The presented study investigated the scheduling regarding jobs on a single machine. Each job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two exact methods are important; a Branch and Bound algorithm (BAB) and a complete enumeration (CEM) method are applied to solve the three proposed MSP criteria by finding a set of efficient solutions. The experimental results showed that CEM can solve problems for up to jobs. Two approaches of the BAB method were applied: the first approach was BAB without dominance rule (DR), and the BAB method used dominance rules to reduce the number of sequences that need to be considered. Also, this method can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. In addition, to find good approximate solutions, two heuristic methods for solving the problem are proposed, the first heuristic method can solve up to jobs, while the second heuristic method can solve up to jobs. Practical experiments prove the good performance regarding the two suggested approaches for the original problem. While for a sub-problem the experimental results showed that CEM can solve problems for up to jobs, the BAB without dominance rule (DR) can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. Finally, the heuristic method can solve up to jobs. Arithmetic results are calculated by coding (programming) algorithms using (MATLAB 2019a)
Abstract
There has been a heated controversy over the role the financial policy plays and how sufficient it is in affording the financial burden. This burden is known as the operational current expenses which the governments of various countries mainly afford, despite the discrepancy in the government’s economic policy. After the deterioration and deficit in the state budget in all countries nowadays, it was necessary to find an appropri
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Arzı Kanber/Kamber hikayesi Anadolu, Rumeli, Azerbaycan, Türkmenistan ve Irak gibi Türk dünyasının birçok yerinde birden fazla varyantı bulunan, çok sevilen ve yaygın olarak anlatılan aşk ve dramatik maceralı bir halk hikayesidir. Türk halk hikayelerinin en popüler olanlarından biri sayılan Arzı Kanber/Kamber hikayesi, Anadolu'nun birçok yöresinde bilinmesine rağmen Irak Türkmenleri arasında daha çok sevildiği ve yaygın olarak anlatıldığı tespit edilen birden fazla varyantından da görülebilir. Irak Türkmenleri arasında günümüze kadar hikayenin iki varyantı tespit edilmi
... Show MoreObjectives: The study aimed to clarify the role of Al-Sayyid Al-Ajall and his family in the service of the Mongol Empire. They worked to develop its administrative and military institutions, benefiting from their extensive experience in administration, politics, economics, and urban affairs. Due to their capabilities, they received the patronage of Genghis Khan and subsequent generations, earning the confidence of the ruling Mongol authority. As a result, they were granted significant powers within the state. Methods: The study relied on the analytical method to analyze historical texts, compare them with others, and discuss them accurately. Results: The study yielded several results, including the minister's keen interes
... Show MoreTo investigate the antiplaque and antigingivitis efficacy in addition to evaluating side effects and subjects’ perceptions of three commercially available mouthwashes.
This study was a double‐blind, parallel, and short‐term trial. A total of 75 dental students with biofilm‐induced gingivitis were included in the final analysis of the current study. Clinical parameters (plaque index and bleeding on probing) and the staining effect were measured at baseline and after 7 days. In addition, a VAS‐based assessment questionnaire was completed by the participants.
The habitat type and food availability always influence the population size of many
organisms. Bird’s feeding pattern should be abstracted to complete avian community structure
data. The agronomy main research farm of Orissa University of Agriculture and Technology
is a well-managed multi-crop agro-ecosystem which provides a suitable ground for ecological
research. In a multi-crop farmland, the association of Barn Swallow Hirundo rustica Linnaeus,
1758, with the Indian mustard Brassica juncea (L.) Czernajew, 1859 crops have been
recorded for the first time while hovering only on this field. A flock of Barn swallows was
recorded in 32 field visits while flying continuously over the Indian mustard field after
flow
Background: Oil refinery workers are continuously exposed to numerous hazardous materials. Petroleum contains the heavy metals as a natural constituent or as additives. These metals induce the production of ROS which associated with an oxidative damage to DNA, proteins, and lipids. This study was conducted to assess the salivary levels of heavy metals, salivary oxidative status, oral immunological activity (salivary sIgA) and assessment of the oral findings among the workers of Al-Daura oil refinery in Baghdad city. Subjects, Materials and Methods: This study was done in Al-Daura oil refinery; samples consist of 60 workers involved in refinery processes (study group) and 20 non-workers (control group). Oral examination and saliva collection
... Show MoreThe research aimed to prepare a psychological counseling program for the coaches of the Sports Care Center in the gymnasium, and to learn about the impact of the psychological counseling program in reducing irrational ideas and causal attribution of the coaches of the Sports Talent Care Center in the gymnasium, to assume that there are statistically significant differences between the results of the tribal and posttests of the research group Experimental in the scale of irrational ideas, and there are statistically significant differences between the results of the tribal and posttests of the experimental research group in the scale of the causal attribution scale, The experimental approach was adopted by designing one experimental
... Show MoreThe present paper(Spacio-Temporal Relations in the Translated Text in Both Russian and Arabic) focuses on the spacio-temporal effect in the translated text; it is possible to compose the translation text simultaneously with the process of the composing the original text. This is carried out during the simultaneous consecutive translation. And, the time and place of composing the translation might greatly differ from the time and place of composing the original textt. The translator may tackle a text of an ancient time and written in a language which might have changed, and may thus appear as another language where the author might have talked on behalf of a people who had lived or are living in apparently different geographic
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