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Article Contents

# Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm

• * Corresponding author:Liangliang Sun
The research is financially sponsored by the National Natural Science Foundation Committee of China (Subject Numbers: 61503259), Hanyu Plan of Shenyang Jianzhu University and Research Funding from the Networked Control System Key Laboratory of the Chinese Academy of Sciences.
• This study investigates a challenging problem of rescheduling a hybrid flow shop in the steelmaking-continuous casting (SCC) process, which is a major bottleneck in the production of iron and steel. In consideration of uncertain disturbance during SCC process, we develop a time-indexed formulation to model the SCC rescheduling problem. The performances of the rescheduling problem consider not only the efficiency measure, which includes the total weighted completion time and the total waiting time, but also the stability measure, which refers to the difference in the number of operations processed on different machines for the different stage in the original schedule and revised schedule. With these objectives, this study develops a Lagrangian heuristic algorithm to solve the SCC rescheduling problem. The algorithm could provide a realizable termination criterion without having information about the problem, such as the distance between the initial iterative point and the optimal point. This study relaxes machine capacity constraints to decompose the relaxed problem into charge-level subproblems that can be solved using a polynomial dynamic programming algorithm. A heuristic based on the solution of the relaxed problem is presented for obtaining a feasible reschedule. An improved efficient subgradient algorithm is introduced for solving Lagrangian dual problems. Numerical results for different events and problem scales show that the proposed approach can generate high-quality reschedules within acceptable computational times.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

• Figure 1.  Steelmaking-continuous casting process

Figure 2.  Connection between started operations and statuses of an operatio

Figure 3.  Illustration of the four performance indexes for the revised scheduling of SCC

Table 1.  The results obtained by SSLRA

 Cast vs. charge(SLLRA) LB UB Gap (%) Time (s) 2 vs.5 937456 983672 4.70 299.5 2 vs.6 1182728 1398892 15.45 313.3 2 vs.7 1497377 1732913 13.59 327.8 2 vs.8 1837244 2252386 18.43 323.7 3 vs.5 1923113 2183725 11.93 309.4 3 vs.6 2487753 2711245 8.24 355.2 3 vs.7 3294573 3690245 10.72 377.2 3 vs.8 3999272 5294742 24.47 466.1 4 vs.5 3100023 3274848 5.34 378.5 4 vs.6 4134749 4591234 9.94 449.2 4 vs.7 5368271 7545422 28.85 598.4 4 vs.8 6650012 9082765 26.78 739.6 5 vs.5 4648823 5119374 9.19 504.7 5 vs.6 6168391 9998116 38.30 663.2 5 vs.7 8102927 11924753 32.05 2199.5 5 vs.8 10373752 13583721 23.63 7824 Average 4106654 7532570 17.60 1008.08

Table 2.  The results obtained by DCSLA

 Cast vs. charge(DCSLA) LB UB Gap (%) Time (s) 2 vs.5 937456 954151 1.75 1.6 2 vs.6 1182728 1294621 8.64 2.2 2 vs.7 1497377 1519847 1.48 3.2 2 vs.8 1837244 1997636 8.03 1.9 3 vs.5 1923113 2003743 4.02 2 3 vs.6 2487753 2505632 0.71 3.2 3 vs.7 3294573 3349425 1.64 1.5 3 vs.8 3999272 4186443 4.47 1.5 4 vs.5 3100023 3153846 1.71 2.1 4 vs.6 4134749 4200474 1.56 2.7 4 vs.7 5368271 5438362 1.29 3.8 4 vs.8 6650012 6739436 1.33 3.1 5 vs.5 4648823 4753628 2.20 2.4 5 vs.6 6168391 6374522 3.23 3.9 5 vs.7 8102927 9193736 11.86 5.9 5 vs.8 10373752 11376463 8.81 8.8 Average 4106654 4315122 3.92 3.11

Table 3.  Computational results of DCSLA for SCC rescheduling

 ET Events EV-1 (s) EV-2 (s) EV-3 (min) DG (%) Time (s) IN 1 R1-T2-M1 0 0 22 12.94 76.63 162 2 R1-T3-M1 0 0 15 11.85 66.31 115 3 R1-T1-M2 0 0 16 13.64 75.92 141 4 R1-T2-M2 0 0 19 13.09 58.7 128 5 R1-T3-M2 0 0 21 11.55 44.76 103 6 R1-T1-M3 0 0 18 8.68 121.91 196 7 R1-T2-M3 0 0 11 12.97 134.73 187 8 R1-T3-M3 0 0 10 11.32 83.66 165 9 R2-T2-M1 0 0 19 7.74 9.32 63 10 R2-T3-M1 0 0 12 8.31 8.69 60 11 R2-T1-M2 0 0 16 9.22 12.81 52 12 R2-T2-M2 0 0 19 7.93 9.33 61 13 R2-T3-M2 0 0 22 8.88 8.89 68 14 R2-T1-M3 0 0 14 9.12 15.9 59 15 R2-T2-M3 0 0 16 8.45 7.63 42 16 R2-T3-M3 0 0 11 8.67 8.69 74 Average 0 0 16.31 10.27 46.49 104 (ET: Event Type, IN: Number of Iterations, DG: Duality Gap, EV: Evaluation Values)
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