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.
Abstract
The study discussed three areas in strategic thinking, namely, (patterns elements, outcomes) , this study aimed to measure extent to which strategic leaders have the type or types of patterns of strategic thinking, and measure the extent of their use of the elements of strategic thinking, and measurement of strategic thinking outcomes for managers at various levels , And to know the relationship between the modes of strategic thinking, elements and outcomes in organizations. the study included five banks and four hospitals and four colleges and universities, has been a research sample consisted of 168 individuals, distributed in positions (Director General , Director of Directorate , Director of
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The main objective of the research is to build an optimal investment portfolio of stocks’ listed at the Iraqi Stock Exchange after employing the multi-objective genetic algorithm within the period of time between 1/1/2006 and 1/6/2018 in the light of closing prices (43) companies after the completion of their data and met the conditions of the inspection, as the literature review has supported the diagnosis of the knowledge gap and the identification of deficiencies in the level of experimentation was the current direction of research was to reflect the aspects of the unseen and untreated by other researchers in particular, the missing data and non-reversed pieces the reality of trading at the level of compani
... Show MoreBackground:Open reduction and internal fixation (ORIF) of using miniplates and screws is the treatment of choice of mandibular fractures. It is important to know both: the region where the bone providesafirm anchorage, andthe topography of the dental apices and inferior alveolar nerve to avoiddamaging them when inserting the screw. The aim of this study is to determine the thickness of buccal cortical plate and that of buccal bone at the parasymphysis and mandibular body, thereby determining the area that provide afirm anchorage and the maximum length of mono-cortical screws that can be safely placed in these regions without injuring the tooth roots or mandibular nerve. Materials and Methods:The sample of the present study was 110 Iraqi sub
... Show MoreLinear regression is one of the most important statistical tools through which it is possible to know the relationship between the response variable and one variable (or more) of the independent variable(s), which is often used in various fields of science. Heteroscedastic is one of the linear regression problems, the effect of which leads to inaccurate conclusions. The problem of heteroscedastic may be accompanied by the presence of extreme outliers in the independent variables (High leverage points) (HLPs), the presence of (HLPs) in the data set result unrealistic estimates and misleading inferences. In this paper, we review some of the robust
... Show MoreThe research aim at identifying the time of motor response to auditory and visual stimuli as well as identifying the accuracy of blocking and finding the relationship between motor repose time and blocking accuracy. The community was (7) primer soccer league of 2019 – 2020 and the subjects were (24) volleyball players from Al Jaish and Al Shorta clubs ten players from Al Shorta club performed the pilot study. The researchers used the descriptive method and the data was collected and treated using SPSS. The results showed a significant relationship between response time and blocking accuracy. The researchers recommended concentrating on applying scientific principles for developing time of motor response in a manner suitable for bl
... Show MoreAn approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly