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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2019, Vol. 14 Issue (4) : 377-392
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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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    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.
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
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.
1 C Becker, A Scholl. Balancing assembly lines with variable parallel workplaces: Problem definition and effective solution procedure. European Journal of Operational Research, 2009, 199(2): 359–374
2 A Scholl, N Boysen. Designing parallel assembly lines with split workplaces: Model and optimization procedure. International Journal of Production Economics, 2009, 119(1): 90–100
3 A Scholl, M Fliedner, N Boysen. Absalom: Balancing assembly lines with assignment restrictions. European Journal of Operational Research, 2010, 200(3): 688–701
4 T Kellegöz, B Toklu. An efficient branch and bound algorithm for assembly line balancing problems with parallel multi-manned workstations. Computers & Operations Research, 2012, 39(12): 3344–3360
5 D Ogan, M Azizoglu. A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements. Journal of Manufacturing Systems, 2015, 36: 46–54
6 M Moghaddam, S Y Nof. Real-time administration of tool sharing and best matching to enhance assembly lines balanceability and flexibility. Mechatronics, 2015, 31: 147–157
7 S Avikal, R Jain, P K Mishra, et al.A heuristic approach for U-shaped assembly line balancing to improve labor productivity. Computers & Industrial Engineering, 2013, 64(4): 895–901
8 M Moreira, J Cordeau, A Costa, et al. Robust assembly line balancing with heterogeneous workers. Computers & Industrial Engineering, 2015, 88: 254–263
9 I Kucukkoc, D Z Zhang. Balancing of parallel U-shaped assembly lines. Computers & Operations Research, 2015, 64: 233–244
10 Z Li, I Kucukkoc, J M Nilakantan. Comprehensive review and evaluation of heuristics and meta-heuristics for two-sided assembly line balancing problem. Computers & Operations Research, 2017, 84: 146–161
11 L Tiacci. Simultaneous balancing and buffer allocation decisions for the design of mixed-model assembly lines with parallel workstations and stochastic task times. International Journal of Production Economics, 2015, 162: 201–215
12 M Chica, J Bautista, O Cordón, et al.A multiobjective model and evolutionary algorithms for robust time and space assembly line balancing under uncertain demand. Omega, 2016, 58: 55–68
13 Y K Kim, W S Song, J H Kim. A mathematical model and a genetic algorithm for two-sided assembly line balancing. Computers & Operations Research, 2009, 36(3): 853–865
14 P Chutima, P Chimklai. Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge. Computers & Industrial Engineering, 2012, 62(1): 39–55
15 H H Huang, W Pei, H H Wu, et al.A research on problems of mixed-line production and the re-scheduling. Robotics and Computer-integrated Manufacturing, 2013, 29(3): 64–72
16 H D Purnomo, H M Wee. Maximizing production rate and workload balancing in a two-sided assembly line using Harmony Search. Computers & Industrial Engineering, 2014, 76: 222–230
17 P Tapkan, L Ozbakir, A Baykasoglu. Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms. Applied Soft Computing, 2012, 12(11): 3343–3355
18 F Yang, K Gao, I W Simon, et al.Decomposition methods for manufacturing system scheduling: A survey. IEEE/CAA Journal of Automatica Sinica, 2018, 5(2):389–400
19 C R Pan, M C Zhou, Y Qiao, et al.Scheduling cluster tools in semiconductor manufacturing: Recent advances and challenges. IEEE Transactions on Automation Science and Engineering, 2018, 15(2): 586–601
20 F J Yang, N Q Wu, Y Qiao, et al.Optimal one-wafer cyclic scheduling of time-constrained hybrid multicluster tools via petri nets. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 47(11): 2920–2932
21 B Przybylski. A new model of parallel-machine scheduling with integral-based learning effect. Computers & Industrial Engineering, 2018, 121: 189–194
22 Y Xi, J Jang. Scheduling jobs on identical parallel machines with unequal future ready time and sequence dependent setup: An experimental study. International Journal of Production Economics, 2012, 137(1): 1–10
23 Y Ouazene, F Yalaoui. Identical parallel machine scheduling with time-dependent processing times. Theoretical Computer Science, 2018, 721: 70–77
24 G Laleh, G Daniel. Scheduling parallel identical machines to minimize makespan: A parallel approximation algorithm. Journal of Parallel and Distributed Computing, 2018 (in press)
25 L Wu, S Wang. Exact and heuristic methods to solve the parallel machine scheduling problem with multi-processor tasks. International Journal of Production Economics, 2018, 201: 26–40
26 J Cheng, F Chu, M Zhou. An improved model for parallel machine scheduling under time-of-use electricity price. IEEE Transactions on Automation Science and Engineering, 2018, 15(2): 896–899
27 J Y Ding, S Song, R Zhang, et al.. Parallel machine scheduling under time-of-use electricity prices: New models and optimization approaches. IEEE Transactions on Automation Science and Engineering, 2016, 13(2): 1138–1154
28 L Wang, S Y Wang, X L Zheng. A hybrid estimation of distribution algorithm for unrelated parallel machine scheduling with sequence-dependent setup times. IEEE/CAA Journal of Automatica Sinica, 2016, 3(3): 235–246
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