In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm). And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restricting the search.
ملخص البحث:
ان الله تعالى هو الذي خلق جميع المخلوقات ، والذي بيده الموت والحياة وان كل هذه المخلوقات تحتاج الى اوامر ، وهذه الاوامر الالهية وجهها الله لعبادة بوساطة انبياءه ( عليهم السلام) فكانوا هم اول المستسلمين والمنقادين لأوامره ، فجاءت الآيات الكريمة مخاطبة للأنبياء واقوامهم بشكل عام ولنبينا محمد (r) بشكل خاص.
اما عن المضمون البحثي فقد جاءت مادته مقسمة الى ثل
... Show MoreThis paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.
In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.
In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov
... Show MoreFour molecular imprinted polymer (MIP) membranes for Mebeverine.HCl (MBV.HCl) were prepared based on PVC matrix. The imprinted polymers were prepared by polymerization of 2-acrylamido-2-methyl-1-propane sulphonic acid (AMPS) as monomer, pentaerythritoltriacrylate (PETRA) as a cross linker ,benzoyl peroxide (BPO) as an initiator and mebeverine as a template. Four different types of plasticizers of different viscosities were used and the electrodes were fully characterized in terms of plasticizer type, response time, lifetime, pH and detection limit.
The MBV-MIP electrodes exhibited Nernstian response in concentration range from 1.0×10-6 to1.0×10-1 M with slopes of 13.98, 19.60, -20.43 and 19.01 mV/ decade. The detection limit and qua
Air pollution from various sources is one of the most serious environmental problems, especially after pollutants are deposited on the surface of the soil and leaves of the plants and then transferred to the rest of the plant and entering food chains. The present study was conducted to determine the effects of air pollution on different biochemical parameters in Eucalyptus sp. and calculation the Air Pollution Tolerance Index. The selected plant leaves were collected from five sites, four of them within the city of Baghdad, namely Al-Jadriya, Al-Andlous, Al-Doura and close to the private generators to represent the urban areas and Abu Ghraib site to represent the rural area. The leaves were taken on a seasonal basis for the period from Octo
... Show MoreImages are important medium for conveying information; this makes improvement of image processing techniques also important. Interpretation of image content is one of the objectives of image processing techniques. Image interpretation that segments the image to number of objects called image segmentation. Image segmentation is an important field to deal with the contents of images and get non overlapping regions coherent in texture and color, it is important to deal only with objects with significant information. This paper presents survey of the most commonly used approaches of image segmentation and the results of those approaches have been compared and according to the measurement of quality presented in this paper the Otsu's threshol
... Show MoreThirty serum samples of patients suffering from rheumatoid arthritis after screening of rheumatoid factor, C-reactive protein and ESR were collected and including in present study to detect the IgG antibody against Chlamydia pneumoniae by ELISA test. The results showed only 2(6%) patients had seropositive of C. pneumoniae, this lead to suggest that C. pneumoniae may be one of the etiological or trigger factor in patients of rheumatoid arthritis.
Gas Lasers are important tools that are used in variety purposes, for their low and (cw) output power. The aim of this study was to prepare a way to calculate an optimum stimulated emission cross-section in a gas laser containing a mixture of Xenon and Neon by (30%-70%). The process was a theoretical study of each gas in separate in terms of their physical properties as an active medium. The results of these calculations are logic and more convenient than other mixtures used before