International Journal of Industrial Mathematics
Volume:9 Issue: 1, Winter 2017

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered. The CLRP-FD is composed of two well-known problems: facility location problem and vehicle routing problem. The problem has many real-life applications of which some have been addressed in the literature such as management of hazardous wastes and food and drink distribution. In CLRP-FD, 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 chance-constrained programming is designed based on fuzzy credibility theory. To solve the CLRP-FD, 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 ýCLRP.ý

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 Gram-Schmidt 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 ýexamples.

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 non-negative 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 multi-period systems in the presence of positive and negative measures. To illustrate, the average efficiency of firms with some negative measures are calculated in multi-period production systems. The suggested approach utilizes the Semi-Oriented Radial Measure (SORM) model (Emrouznejad et al. \cite{4}) for incorporating some negative factors (inputs and outputs) and determining the efficiency of multi-period production systems. A real world data set related to banking sector is used to illustrate and clarify the proposed approach.

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 ýused.ý

ýLet 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: $M_1(G)=\sum_{u\in V} d(u)^2, \hspace {.1 cm} M_2(G)=\sum_{uv\in E} d(u).d(v)$ and $ M_3(G)=\sum_{uv\in 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: $PM_1(G)=\prod_{u\in V} d(u)^2$ and $PM_2(G)=\prod_{u\in V} d(u)^{d(u)}$. The first and second Zagreb coindices of G are defined by: $ \overline {M_1}(G) =\sum_{uv\notin E} ( d(u)(v))$ and $ \overline {M_2}(G) =\sum_{uv\notin E} d(u).d(v)$. The indices $ \overline {PM_1}(G) =\prod_{uv\notin E} d(u)(v)$ and $ \overline {PM_2}(G) =\prod_{uv\notin 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 ýgraphs.

Introduction of Human Development Index (HDI) by UNDP in early 1990 followed a surge in use of non-parametric and parametric indices for measurement and comparison of countries performance in development, globalization, competition, well-being 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 non-parametric 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 non-parametric index assumes the weights, while the parametric approach estimates them. In this research, it is aimed to purpose a new weighting approach to non-parametric indices when they are used simultaneous with principal components ýanalysis.ý

In the present study, the nonlinear model of non-Newtonian blood flow in cosine-shape stenosed elastic artery is numerically examined. The model is carried out for axisymmetric, two-dimensional and fully developed blood flow. The vessel wall is assumed to be have time-dependent radius that is important factor for study of blood flow. The cosine-shape stenosis convert to rigid artery by using a appropriate coordinate transformation and closed form solutions are discovered. The Sisko non-Newtonian fluid model is used for discribing blood rheology. The Navier-stokes 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 non-Newtonian rheological properties of unsteady blood flow and stenosis severity are found and computer modeling and simulation shown ýgraphically.

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 two-phase 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 multi-phase 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 ýresults.ý

ýThe 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 ýgiven.ý