A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous-casting production

Naval Research Logistics

Volumn 58, Issue 4, 2011, Pages 370-388

  Tang, Lixin ^a   Wang, Gongshu ^a   Liu, Jiyin ^b   Liu, Jingyi ^c  

^a NORTHEASTERN UNIVERSITY   (China)

^b LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^c NORTHEASTERN UNIVERSITY   (China)

Author keywords

batching; column generation; Lagrangian relaxation; mixed integer programming; steelmaking and continuous casting

Indexed keywords

BATCHING; CASTING PRODUCTION; COLUMN GENERATION; COMBINED ALGORITHMS; COMPUTATION TIME; COMPUTATIONAL EXPERIMENT; CUSTOMER ORDERS; DOUBLE-LOOP; DUAL FORM; INNER LOOPS; LAGRANGIAN DUAL PROBLEM; LAGRANGIAN MULTIPLIERS; LAGRANGIAN RELAXATION; LOWER BOUNDS; MIXED INTEGER PROGRAMMING; MIXED INTEGER PROGRAMMING MODEL; ORDER ASSIGNMENT; ORDER BATCHING; OUTER LOOP; PROBLEM INSTANCES; PRODUCTION BATCHES; STEEL COMPANIES; SUBGRADIENT METHODS;

ALGORITHMS; INTEGER PROGRAMMING; STEELMAKING;

LAGRANGE MULTIPLIERS;

EID: 79954425247     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.20452     Document Type: Article

References (27)

1. I. Harjunkoski, I. E. Grossmann, A decomposition approach for the scheduling of steel plant production, Comput Chem Eng 25 (2001), 1647-1660. (Pubitemid 33086119)
2. D. Pacciarelli, M. Pranzo, Production scheduling in a steelmaking continuous-casting plant, Comput Chem Eng 28 (2004), 2823-2835. (Pubitemid 39572743)
3. S. Zanoni, L. Zavanella, Model and analysis of integrated production-inventory system: The case of steel production, Int J Prod Econ 93-94 (2005), 197-205.
4. I. Ferretti, S. Zanoni, L. Zavanella, Production-inventory scheduling using Ant System metaheuristic, Int J Prod Econ 104 (2006), 317-326. (Pubitemid 44403068)
5. A. Bellabdaoui, J. Teghem, A mixed-integer linear programming model for the continuous-casting planning, Int J Prod Econ 104 (2006), 260-270. (Pubitemid 44403061)
6. H. Missbauer, W. Haube, W. Stadler, A scheduling system for the steelmakingâContinuous casting processâA case study from the steel-making industry, Int J Prod Res 47 (2009), 4147-4172.
7. L. X. Tang, J. Y. Liu, A. Y. Rong, Z. H. Yang, A mathematical programming model for scheduling steelmaking-continuous-casting production, Eur J Oper Res 120 (2000), 423-435.
8. L. X. Tang, P. B. Luh, J. Y. Liu, L. Fang, Steelmaking process scheduling using Lagrangian relaxation, Int J Prod Res 40 (2002), 55-70. (Pubitemid 34593845)
9. R. E. Box, D. G. Herbe, A scheduling model for LTV Steel's Cleveland works' twin strand continuous slab caster, Interfaces 18 (1988), 42-56.
10. H. S. Lee, S. S. Murthy, S. W. Haider, D. V. Morse, Primary production scheduling at steel making industries, IBM J Res Dev 40 (1996), 231-252. (Pubitemid 126534375)
11. S. Y. Chang, M. R. Chang, Y. S. Hong, A lot grouping algorithm for a continuous slab caster in an integrated steel mill, Prod Plan Control 11 (2000), 363-368. (Pubitemid 35394344)
12. L. X. Tang, G. S. Wang, Decision support system for the batching problems of steelmaking and continuous-casting production, Omega 36 (2008), 976-991.
13. G. S. Wang, L. X. Tang, A Lagrangian relaxation for flexible order batching problem in iron and steel industry, Presented at the IEEE International Conference on Industrial Technology, Chengdu, China, April 2008, pp. 1-5.
14. A. Klose, S. Gortz, A branch-and-price algorithm for the capacitated facility location problem, Eur J Oper Res 179 (2007), 1109-1125. (Pubitemid 46038601)
15. M. L. Fisher, Lagrangian relaxation method for solving integer programming, Manage Sci 27 (1981), 221-18.
16. &1E62;. A&011F;ca, B. Eksioglu, J. B. Ghosh, Lagrangian solution of maximum dispersion problems, Nav Res Logist 47 (2000), 97-114. (Pubitemid 30563279)
17. S. Kunnumkal, H. Topaloglu, A duality-based relaxation and decomposition approach for inventory distribution systems, Nav Res Logist 55 (2008), 612-631.
18. Z. L. Chen, W. B. Powell, Exact algorithms for scheduling multiple families of jobs on parallel machines, Nav Res Logist 50 (2003), 823-840.
19. O. Kwon, K. Lee, D. Kang, S. Park, A branch-and-price algorithm for a targeting problem, Nav Res Logist 54 (2007), 732-741. (Pubitemid 47518516)
20. L. X. Tang, G. S. Wang, J. Y. Liu, A branch-and-price algorithm to solve the molten iron allocation problem in iron and steel industry, Comput Oper Res 34 (2007), 3001-3015.
21. J. M. Van den Akker, J. A. Hoogeveen, S. L. Van de Velde, Combining column generation and Lagrangean relaxation to solve a single-machine common due date problem, INFORMS J Comput 14 (2002), 37-51.
22. R. Jans, Z. Degraeve, An industrial extension of the discrete lot sizing and scheduling problem, IIE Trans 36 (2004), 47-58.
23. K. Bülbül, P. Kaminsky, C. Yano, Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs, Nav Res Logist 51 (2004), 407-445.
24. D. Huisman, R. Jans, M. Peeters, A. P. M. Wagelmans, Combining column generation and Lagrangian relaxation, G. Desaulniers, J. Desorsiers, M. M. Solomon, (Editors), Column generation, Springer, US, Boston, 2005, pp. 247-270.
25. K. Mathur, P. Venkateshan, A new lower bound for the linear knapsack problem with general integer variables, Eur J Oper Res 178 (2007), 738-754. (Pubitemid 44765144)
26. P. Wentges, Weighted Dantzig-Wolfe decomposition for linear mixed-integer programming, Int Trans Oper Res 4 (1997), 151-162. (Pubitemid 127097012)
27. X. Zhao, P. B. Luh, J. Wang, Surrogate gradient algorithm for Lagrangian relaxation, J Opt Theor Appl 100 (1999), 699-712.