缓冲区容量为2的单臂树形多组合设备的建模与调度
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摘要
在半导体制造中,多组合设备被广泛应用于晶圆加工.对于缓冲区容量为2的单臂树形多组合设备,当机械手的移动时间远远小于晶圆加工时间时,它是否存在一个1-晶圆最优周期调度仍是个有待解决的问题.针对此问题,本文首先运用Petri网对系统进行建模,经过对单组合设备调度和相邻设备协调运作的分析,证明系统的1-晶圆周期达到下界值时总是可调度的,并给出相应的调度算法.最后通过实例验证了算法的有效性以及实用性.
Multi-cluster tools have been widely adopted in wafer fabrication in semiconductor manufacturing. For single arm tree-like multi-cluster tools with two-space buffering modules, when the moving time of robots is much less than wafer processing time, whether there is one-wafer optimal cyclic scheduling is still a problem remaining to be solved. Aiming at this problem, a Petri net model has been built up to analysis the tool system. Based on the Petri net model,conditions are presented under which a one-wafer cyclic schedule with the lower bound of cycle time can be found and an algorithm is developed to coordinate the activities of adjacent arms. Finally, an illustrative example is given to show the effectiveness and application of the algorithm.
Multi-cluster tools have been widely adopted in wafer fabrication in semiconductor manufacturing. For single arm tree-like multi-cluster tools with two-space buffering modules, when the moving time of robots is much less than wafer processing time, whether there is one-wafer optimal cyclic scheduling is still a problem remaining to be solved. Aiming at this problem, a Petri net model has been built up to analysis the tool system. Based on the Petri net model,conditions are presented under which a one-wafer cyclic schedule with the lower bound of cycle time can be found and an algorithm is developed to coordinate the activities of adjacent arms. Finally, an illustrative example is given to show the effectiveness and application of the algorithm.
引文
[1]Yang F J, Wu N Q, Qiao Y, et al. Optimal one-wafer cyclic scheduling of single-arm multi-cluster tools with two-space buffering modules[J]. IEEE Transactions on Systems, Man, Cybernetics:Systems, 2014, 44(12):1584-1597.
[2]Kim J H, Lee T E, Lee H Y, et al. Scheduling analysis of timed-constrained dual-armed cluster tools[J]. IEEE Transactions on Semiconductor Manufacturing, 2003, 16(3):521-534.
[3]Lee T E, Lee H Y, Shin Y H. Workload balancing and schedulingof a single-armed cluster tool[C]//Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference, Gold Coast, Australia,2004:1-15.
[4]Yang F J, Wu N Q, Qiao Y, et al. Petri net-based polynomially complex approach to optimal one-wafer cyclic scheduling of hybrid multi-cluster tools in semiconductor manufacturing[J]. IEEE Transactions on Systems, Man,and Cybernetics:Systems, 2014, 44(12):1598-1610.
[5]李文涛,白丽平,伍乃骐,等.具有2-空间缓冲模块的多组合设备的优化调度[J].系统工程理论与实践,2016, 36(9):2408-2415.Li W T, Bai L P, Wu N Q, et al. Optimal scheduling of multi-cluster tools with two-space buffering module[J].Systems Engineering—Theory&Practice, 2016, 36(9):2408-2415.
[6]Chan W K V, Yi J G, Ding S W, et al. Optimal scheduling of multi-cluster 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.
[7]Sethi S, Sriskandarajah C, Sorger G, et al. Sequencing of parts and robot moves in a robotic cell[J]. International Journal of Flexible Manufacturing Systems, 1992, 4(3):331-358.
[8]Dawande M, Sriskandarajah C, Sethi S. On throughput maximization in constant travel-time robotic cells[J].Manufacturing&Service Operations Management, 2002, 4(4):296-312.
[9]Drobouchevitch I G, Sethi S P,Sriskandarajah C. Scheduling dual gripper robotic cells:One-unit cycles[J].European Journal of Operational Research, 2006, 171(2):598-631.
[10]Zhu Q H, Wu N Q, Qiao Y, et al. Optimal scheduling of complex multi-cluster tools based on timed resourceoriented Petri Nets[J]. IEEE Access, 2016, 4:2096-2109.
[11]Yang F J, Wu N Q, Qiao Y, et al. Optimal one-wafer cyclic scheduling of hybrid multirobot cluster tools with tree topology[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2017, PP(99):1-10.
[12]Zhu Q H, Wu N Q, Qiao Y, et al. Petri net-based optimal one-wafer scheduling of single-arm multi-cluster tools in semiconductor manufacturing[J]. IEEE Transactions on Semiconductor Manufacturing, 2013, 26(4):578-591.
[13]Wu N Q. Avoiding deadlocks in automated manufacturing systems with shared ma-terial handling system[C]//1997 IEEE International Conference on Robotics and Automation, IEEE, 1997:2427-2432.
[14]Wu N Q, Zhou M C. Avoiding deadlock and reducing starvation and blocking in automated manufacturing systems based on a Petri net model[J]. IEEE Transactions on Robotics and Automation, 2001, 17(5):658-669.
[15]Wu N Q, Zhou M C. System modeling and control with resource-oriented Petri Nets[M]. Boca Raton, FL, USA:CRC Press, 2009.
[16]Bai L P, Wu N Q, Li Z W, et al. Optimal one-wafer cyclic scheduling and buffer space configuration for single-arm multi-cluster tools with linear topology[J]. IEEE Transactions on Systems, Man, Cybernetics:Systems, 2016,46(10):1456-1467.
[17]Wu N Q, Chu F, Chu C B, et al. Petri net-based scheduling of single-arm cluster tools with reentrant atomic layer deposition processes[J]. IEEE Transactions on Automation Science and Engineering, 2011,8(1):42-55.
[18]Zhu Q H,Wu N Q, Qiao Y,et al. Scheduling of single-arm multi-cluster tools with wafer residency time constraints in semiconductor manufacturing[J]. IEEE Transactions on Semiconductor Manufacturing, 2015, 28(1):117-125.
[19]Wu N Q, Chu C B, Chu F, et al. A Petri net method for schedulability and scheduling problems in single-arm cluster tools with wafer residency time constraints[J]. IEEE Transactions on Semiconductor Manufacturing, 2008,21(2):224-237.
[2]Kim J H, Lee T E, Lee H Y, et al. Scheduling analysis of timed-constrained dual-armed cluster tools[J]. IEEE Transactions on Semiconductor Manufacturing, 2003, 16(3):521-534.
[3]Lee T E, Lee H Y, Shin Y H. Workload balancing and schedulingof a single-armed cluster tool[C]//Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference, Gold Coast, Australia,2004:1-15.
[4]Yang F J, Wu N Q, Qiao Y, et al. Petri net-based polynomially complex approach to optimal one-wafer cyclic scheduling of hybrid multi-cluster tools in semiconductor manufacturing[J]. IEEE Transactions on Systems, Man,and Cybernetics:Systems, 2014, 44(12):1598-1610.
[5]李文涛,白丽平,伍乃骐,等.具有2-空间缓冲模块的多组合设备的优化调度[J].系统工程理论与实践,2016, 36(9):2408-2415.Li W T, Bai L P, Wu N Q, et al. Optimal scheduling of multi-cluster tools with two-space buffering module[J].Systems Engineering—Theory&Practice, 2016, 36(9):2408-2415.
[6]Chan W K V, Yi J G, Ding S W, et al. Optimal scheduling of multi-cluster 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.
[7]Sethi S, Sriskandarajah C, Sorger G, et al. Sequencing of parts and robot moves in a robotic cell[J]. International Journal of Flexible Manufacturing Systems, 1992, 4(3):331-358.
[8]Dawande M, Sriskandarajah C, Sethi S. On throughput maximization in constant travel-time robotic cells[J].Manufacturing&Service Operations Management, 2002, 4(4):296-312.
[9]Drobouchevitch I G, Sethi S P,Sriskandarajah C. Scheduling dual gripper robotic cells:One-unit cycles[J].European Journal of Operational Research, 2006, 171(2):598-631.
[10]Zhu Q H, Wu N Q, Qiao Y, et al. Optimal scheduling of complex multi-cluster tools based on timed resourceoriented Petri Nets[J]. IEEE Access, 2016, 4:2096-2109.
[11]Yang F J, Wu N Q, Qiao Y, et al. Optimal one-wafer cyclic scheduling of hybrid multirobot cluster tools with tree topology[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2017, PP(99):1-10.
[12]Zhu Q H, Wu N Q, Qiao Y, et al. Petri net-based optimal one-wafer scheduling of single-arm multi-cluster tools in semiconductor manufacturing[J]. IEEE Transactions on Semiconductor Manufacturing, 2013, 26(4):578-591.
[13]Wu N Q. Avoiding deadlocks in automated manufacturing systems with shared ma-terial handling system[C]//1997 IEEE International Conference on Robotics and Automation, IEEE, 1997:2427-2432.
[14]Wu N Q, Zhou M C. Avoiding deadlock and reducing starvation and blocking in automated manufacturing systems based on a Petri net model[J]. IEEE Transactions on Robotics and Automation, 2001, 17(5):658-669.
[15]Wu N Q, Zhou M C. System modeling and control with resource-oriented Petri Nets[M]. Boca Raton, FL, USA:CRC Press, 2009.
[16]Bai L P, Wu N Q, Li Z W, et al. Optimal one-wafer cyclic scheduling and buffer space configuration for single-arm multi-cluster tools with linear topology[J]. IEEE Transactions on Systems, Man, Cybernetics:Systems, 2016,46(10):1456-1467.
[17]Wu N Q, Chu F, Chu C B, et al. Petri net-based scheduling of single-arm cluster tools with reentrant atomic layer deposition processes[J]. IEEE Transactions on Automation Science and Engineering, 2011,8(1):42-55.
[18]Zhu Q H,Wu N Q, Qiao Y,et al. Scheduling of single-arm multi-cluster tools with wafer residency time constraints in semiconductor manufacturing[J]. IEEE Transactions on Semiconductor Manufacturing, 2015, 28(1):117-125.
[19]Wu N Q, Chu C B, Chu F, et al. A Petri net method for schedulability and scheduling problems in single-arm cluster tools with wafer residency time constraints[J]. IEEE Transactions on Semiconductor Manufacturing, 2008,21(2):224-237.