Semi-online Algorithms for Hierarchical Scheduling on Three Parallel Machines with a Buffer Size of 1

Author(s):  
Man Xiao ◽  
Lu Ding ◽  
Shu Zhao ◽  
Weidong Li
2014 ◽  
Vol 22 (5) ◽  
pp. 913-927 ◽  
Author(s):  
Yiwei Jiang ◽  
Feng Yu ◽  
Ping Zhou ◽  
Jueliang Hu

2019 ◽  
Vol 36 (01) ◽  
pp. 1950002
Author(s):  
Xianglai Qi ◽  
Jinjiang Yuan

This paper investigates semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the [Formula: see text]-norm of the machines’ loads. We consider two semi-online versions with knowing the total processing time [Formula: see text] of all jobs, or knowing the total processing time [Formula: see text] of the jobs of hierarchy [Formula: see text] for [Formula: see text] in advance. For the two semi-online versions, the best possible online algorithms are designed with competitive ratios of [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the maximum value of the function [Formula: see text] in [Formula: see text]. When [Formula: see text], our results cover the known results for minimizing the makespan.


2012 ◽  
Vol 04 (01) ◽  
pp. 1250012
Author(s):  
YIWEI JIANG ◽  
AN ZHANG ◽  
JUELIANG HU

This paper investigates an online hierarchical scheduling problem with resource augmentation, i.e., the resources of the online algorithms are different from those of the offline algorithms. The machines are provided with different capacity according to their hierarchies. One with the hierarchy 1 has a speed of s(q) in the online (offline) algorithms and can process all the jobs. The other with hierarchy 2 has a speed of 1 in the online/offline algorithms and can only process partial jobs. The objective is to minimize makespan. For any 0 < q, s < ∞, we present optimal online algorithms with parametric competitive ratios.


2015 ◽  
Vol 32 (04) ◽  
pp. 1550027
Author(s):  
Xiao Min ◽  
Jing Liu ◽  
Yanxia Dong ◽  
Ming Jiang

This paper studies the online hierarchical scheduling problem on two uniform machines with rejection. Two uniform machines M1, M2 run at the speeds of s ∈ (0, +∞), 1 separately; and they are provided with different capabilities. Each machine has a certain GOS level 1 or 2 and every job is also associated with a hierarchy 1 or 2. The job can only be assigned to the machine whose GOS level does not exceed the job's hierarchy. Preemption is permitted but idle is not introduced. Jobs come one by one over list. When a job arrives, it can be accepted and scheduled on some machine or rejected by paying its penalty. The objective is to minimize the sum of makespan yielded by accepted jobs and total penalties of all rejected jobs. For this problem, we propose a family of several online algorithms according to the range of s and the related lower bound is also obtained. These algorithms achieve optimal competitive ratio when s ∈ (0, 1) ∪ [1.618, +∞), but have a small gap between upper bound and lower bound in interval [1, 1.618).


MACRo 2015 ◽  
2015 ◽  
Vol 1 (1) ◽  
pp. 193-200
Author(s):  
István Szalkai ◽  
György Dósa

AbstractWe consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the second section. This problem is the generalization of the classical parallel machine scheduling problem, when the makespan is minimized; in that case each job contains only one task. On the other hand, the problem in consideration is still a special version of the workflow scheduling problem. We present several heuristic algorithms and compare them by computer tests.


Author(s):  
Fransiskus Lauson Matondang ◽  
Rosnani Ginting

PT XYZ sering mengalami keterlambatan waktu karena dalam setiap keterlambatan yang dilakukan selalu ada penalty yang diberikan kepada perusahaan dan hal ini mengakibatkan tambahan biaya , oleh karena itu hal ini harus dihindari dengan membuat penjadwalan yang efisien, dalam hal ini dilakukanlah perbaikan dengan meminimisasi waktu penyelesaian maksimum Cmax pada mesin paralel yang berpola aliran flowshop (dan tidak boleh dilakukan interupsi yang dilakukan pada pekerjaan yang sedang diproses, untuk melakukan pekerjaan lainnya, satu lintasan hanya memproduksi satu produk dan hanya satu produk juga yang dikerjakan secara langsung. Waktu penyelesaian yang berbeda dari setiap mesin dengan pengerjaannya juga adalah masalah yang dihadapi untuk menjadikan mesin mesin ini sesuai menjadi satu penjadwalan yang terintegrasi dengan metode integer programming yang membuat penjadwalan dengan konsep riset operasi dengan metode pendekatan 0-1 utuk menjadi lebih efisien lagi , dihasilkan minimisasi keterlambatan total penyelesaian order dengan 42,28 menit lebih baik dari sebelumnya.   PT XYZ often experiences time delays because in every delay made there is always a penalty given to the company and this results in additional costs, therefore this must be avoided by making efficient scheduling, in this case repairs are carried out by minimizing the maximum completion time of Cmax on parallel machines that are patterned with flowshop flow (and no interruptions should be carried out on the work being processed, to do other work, one track only produces one product and only one product is directly worked. Different completion times of each machine with the workmanship is also the problem faced to make this machine suitable to be one scheduling integrated with integer programming methods that makes scheduling with the operational research concept with the 0-1 approach method to be more efficient, resulting in minimization of the delay in the total settlement of orders with 42.28 minutes was better than before.


2019 ◽  
Author(s):  
Dimitrios Kolokouris ◽  
Iris Kalenderoglou ◽  
Panagiotis Lagarias ◽  
Antonios Kolocouris

<p>We studied by molecular dynamic (MD) simulations systems including the inward<sub>closed</sub> state of influenza A M2 protein in complex with aminoadamantane drugs in membrane bilayers. We varied the M2 construct and performed MD simulations in M2TM or M2TM with amphipathic helices (M2AH). We also varied the lipid bilayer by changing either the lipid, DMPC or POPC, POPE or POPC/cholesterol (chol), or the lipids buffer size, 10x10 Å<sup>2 </sup>or 20x20 Å<sup>2</sup>. We aimed to suggest optimal system conditions for the computational description of this ion channel and related systems. Measures performed include quantities that are available experimentally and include: (a) the position of ligand, waters and chlorine anion inside the M2 pore, (b) the passage of waters from the outward Val27 gate of M2 S31N in complex with an aminoadamantane-aryl head blocker, (c) M2 orientation, (d) the AHs conformation and structure which is affected from interactions with lipids and chol and is important for membrane curvature and virus budding. In several cases we tested OPLS2005, which is routinely applied to describe drug-protein binding, and CHARMM36 which describes reliably protein conformation. We found that for the description of the ligands position inside the M2 pore, a 10x10 Å<sup>2</sup> lipids buffer in DMPC is needed when M2TM is used but 20x20 Å<sup>2</sup> lipids buffer of the softer POPC; when M2AH is used all 10x10 Å<sup>2</sup> lipid buffers with any of the tested lipids can be used. For the passage of waters at least M2AH with a 10x10 Å<sup>2</sup> lipid buffer is needed. The folding conformation of AHs which is defined from hydrogen bonding interactions with the bilayer and the complex with chol is described well with a 10x10 Å<sup>2</sup> lipids buffer and CHARMM36. </p>


2017 ◽  
Vol 58 ◽  
pp. 314
Author(s):  
Yiwei Jiang ◽  
Ping Zhou ◽  
Huijuan Wang ◽  
Jueliang Hu

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