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Scheduling method for double-cluster tools with parallel chambers based on capacity constraint resource
ZHOU Binghai , LI Ming
School of Mechanical Engineering, Tongji University, Shanghai 201804, China
Received: 2015-08-24; Accepted: 2015-10-30; Published online: 2016-01-05 10:36
Foundation item: National Natural Science Foundation of China (71471135, 61273035)
Corresponding author. Tel.: 021-54810409 E-mail: bhzhou@tongji.edu.cn
Abstract: To effectively solve scheduling problems of multiple cluster tools of 450 mm wafer fabrication systems with parallel processing chambers, a scheduling method based on capacity constraint resource (CCR) was proposed. Firstly, with comprehensive consideration of the characteristics of different types of wafers, resources and residency constraints, a mathematical programming model of double-cluster tools with parallel chambers was established to minimize the makespan of the system. Then, to optimize manipulator movements by adopting locking-tightening-loosening (LTL) strategy to the CCR, a piecewise scheduling algorithm was constructed with the CCR．Finally, through the analysis of simulation experiments, the results indicate that the proposed algorithm is valid and competitive.
Key words: multiple cluster tools     parallel chambers     residency constraint     capacity constraint resource     scheduling algorithm

1 问题描述

 图 1 带并行腔的双集束型设备群示意图 Fig. 1 Schematic of double-cluster tools with parallel chambers

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2 算法构建

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CIP(t)<KIw<KI，则

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 图 2 计算实例甘特图 Fig. 2 Gantt chart of calculative example
3 仿真实验与分析

3.1 运算时间

 图 3 算法运行时间分析 Fig. 3 Running time analysis of algorithm

3.2 加工时间对调度的影响

MH=4；tM=2；Pn={1,2,1,3,1,1,1,1}；晶圆在各个处理模块的处理时间服从期望μ=40，方差σ=0,1/8,1/4,1/2均值的正态分布；驻留约束时间分别服从UN(20,5)。仿真运行的结果如图 4所示。由图 4可见，随着加工晶圆的数量增加，R值逐渐增加，说明在加工批量越大的情况下本文算法的调度结果相对于Benchmark的提升越大。同时，图 4中的4条不同曲线的走向趋势基本一致，且在σ的较大的情况下，本文算法的优化结果更为明显，说明了算法对不同处理时间波动的适应性。

 图 4 不同方差下R值与晶圆数目的关系 Fig. 4 Relationship between R value and number of wafer with different variance
3.3 CCR并行腔对调度的影响

MH=4，tM=2 s；晶圆在各个处理模块的处理时间服从PN(40,10)；驻留约束时间分别服从UN(20,5)；CCR模块的并行腔数目KI=1,2,…,7。仿真运行的结果如图 5所示。

 图 5 CCR并行腔对调度的影响 Fig. 5 Effect of parallel chambers at CCR on scheduling

3.4 机械手对调度的影响

MH=4，tM=2 s，Pn={1,2,1,3,1,1,1,1}；晶圆在各个处理模块的处理时间服从PN(40,10)；驻留约束时间分别服从UN(20,5)；分别令FC=1,2,…,6。仿真运行的结果如图 6所示。

 图 6 机械手对调度的影响 Fig. 6 Effect of manipulator on scheduling

4 结 论

1) 算法可以有效解决在集束型设备群的调度过程中普遍存在的带并行腔多品种加工的问题，特别在减少驻留提升CCR设备利用率方面有明显优势。

2) 在晶圆批量较小(每批少于20片)的情况下，得出算法的仿真运行时间几乎为零，可有效地进行实时调度，即使批量较大(每批达到200片)也能满足调度的要求，证明了算法的高效性。

3) 随着晶圆数目和σ增大，R值不断增加，表明本文算法相对于LCM算法的提升效果明显，且在并行腔数目和设备因子变化的情况下，也能获得较优的调度结果。

4) 算法对于晶圆加工时间波动性、并行腔数目和机械手繁忙程度的仿真证明算法对不同的加工数据和设备具有非常好的适应性。

 [1] PERKINSON T L, MCLARTY P K, GYURCSIK R S, et al. Single-wafer cluster tool performance: An analysis of throughput[J]. IEEE Transactions on Semiconductor Manufacturing, 1994, 7 (3) : 369 –373. DOI:10.1109/66.311340 [2] YI J, DING S, SONG D, et al. Steady-state throughput and scheduling analysis of multi-cluster tools: A decomposition ap-proach[J]. IEEE Transactions on Automation Science and Engineering, 2008, 5 (2) : 321 –336. DOI:10.1109/TASE.2007.906678 [3] CHAN W K, YI J, DING S. Optimal scheduling of multi-cluster tools with constant robot moving times, Part I: Two-cluster analysis[J]. IEEE Transactions on Automation Science and Engineering, 2011, 8 (1) : 5 –16. DOI:10.1109/TASE.2010.2046891 [4] CHAN W K, DING S, YI J, et al. Optimal scheduling of multicluster tools with constant robot moving times, Part II: Tree-like topology configurations[J]. IEEE Transactions on Automation Science and Engineering, 2011, 8 (1) : 17 –28. DOI:10.1109/TASE.2010.2046893 [5] DING S, YI J, ZHANG M T, et al. Performance evaluation and schedule optimization of multi-cluster tools with process times uncertainty[C]//Proceeding of the 2006 IEEE International Conference on Automation Science and Engineering. Piscataway, NJ: IEEE Press, 2006: 7-10. [6] LIU M X, ZHOU B H. Modeling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets[J]. International Journal of Production Research, 2013, 51 (16) : 4835 –4852. DOI:10.1080/00207543.2013.774490 [7] PERKINSON T L, GYURCSIK R S, MCLARTY P K. Single-wafer cluster tool performance: An analysis of the effects of redundant chambers and revisitation sequences on throughput[J]. IEEE Transactions on Semiconductor Manufacturing, 1996, 9 (3) : 384 –400. DOI:10.1109/66.536110 [8] GEISMAR H N, DAWANDE M W, SRISKANDARAJAH C. Robotic cells with parallel machines: Throughput maximization in constant travel-time cells[J]. Journal of Scheduling, 2004, 7 (5) : 375 –395. DOI:10.1023/B:JOSH.0000036861.28456.5d [9] ZHENG X H, YU H B, HU J T. A general throughput model for parallel cluster tools[C]//International Conference on ICCE2011, AISC 110. Berlin: Springer Press, 2011: 215-222. [10] 卢睿, 李林瑛. 有晶滞留时间约束的集束型装备调度问题研究[J]. 控制仿真学报, 2014, 26 (8) : 1775 –1780. LU R, LI L Y. Research on scheduling problem of cluster tools with residency time constraints[J]. Journal of System Simulation, 2014, 26 (8) : 1775 –1780. (in Chinese) [11] WIKBORG U, LEE T E. Noncyclic scheduling for timed discrete-event systems with application to single-armed cluster tools using pareto-optimal optimization[J]. IEEE Transactions on Automation Science and Engineering, 2013, 10 (3) : 699 –710. DOI:10.1109/TASE.2012.2217128 [12] ZHANG J, FANG X, QI L. LCM cycle based optimal scheduling in robotic cell with parallel workstations[C]//2014 IEEE International Conference on Robotics and Automation (ICRA). Piscataway, NJ: IEEE Press, 2014: 1367-1373. [13] DING S, YI J. An event graph based simulation and scheduling analysis of multi-cluster tools[C]//Proceedings of 2004 Winter Simulation Conference. Piscataway, NJ: IEEE Press, 2004: 1915-1924. [14] KUMAR S, RAMANAN N, SRISKANDARAJAH C. Minimizing cycle time in large robotic cells[J]. IIE Transactions, 2005, 37 (2) : 123 –136. DOI:10.1080/07408170590885279 [15] ROSER C, NAKANO M, TANAKA M. A practical bottleneck detection method[C]//Proceedings of Winter Simulation Conference, 2001. Piscataway, NJ: IEEE Press, 2001, 2: 949-953.

#### 文章信息

ZHOU Binghai, LI Ming

Scheduling method for double-cluster tools with parallel chambers based on capacity constraint resource

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(7): 1361-1367
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0538