INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2021 | Volume:13 | Issue:3|Papers Count:15

In this paper, we investigate the Single-Source Capacitated Multi-Facility Weber Problem. The aim is to locate several new facilities among existing customers and simultaneously allocate customers to facilities, so that capacity constraints are met and each customer will provide all its demand from just one facility, and as a result, the total cost of transporting between new facilities and existing customers gets minimum. A Genetic Algorithm is proposed for solving the problem, in which a local search method is embedded. The proposed Genetic Algorithm is tested on existing data sets to evaluate its robustness over available methods in the literature.

The passage of time always makes us aware of the issues around us. Time projects also reveal the hidden issues of the project. So the logical step is to include transparent points in the project. Stopping or slowing down the project process is necessary to apply these to the project, which will delay the projects. So project managers need to tightly control project risk with reasonable costs. Existence of delays is always an inseparable part of projects and subject of fundamental disagreements among their stakeholders in all countries. As delay in projects is equal to increased costs, thus, by having delay and spending too much cost out of the pre-planned cash ow, a project can even reach a point that it will get out of pro t. In the present study the researchers believes that, risk of delays should be managed, minimized, shared, transferred or accepted, but it cannot be ignored. Therefore, it must be predicted, covered, managed and optimized. Now, the fact that any delay and prolongation of project time results in signi cant qualitative and quantitative costs more than the initial estimates shows importance and necessity of research in this area. By providing an innovative method with the help of the Work breakdown Structure, Baseline, Hierarchical Technique and Data Envelopment Analysis (DEA), the researchers will control the risk of projects and even prevent them from occurring.

The  rst leap Zagreb index LM1 of a (molecular) graph, is the sum of squares of the second degrees of vertices (number of their second neighbors), and the second leap Zagreb index LM2 is the sum of the products of the second degrees of pairs of adjacent vertices, and the third leap Zagreb index LM3 is the sum of the product of the degree and second degree of the vertices. In this paper, we determine the  rst, second and third leap Zagreb indices of some graph operations.

In this paper,  rst the Newton's divided di erence interpolation method based on the gH di erence on fuzzy data is introduced. Then the numerical methods entitled fuzzy Euler and modi ed fuzzy Euler are used to solve fuzzy impulsive initial value problem. Moreover the algorithms for the fuzzy impulsive initial value problem are explained and their local truncation errors are obtained in details. Finally, for more illustration some numerical examples are solved.

Data Envelopment Analysis (DEA) is recognized as a robust analytical tool extensively utilized in measuring the relative e ciency of a group of Decision Making Units (DMUs) with multiple inputs and outputs. The DEA models require inputs and outputs equipped with precise information. However in real-world situations inputs and outputs may be unstable and complicated thus unable to be accurately measured. This problem resulted in the investigation of uncertain DEA models. The BCC model is studied in this paper in an uncertain environment where uncertain inputs and outputs were belief degree-based uncertainty useful for the cases for which no historical information of an uncertain event is available. As the solution method the uncertain BCC model was converted to a crisp form using two approaches of expected value method (EV) and expected value and chance-constrained method (EVCC) separately. Finally, an applied example regarding the Iranian Banking system is presented to document the proposed models.

Conventional Data Envelopment Analysis (DEA) models de ne returns to scale (RTS) based on some local information about the proportional variation in outputs with respect to the proportional variation in inputs. Generalized RTS has been introduced to compute the rate of variation in outputs with respect to the variation in inputs up to the most productive scale size (MPSS) pattern. In this paper, we address the generalized RTS in the multiplicative models and we propose an algorithm to calculate the rate of variations in di erent intervals. We also demonstrate that the non-discretionary factors can be easily taken into account in the algorithm.

The use of proportions derived from nature in traditional architecture is a constant principle in the interactions between structural and physical environments. It has been shown that having an intrinsic relationship with nature can lead to formal similarities. This study attempts to determine the compatibility of common geometric proportions used in traditional houses with daylight performance and natural proportions of the surrounding physical environment so as to recognize the most compatible structural layout with nature. To this end, 28 Shahneshin rooms were chosen from 21 traditional houses in Ardabil. The required data were collected via  eld observation and logical reasoning and then numerical analyses were conducted on them. After that, using frequency diagram and mean coe cient of variation, the distribution pattern of the proportions employed in the Shahneshin rooms were determined. Finally, the compatibility of geometric proportions and skylight characteristics with daylight perimeter zone was examined through numerical analyses. The results obtained from the most common structural layouts indicated that in traditional architecture, physical environment and structural environment were compatible and interacted with each other; 95% of the prevalent proportions in the traditional houses of Ardabil appeared to follow arithmetic ratios and many of them were found to follow golden proportions. Moreover, they were observed to have the highest level of overlap with the frequency distribution and perimeter zone of daylight. Furthermore, the analysis of no-sky line area showed that in all of the cases, sky was visible from the inner space of the rooms.

One of the key issues raised in networks ow is its interdiction. Keshavarzi et al. scrutinized the issue with the multi-sources and multi-sinks conditions in mind while considering the speci c conditions of ow being sent from sources to sinks [R. Keshavarzi et al., Multi-source-sinks network ow interdiction problem, International Journal of Academic Research, 2015]. Moreover, the matter was also examined in the state of multi-interdictors and a practical solution was presented [Keshavarzi and, Salehi, Multi commodity multi source-sinks network ow interdiction problem with several interdictors, Journal of Engineering and Applied Sciences, 2015]. In this paper, the networks ow interdiction in multi-source and multi-sink conditions was addressed; meanwhile, bearing in mind the uncertain data (from a speci ed beginning to an ending interval), an optimal interval was presented. Finally, a numerical example for this issue was provided and then solved by the program "Lingo".

In most of real world problems data su er from inaccuracy, thus considering an interval for data perturbation seems to be a good idea. There exist many papers in literature about Interval linear programming problems (ILP) dealing with non negative variables. Here the general form of an ILP is considered where all the parameters and variables are considered to be intervals. Moreover, in this study more general conditions for variables are considered, variables which are unrestricted in sign. Although this is the case in most of the real world problems, due to high complexity it has not been dealt with in literature yet. In this paper a new method is presented in order to obtain fully interval linear programming problems (F ILPP ) using a nonlinear programming problem (NLP). Furthermore, in order to demonstrate how the proposed method works two numerical examples are illustrated.

This paper proposes a novel problem on the e ciency in the location problem. We consider the problem of  nding optimal location of an e cient facility in the plane. This yields to a novel combination of the location problem and e ciency measurement. We describe the di erence between our model and the principle existing models in the literature. We then present a bi-objective programming models for the e cient median and center problems.

In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of di erential equations of fraction. By using the Dickson-based collocation method and using Chebyshev's spatial points, we transform the system of de cit di erential equations into a system of algebraic equations. In this way, an approximate solution can be found for the proposed model. By introducing the error functions for the expressed fractional model, the accuracy and convergence of the obtained solutions are investigated. Some of the approximate results obtained using this method is displayed in the numerical results section.

In this paper, two adaptive methods with memory are improved based on the Cordero-Torregrosa method. The technique of adaptive method increases the e ciency index as high as possible. The new proposed derivative free methods have possessed the convergence order 7: 46315 and 7: 99315, and they use the information from the last two iterations. Finally, we provide convergence analysis and numerical examples to illustrate the e ciency and applicability of the proposed methods.

In this paper we introduce the concept of multiplication-like modules and we obtain some related results. We show that an R-module M is multiplication-like if and only if for each ideal I of R, I = (IM: R M). We prove that any multiplication-like module is faithful and r-multiplication. So we get that any at and multiplication-like module is faithfully at.

Micromixers are an important part of micro uidics systems. In the present work, mixing was enhanced through the three helix types of micromixers. As a result of Dean vortices, a mixing index of 99% obtained at a very short length of the micromixers for the Reynolds number of 10. It is also obtained that the micromixer with rectangular cross-section showed better enhancement compared to the circular and triangular cross-section.