2017
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A Hybrid Heuristic Algorithm to Solve Capacitated Locationrouting Problem With Fuzzy Demands
2
2
In this paper, the capacitated locationrouting problem with fuzzy demands (CLRPFD) is considered. The CLRPFD is composed of two wellknown problems: facility location problem and vehicle routing problem. The problem has many reallife applications of which some have been addressed in the literature such as management of hazardous wastes and food and drink distribution. In CLRPFD, a set of customers with fuzzy demands should be supplied by a fleet of vehicles that start and end their tours at a single depot. Moreover, the vehicles and the depots have a limited capacity. To model this problem, a fuzzy chanceconstrained programming is designed based on fuzzy credibility theory. To solve the CLRPFD, a hybrid heuristic algorithm (HHA) including two main phases is proposed. In the first phase, an initial population of solutions is generated by the greedy clustering method (GCM) obtained from the literature of the problem, while in the second phase, a genetic algorithm is applied for further improvement of the solutions of first phase. While the first phase of the HHA consists of four steps, the second phase includes two main steps. To achieve the best value of the major parameter of the model, named dispatcher preference index, and to analyze its influence on the changes of the final solution, numerical experiments with different sizes on the number of customers and candidate depots are carried out. The computational results show that the HHA is efficient so that it has improved all solutions that obtained from the GCM. Finally, performance of the proposed model to the similar model exists in the literature is evaluated by several standard test problems of the CLRP.
1

1
20


A.
Nadizadeh
Department of Industrial Engineering, Faculty of Engineering, Ardakan University, Ardakan, Iran.
Department of Industrial Engineering,
Iran
nadizadeh@ardakan.ac.ir


A.
Sadegheih
Industrial Engineering Department, Faculty of Engineering, Yazd University, Yazd, Iran.
Industrial Engineering Department, Faculty
Iran


A.
Sabzevari Zadeh
Industrial Engineering Department, Faculty of Engineering, Shahed University, Tehran, Iran.
Industrial Engineering Department, Faculty
Iran
Capacitated locationrouting problem
Fuzzy demand
Credibility theory
Stochastic simulation
Fuzzychance constrained programming
Genetic algorithm.
A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel Method
2
2
This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the GramSchmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The convergence analysis is established theoretically. The applicability of the iterative method is demonstrated by testing some various examples.
1

21
26


R.
Ketabchi
Department of Mathematics, Science and Research branch, Islamic Azad University,Tehran,Iran.
Department of Mathematics, Science and Research
Iran


R.
Mokhtari
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran.
Department of Mathematical Sciences, Isfahan
Iran


E.
Babolian
Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran
Reproducing kernel method
Volterra integral equations
GramSchmidt orthogonalization process
Evaluating the Efficiency of Firms with Negative Data in MultiPeriod Systems: An Application to Bank Data
2
2
Data Envelopment Analysis (DEA) is a mathematical technique to evaluate the performance of firms with multiple inputs and outputs. In conventional DEA models, the efficiency scores of Decision Making Units (DMUs) with nonnegative inputs and outputs are evaluated in a special period of time. However, in the real world there are situations wherein performance of firms must be evaluated in multiple periods of time while negative data are present; for this matter the current paper proposes an approach for assessing the efficiency of multiperiod systems in the presence of positive and negative measures. To illustrate, the average efficiency of firms with some negative measures are calculated in multiperiod production systems. The suggested approach utilizes the SemiOriented Radial Measure (SORM) model (Emrouznejad et al. cite{4}) for incorporating some negative factors (inputs and outputs) and determining the efficiency of multiperiod production systems. A real world data set related to banking sector is used to illustrate and clarify the proposed approach.
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27
35


S.
Kordrostami
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Department of Mathematics, Lahijan Branch,
Iran
kordrostami@liau.ac.ir


M.
Jahani Sayyad Noveiri
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Department of Mathematics, Lahijan Branch,
Iran
Data Envelopment Analysis (DEA)
Efficiency
Multiperiod systems
Negative data
The fuzzy logic in air pollution forecasting model
2
2
In the paper a model to predict the concentrations of particulate matter PM10, PM2.5, SO2, NO, CO and O3 for a chosen number of hours forward is proposed. The method requires historical data for a large number of points in time, particularly weather forecast data, actual weather data and pollution data. The idea is that by matching forecast data with similar forecast data in the historical data set it is possible then to obtain actual weather data and through this pollution data. To aggregate time points with similar forecast data determined by a distance function, fuzzy numbers are generated from the forecast data, covering forecast data and actual data. Again using a distance function, actual data is compared with the fuzzy number to determine how the grade of membership. The model was prepared in such a way that all the data which is usually imprecise, chaotic, uncertain can be used.
1

39
45


F.
Abbasi
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.
Department of Mathematics, Ayatollah Amoli
Iran
k.9121946081@gmail.com
Suspended particles
Fuzzy number
Mathematical model
Distance function
Zagreb, multiplicative Zagreb Indices and Coindices of graphs
2
2
Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The first, second and third Zagreb indices of G are respectivly defined by: $M_1(G)=sum_{uin V} d(u)^2, hspace {.1 cm} M_2(G)=sum_{uvin E} d(u).d(v)$ and $ M_3(G)=sum_{uvin E} d(u)d(v) $ , where d(u) is the degree of vertex u in G and uv is an edge of G connecting the vertices u and v. Recently, the first and second multiplicative Zagreb indices of G are defined by: $PM_1(G)=prod_{uin V} d(u)^2$ and $PM_2(G)=prod_{uin V} d(u)^{d(u)}$. The first and second Zagreb coindices of G are defined by: $ overline {M_1}(G) =sum_{uvnotin E} ( d(u)+d(v))$ and $ overline {M_2}(G) =sum_{uvnotin E} d(u).d(v)$. The indices $ overline {PM_1}(G) =prod_{uvnotin E} d(u)+d(v)$ and $ overline {PM_2}(G) =prod_{uvnotin E} d(u).d(v)$ , are called the first and second multiplicative Zagreb coindices of G, respectively. In this article, we compute the first, second and third Zagreb indices and the first and second multiplicative Zagreb indices of some classes of dendrimers. The first and second Zagreb coindices and the first and second multiplicative Zagreb coindices of these graphs are also computed.Also, the multiplicative Zagreb indices are computed using link of graphs.
1

47
57


V.
Ahmadi
Department of Mathematics, Shahid Chamran University, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran
Iran
vidaahmadi_math@yahoo.com


M. R.
Darafsheh
Department of Mathematics, Tehran University, Tehran, Iran.
Department of Mathematics, Tehran University,
Iran


J.
Hashemi
Department of Mathematics, Shahid Chamran University, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran
Iran
Zagreb indices
Multiplicative Zagreb indices
Zagreb coindices
Multiplicative Zagreb coindices
Link
A new weighting approach to NonParametric composite indices compared with principal components analysis
2
2
Introduction of Human Development Index (HDI) by UNDP in early 1990 followed a surge in use of nonparametric and parametric indices for measurement and comparison of countries performance in development, globalization, competition, wellbeing and etc. The HDI is a composite index of three indicators. Its components are to reflect three major dimensions of human development: longevity, knowledge and access to resources represented by GDP per capita, educational attainment and life expectancy. In recent years additional gender and poverty aspects are included. A known example of the nonparametric index is the HDI, while Principal Components Analysis (PCA) and Factor Analysis (FA) are among the parametric counterparts. The indices differ mainly in respect to weighting the indicators in their aggregation. The nonparametric index assumes the weights, while the parametric approach estimates them. In this research, it is aimed to purpose a new weighting approach to nonparametric indices when they are used simultaneous with principal components analysis.
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59
73


M.
Rahimpoor
Department of Industrial Engineering, Kharazmi University, Tehran, Iran.
Department of Industrial Engineering, Kharazmi
Iran
mrehimpoor@gmail.com


A.
Heshmati
Department of of Economics, Sogang University, Seoul, Korea.
Department of of Economics, Sogang University,
Iran


A.
Ahmadizad
Department of Systems Management, University of Kurdistan, Sanandaj, Iran.
Department of Systems Management, University
Iran
Principal Components Analysis
NonParametric Indicators
Composite Indices
Weighting Schemes
Mathematical modelling of Sisko fluid flow through a stenosed artery
2
2
In the present study, the nonlinear model of nonNewtonian blood flow in cosineshape stenosed elastic artery is numerically examined. The model is carried out for axisymmetric, twodimensional and fully developed blood flow. The vessel wall is assumed to be have timedependent radius that is important factor for study of blood flow. The cosineshape stenosis convert to rigid artery by using a appropriate coordinate transformation and closed form solutions are discovered. The Sisko nonNewtonian fluid model is used for discribing blood rheology. The Navierstokes equations of momentom containing pulastic pressure gradient. The resulting explicit of the governing nonlinear equations have been obtained numerically with the help of the finite differece scheme and Matlab program. The key dynamic parametrs similar resistance impedance, velocity profiles and the volumetric flow rate are studied. The influence of nonNewtonian rheological properties of unsteady blood flow and stenosis severity are found and computer modeling and simulation shown graphically.
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75
82


AR.
Haghighi
Department of Mathematics, Urmia University of Technology, Urmia, Iran.
Department of Mathematics, Urmia University
Iran
ah.haghighi@gmail.com


S.
Asadi chalak
Department of Mathematics, Urmia University of Technology, Urmia, Iran.
Department of Mathematics, Urmia University
Iran
NavierStokes equation
Finite difference Method
Timedependent Stenosis
Sisko fluid
Numerical study of heat transfer in fluidized bed dryers by volume of fluid method
2
2
The purpose of this study is numerical modeling of temperature variation of phases in a two phase regime in fluidized bed dryers including particles belonging to Group D of geldart classification. The mass transfer between phases is not taken into consideration in this modeling which has been assumed in three dimensional, unsteady, and twophase regime.To verify the modeling we consider the domain so that we will be able to compare the results with the experimental study has done by khorshidi et al [1]. At first we choose the governing equations according to problem physics and solving method. Then by designing an appropriate grid, we solved the governing equation by the volume of fluid (VOF) method, a suitable method to solve multiphase problems; finally we obtained thermal variations of gas and solid phase, the contours of temperature, pressure, and volume fraction.The comparison of numerical and experimental study results revealed that there was an appropriate adaptation between them. Also, the temperature contours proved that perfect mixing hypothesis that has been introduced by some researchers is a true one and has adaptation with this research results.
1

83
90


J.
Khorshidi
Department of Mechanical Engineering, Hormozgan University, Bandarabbas, Iran.
Department of Mechanical Engineering, Hormozgan
Iran
jkhorshidi@yahoo.com


T.
Zarei
Department of Mechanical Engineering, Hormozgan University, Bandarabbas, Iran.
Department of Mechanical Engineering, Hormozgan
Iran


H.
Davari
Department of Mechanical Engineering, Hormozgan University, Bandarabbas, Iran.
Department of Mechanical Engineering, Hormozgan
Iran
Volume of fluid (VOF) method
Heat transfer
Fluidized bed
Two phase flow.
Distribution of Ratios of Generalized Order Statistics From Pareto Distribution and Inference
2
2
The aim of this paper is to study distribution of ratios of generalized order statistics from pareto distribution. parameter estimation of Pareto distribution based on generalized order statistics and ratios of them have been obtained. Inferences using method of moments and unbiased estimator have been obtained to develop point estimations. Consistency of unbiased estimator has been illustrated. To compare the performances of the employed methods, numerical results have been computed. Illustrative example using real data is also given.
1

91
97


M.
Rajaei Salmasi
Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Statistics, Science and Research
Iran


G.
Yari
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.
Department of Mathematics, Iran University
Iran
yari@iust.ac.ir
Generalized Order Statisitcs
Pareto Distribution
Parameter Estimation