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Frontiers of Mechanical Engineering

Front. Mech. Eng.
RESEARCH ARTICLE
A naive optimization method for multi-line systems with alternative machines
Weichang KONG, Fei QIAO(), Qidi WU
School of Electronics and Information Engineering, Tongji University, Shanghai 201804, China
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Abstract

The scheduling of parallel machines and the optimization of multi-line systems are two hotspots in the field of complex manufacturing systems. When the two problems are considered simultaneously, the resulting problem is much more complex than either of them. Obtaining sufficient training data for conventional data-based optimization approaches is difficult because of the high diversity of system structures. Consequently, optimization of multi-line systems with alternative machines requires a simple mechanism and must be minimally dependent on historical data. To define a general multi-line system with alternative machines, this study introduces the capability vector and matrix and the distribution vector and matrix. A naive optimization method is proposed in accordance with classic feedback control theory, and its key approaches are introduced. When a reasonable target value is provided, the proposed method can realize closed-loop optimization to the selected objective performance. Case studies are performed on a real 5/6-inch semiconductor wafer manufacturing facility and a simulated multi-line system constructed on the basis of the MiniFAB model. Results show that the proposed method can effectively and efficiently optimize various objective performance. The method demonstrates a potential for utilization in multi-objective optimization.

Keywords multi-line systems      alternative machines      feedback control      closed-loop optimization     
Corresponding Authors: Fei QIAO   
Just Accepted Date: 04 July 2019   Online First Date: 16 August 2019   
 Cite this article:   
Weichang KONG,Fei QIAO,Qidi WU. A naive optimization method for multi-line systems with alternative machines[J]. Front. Mech. Eng., 16 August 2019. [Epub ahead of print] doi: 10.1007/s11465-019-0544-z.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0544-z
http://journal.hep.com.cn/fme/EN/Y/V/I/0
Fig.1  Example of a multi-line manufacturing system. (a) Line topology; (b) machine classification.
Fig.2  Block diagrams of classic feedback control and the proposed optimization method. (a) Classic feedback control; (b) proposed optimization method.
Fig.3  Flow diagram of the feedback optimization method.
Step Key approach
Step 1 Selection of key multi-line machines
Step 2
Step 3
Step 5
Step 5
Step 6
Calibration
Setting of the target performance value
Acquisition of performance
Updating mechanism of the distribution matrix
Convergence criterion
Tab.1  Summary of the key approaches
Processing step 5-inch 6-inch
BLOCK Number Block Number
LT (lithography) B7 27 B5 25
B7 17
WT (wet etching) B6 1 B10 2
B12 6 B14 18
EP (epitaxy) B16 6 B16 8
DF (diffusion) B8 2 B8 2
B2 9
PE (dry etching) B15 2 B11 1
B3 1 B3 4
PD (deposition) B15 3 B15 2
B1 1 B1 1
IM (implantation) B4 2 B4 2
B9 2
OT (outsourcing) Null Null B5 2
Null Null Other 1
OS (outsourcing) B16 1 B 1
Tab.2  Number of dedicated multi-line machines
Machine type 5-inch 6-inch Total number
6LD1 7 5 12
6LR1 6 4 10
6LU1 4 6 10
Tab.3  Number of key multi-line machines
Fig.4  Calibration datasets of the average utilization.
Target value Average utilization
1st 2nd 3rd 4th
Utar1=28.00% 25.92% 27.60% 27.60% Converged
Utar2=30.00 % 29.63% 29.64% 29.64% Converged
Utar3=35.00 % 36.78% 30.94% 36.78% 30.94%
Tab.4  Changes in objective performance values (the average utilization) during iteration
Fig.5  Optimization process and results of the average utilization.
Target value of the average utilization Average utilization Absolute error Relative error
Utar1=28.00% 27.60% 0.40% 1.43%
Utar2=30.00 % 29.64% 0.36% 1.20%
Utar3=35.00 % 36.78% 1.78% 5.09%
Tab.5  Results of the average utilization and errors of optimization
Fig.6  MiniFAB model and the simulated multi-line system. (a) MiniFAB model; (b) simulated multi-line system. LT: Lithography; DF: Diffusion; IM: Implantation.
Fig.7  Calibration datasets of the average cycle time.
Value type Value Average cycle time/s
0th 1st 2nd 3rd
Target value CT Patar=660 s 846 674 658 659
Reference value CT Pb 661 663 667 664
CT Pc 656 658 661 659
Tab.6  Change in objective performance values (the average cycle time) during iteration
Fig.8  Optimization results of the average cycle time.
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