A naive optimization method for multi-line systems with alternative machines

doi:10.1007/s11465-019-0544-z

Front. Mech. Eng.

2019, Vol. 14

Issue (4) : 377-392 https://doi.org/10.1007/s11465-019-0544-z

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 Author(s): Fei QIAO

Just Accepted Date: 04 July 2019 Online First Date: 16 August 2019 Issue Date: 02 December 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., 2019, 14(4): 377-392.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0544-z
https://academic.hep.com.cn/fme/EN/Y2019/V14/I4/377

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.

Tab.1 Summary of the key approaches

Tab.2 Number of dedicated multi-line machines

Tab.3 Number of key multi-line machines

Fig.4 Calibration datasets of the average utilization.

Target value	Average utilization
Target value	1st	2nd	3rd	4th
$U tar1 = 28.00 %$	25.92%	27.60%	27.60%	Converged
$U tar2 = 30 .00 %$	29.63%	29.64%	29.64%	Converged
$U tar3 = 35 .00 %$	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
$U tar1 = 28.00 %$	27.60%	0.40%	1.43%
$U tar2 = 30 .00 %$	29.64%	0.36%	1.20%
$U tar3 = 35 .00 %$	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
Value type	Value	0th	1st	2nd	3rd
Target value	$C T P a tar = 660$ s	846	674	658	659
Reference value	$C T P b$	661	663	667	664
Reference value	$C T P c$	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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