This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parall...This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a （j∈N）, and the processing time of job Jj is bj（j∈N） on a batch processorM. We take makespan （Cmax） as our minimization objective. In this paper, for the problem of FSMP-BI （m identical parallel machines on the first stage and a batch processor on the second stage）, based on the algorithm given by Sung and Choung for the problem of 1 ｜ri, BI｜Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O（nlogn）, O（nB）} time. A max {O（nlogn） , O（nB）}time symmetric Algorithm H2 is given then for the problem of BI-FSMP （a batch processor on the first stage and m identical parallel machines on the second stage）.展开更多
A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. Thi...A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.展开更多
针对可重入制造系统多具有多品种、大规模、混流生产等特点,构建带批处理机的可重入混合流水车间调度问题(reentrant hybrid flow shop scheduling problem with batch processors,BPRHFSP)模型,提出一种改进的多目标蜉蝣算法(multi-obj...针对可重入制造系统多具有多品种、大规模、混流生产等特点,构建带批处理机的可重入混合流水车间调度问题(reentrant hybrid flow shop scheduling problem with batch processors,BPRHFSP)模型,提出一种改进的多目标蜉蝣算法(multi-objective mayfly algorithm,MOMA)进行求解。提出了单件加工阶段和批处理阶段的解码规则;设计了基于Logistic混沌映射的反向学习初始化策略、改进的蜉蝣交配和变异策略,提高了算法初始解的质量和局部搜索能力;根据编码规则设计了基于变邻域下降搜索的蜉蝣运动策略,优化了种群方向。通过对不同规模大量测试算例的仿真实验,验证了MOMA相比传统算法求解BP-RHFSP更具有效性和优越性。所提出的模型能够反映生产的基础特征,达到减少最大完工时间、机器负载和碳排放的目的。展开更多
基金Sponsored by the Innovation Foundation of Shanghai University(Grant No.A.10-0101-07 -406)NNSF of China(Grant No.60874039)
文摘This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a （j∈N）, and the processing time of job Jj is bj（j∈N） on a batch processorM. We take makespan （Cmax） as our minimization objective. In this paper, for the problem of FSMP-BI （m identical parallel machines on the first stage and a batch processor on the second stage）, based on the algorithm given by Sung and Choung for the problem of 1 ｜ri, BI｜Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O（nlogn）, O（nB）} time. A max {O（nlogn） , O（nB）}time symmetric Algorithm H2 is given then for the problem of BI-FSMP （a batch processor on the first stage and m identical parallel machines on the second stage）.
基金Project supported by the Science and Technology Development Fund of Shanghai University(Grant No.A.10-0101-06-0017)
文摘A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.
