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AN IMPROVED BRANCH-AND-BOUND ALGORITHM TO MINIMIZE THE WEIGHTED FLOWTIME ON identical parallel machines WITH FAMILY SETUP TIMES

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Journal of Systems Science and Systems Engineering 2008年第4期17卷 446-459页

作者： Belgacem BETTAYEB Imed KACEM Kondo H.ADJALLAH LOSI-ICD CNRS FRE 2848 Université de technologie de Troyes France

This article investigates identical parallel machines scheduling with family setup times. The objective function being the weighted sum of completion times, the problem is known to be strongly NP-hard. We propose a constructive heuristic algorithm and three complementary lower bounds. Two of these bounds proceed by elimination of setup times or by distributing each of them to jobs of the corresponding family, while the third one is based on a lagrangian relaxation. The bounds and the heuristic are incorporated into a branch-and-bound algorithm. Experimental results obtained outperform those of the methods presented in previous works, in term of size of solved problems.

关键词： Scheduling heuristic lower bound branch-and-bound algorithm identical parallel machines family setup times

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Scheduling Multiple Orders per Job with Multiple Constraints on identical parallel machines

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Journal of Donghua University(English Edition) 2013年第6期30卷 466-471页

作者：王腾周炳海 School of Mechanical Engineering Tongji University

With a comprehensive consideration of multiple product types, past-sequence-dependent （ p-s-d ） setup times, and deterioration effects constraints in processes of wafer fabrication systems, a novel scheduling model of multiple orders per job（MOJ） on identical parallel machines was developed and an immune genetic algorithm（IGA） was applied to solving the scheduling problem. A scheduling problem domain was described. A non-linear mathematical programming model was also set up with an objective function of minimizing total weighted earliness-tardlness penalties of the system. On the basis of the mathematical model, IGA was put forward. Based on the genetic algorithm （GA）, the proposed algorithm （IGA） can generate feasible solutions and ensure the diversity of antibodies. In the process of immunization programming, to guarantee the algorithm＇s convergence performance, the modified rule of apparent tardiness cost with setups （ATCS） was presented. Finally, simulation experiments were designed, and the results indicated that the algorithm had good adaptability when the values of the constraints＇ characteristic parameters were changed and it verified the validity of the algorithm.

关键词： multiple product types past-sequence-dependent ( p-s-d ) setup times deterioration effects identical parallel machines scheduline : immune Penetic algorithm ( IGA )

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维普期刊数据库

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ON-LINE SCHEDULING WITH REJECTION ON identical parallel machines

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Journal of Systems Science & Complexity 2006年第3期19卷 431-435页

作者： Cuixia MIAO Yuzhong ZHANG Department of Mathematics Qufu Normal University Qufu 273165 China. Institute of Operations Research Qufu Normal University Rizhao 276826 China.

In this paper, we consider the on-line scheduling of unit time jobs with rejection on rn identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty of the rejected jobs. We give an on-line algorithm for the problem with competitive ratio 1/2 （2 ＋√3） ≈ 1.86602.

关键词： Competitive ratio identical parallel machines on-line algorithm rejection penalty.

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维普期刊数据库

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