Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an efficient solution to the problem (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥). Because these problems are NP-hard problems so it is difficult to determine the efficient (optimal) solution set for these problems so some special cases are shown and proven which find some efficient (optimal) solutions suitable for the discussed problem, and highlight the significance of the Dominance Rule (DR), which can be applied to this problem to enhance efficient solutions.
The importance of forecasting has emerged in the economic field in order to achieve economic growth, as forecasting is one of the important topics in the analysis of time series, and accurate forecasting of time series is one of the most important challenges in which we seek to make the best decision. The aim of the research is to suggest the use of hybrid models for forecasting the daily crude oil prices as the hybrid model consists of integrating the linear component, which represents Box Jenkins models and the non-linear component, which represents one of the methods of artificial intelligence, which is long short term memory (LSTM) and the gated recurrent unit (GRU) which represents deep learning models. It was found that the proposed h
... Show MoreForecasting is one of the important topics in the analysis of time series, as the importance of forecasting in the economic field has emerged in order to achieve economic growth. Therefore, accurate forecasting of time series is one of the most important challenges that we seek to make the best decision, the aim of the research is to suggest employing hybrid models to predict daily crude oil prices. The hybrid model consists of integrating the linear component, which represents Box Jenkins models, and the non-linear component, which represents one of the methods of artificial intelligence, which is the artificial neural network (ANN), support vector regression (SVR) algorithm and it was shown that the proposed hybrid models in the predicti
... Show MoreSamples prepared by using carbon black as a filler material and phenolic resin as a binder. The samples were pressed in a (3) cm diameter cylindrical die to (250)MPa and treated thermally within temperature range of (600-1000)oC for two and three hours. Physical properties tests were performed, like density, porosity, and X-ray tests. Moreover vicker microhardness and electric resistivity tests were done. From the results, it can be concluded that density was increased while porosity was decreased gradually with increasing temperature and treating time. In microhardness test, it found that more temperature and treating time cause more hardness. Finally the resistivity was decreased in steps with temperature and treating time. It can be c
... Show MoreOften times, especially in practical applications, it is difficult to obtain data that is not tainted by a problem that may be related to the inconsistency of the variance of error or any other problem that impedes the use of the usual methods represented by the method of the ordinary least squares (OLS), To find the capabilities of the features of the multiple linear models, This is why many statisticians resort to the use of estimates by immune methods Especially with the presence of outliers, as well as the problem of error Variance instability, Two methods of horsepower were adopted, they are the robust weighted least square(RWLS)& the two-step robust weighted least square method(TSRWLS), and their performance was verifie
... Show MoreThis paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.