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)
Praise be to God, Lord of the Worlds, and the best blessings and peace be upon our master Muhammad and all his family and companions, and those who follow them with goodness until the Day of Judgment. . And after:
God created man in the best manner, and subjugated the universe to him and favored him over the rest of creation when he gave him a mind to contemplate and know how to distinguish between the harmful and the beneficial, the bad and the good, in order to exploit him in achieving the meaning of worship, because it is the highest goal of his creation. God Almighty said (And I did not create the jinn and mankind. Except that they worship them.” [Al-Dhariyat: 56]
If knowing what is harmful from what is beneficial a
... Show MoreHS Saeed, SS Abdul-Jabbar, SG Mohammed, EA Abed, HS Ibrahem, Solid State Technology, 2020
This paper is devoted to the discussion the relationships of connectedness between some types of graphs (resp. digraph) and Gm-closure spaces by using graph closure operators.
The obligatory duty must be fulfilled for attachment to the discharge, whatever the reasons for the missingness, whether it is left by mistake or omission or deliberate, whether with or without excuse. What is likely in this research to spend Ramadan on laxity.
The one who delayed making up Ramadaan fasts until he realized another Ramadaan, fasted the second and spent the first after him, and no ransom on him, either with an excuse or without an excuse.
In mammals, the kidneys originate in an embryo from the mesoderm through three excretory organs, namely: Pronephros, Mesonephros, and Metanephros. After the formation of Metanephros is completed, the kidneys begin to form nephrogenesis through mesenchymal cells located at the tip of the ureteric bud, that contribute in the formation of glomerulus and Renal tubules. The stages of glomerulus formation in the embryo of albino mice at the age of 14 to 19 days of gestation were studied. It was obtained after the sacrifice of the expectant mother and the kidneys were excised from the embryos and fixed using Aqueous Bouin's solution, Microscopic slices with a thick
... Show MoreIn this work, we have examined the spectral response of (p-CuAlSe2/n-Si) detector, (CAS) thin films deposited by thermal evaporation at RT with a thickness (450) nm, and annealing temperature at (473K) for 2 h. Optical transmission measurements displayed reasonably slight transmission besides higher absorbance trendy the visible region, energy gaps were observed by annealing, were found to be direct, and decreased with the effect of annealing. The extreme responsivity value arises at wavelength 459 nm, with improvement value of specific detectivity and quantum efficiency the annealing films be situated originate as greatest suitable aimed at numerous device application.
In the present paper we report the synthesis of a new ligand [HL][(2-1-[(2-hydroxy-benzylidene)-hydrazono]-ethyl) benzene-1, 3, 5-triol and its complexes with (Mn", Fe", Cd", and Hg") The ligand was prepared in two steps. In the first step a solution of salicylaldehyed in methanol reacted under reflux with hydrazinemonohydrate to give an intermediate compound which reacted in the second step with 2, 4, 6-trihydroxidernonohydrate giving the tientioned ligand. The complexes were synthesis by direct reaction of the corresponding metal chloride with ligand. The ligand and the complexes have been characterized by spectroscopic methods [" H NMR, IR, UV-Vis,, atomic absorption], HPLC microanalysis along with conductivity measurements. From the abo
... Show MoreRMK Al-Zaid, AT Al-Musawi, SJ Mohammad
Ectopic growth of normal cells or debris originating from endometrium, the inner layer of female reproductive tube leads to endometriosis. The main symptoms are dyspareunia, dysmenorrhea, and sometimes chronic pelvic pain. Unfortunately, it has no cure or treatment, only symptoms relief medication or surgical removal. Endometriosis causes estrogen imbalance leading to intestinal bacterial estrobolome dysregulation and subsequent change in immune response. Our study aims to investigate the linkage between gut dysbiosis and immunological response in endometriotic mice. Balb/c mice were ovariectomized (OVX) 7 days before intraperitoneal transplantation of 2mm2 endometrial tissue from OVX