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On a BMAP/G/1 G-queue with setup times and Multiple Vacations

Acta Mathematicae Applicatae Sinica 2011年第4期27卷 625-638页

作者： Yi PENG Xiang-qun YANG School of Mathematical Science and Computing Technology Central South University Changsha 410075 Hunan China College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China

In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.

关键词： G-queues batch Markovian arrival process (BMAP) setup times multiple vacations censoring technique Markov chains

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Hybrid Flow Shop with setup times Scheduling Problem

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Computer Systems Science & Engineering 2023年第1期44卷 563-577页

作者： Mahdi Jemmali Lotfi Hidri Department of Computer Science and Information College of Science at ZulfiMajmaah UniversityMajmaah11952Saudi Arabia Mars Laboratory University of SousseSousseTunisia Department of Computer Science Higher Institute of Computer Science and Mathematics of MonastirMonastir UniversityMonastir5000Tunisia Industrial Engineering Department College of EngineeringKing Saud UniversityRiyadh11421Saudi Arabia

The two-stage hybridflow shop problem under setup times is addressed in this *** problem is *** the other hand,the studied problem is modeling different real-life applications especially in manufacturing and high *** this kind of problem requires the development of adapted *** this context,a metaheuristic using the genetic algorithm and three heuristics are proposed in this *** approximate solutions are using the optimal solution of the parallel machines under release and delivery ***,these solutions are iterative procedures focusing each time on a particular stage where a parallel machines problem is called to be *** general solution is then a concatenation of all the solutions in each *** addition,three lower bounds based on the relaxation method are *** lower bounds present a means to evaluate the efficiency of the developed algorithms throughout the measurement of the relative *** experimental result is discussed to evaluate the performance of the developed *** total,8960 instances are implemented and tested to show the results given by the proposed lower bounds and *** indicators are given to compare between *** results illustrated in this paper show the performance of the developed algorithms in terms of gap and running time.

关键词： Hybridﬂow shop genetic algorithm setup times heuristics lower bound

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