing of a left regular representation in the form of direct sum of irreducible representations. In this article, we use this important issue with the existence of admissible vectors composition and use it for the compactness properties of the group. According to the reference which evaluates the amenability display abilities, the poor appearance of the views is presented, so the first result is the results that are admissibility for the unpublished show.

Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set of all lattice homomorphisms ϕ:L→[2] according to the set of all lattice homomorphisms ϕ_1:L_1→[2] and the set of all lattice homomorphisms ϕ_2:L_2→[2]. Then, by using it and the set of associated prime ideals of both J(L_1,[2] ) and J(L_2,[2]), we study the associated prime ideals of J(L,[2]). Next, we assume that L_1=[2] and we characterized ass (J (L,[2])). Then by mapping cone technique and minimal free resolution of J(L_2,[2]), we find a free resolution of J(L,[2]) and an upper bound for the projective dimension of J(L,[2]). Finally, under the above assumptions and for the case that L_2=[n], we compute the minimal free resolution of J(L,[2]).

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we prove some fixed point theorems. With the help of the above process we try to generalize some theorems which were proved by other authors such as [3, 19] about existence of solution by fixed point theorems. Then for validity and applicationý of our proposed theorems, we prove existence of solution for infinite system of nonlinear integral equations. Finally for ability and more attractiveness of this research, we construct an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to obtain approximation of solution of the infinite system of nonlinear integral equations.

Research centers have an important place in promoting science and technology nationwide. On the other hand, given the limitations in allocating the funds and the facilities needed to establish these centers, it is important to decide on the selection of priority centers. In this decision - making process, several factors, such as requirements, priorities and strategies, capabilities, and balanced and sustainable development, should be considered. The total of the above items will make decision-making on ranking and selecting proposed projects a complex, time - consuming and costly resource. To this end, designing and developing a decision support tool is considered. In this research, a DSS is designed and evaluated to evaluate the design of research centers for Islamic Azad University units. This decision - making system, based on information from research centers and indicators gathered by experts, as well as the history of successful and failed research centers, is better explored with the discriminatory analysis and data envelopment analysis, and ultimately prediction that is it possible that the research center of the applicant be successful.