One-dimensional cutting stock problem with a given number of setups: A hybrid approach of metaheuristics and linear programming

Journal of Mathematical Modelling and Algorithms

Volumn 5, Issue 1, 2006, Pages 43-64

  Umetani, Shunji ^a   Yagiura, Mutsunoti ^b   Ibaraki, Toshihide ^c  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b NAGOYA UNIVERSITY   (Japan)

^c KWANSEI GAKUIN UNIVERSITY   (Japan)

Author keywords

Linear programming; Local search; One dimensional cutting stock problem; Sensitivity analysis

Indexed keywords

EID: 33645315765     PISSN: 15701166     EISSN: 15729214     Source Type: Journal    
DOI: 10.1007/s10852-005-9031-0     Document Type: Article

References (19)

1. Belov G. and Scheithauer G.: A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting, European Journal of Operational Research 171 (2006), 85-106.
2. Belov G. and Scheithauer G.: The number of setups (different patterns) in one-dimensional stock cutting, Technical Report MATH-NM-15-2003, Dresden University, 2003.
3. Burkard R. E. and Zelle C.: A local search heuristic for the real cutting problem in paper production, Technical Report SFB-257, Institute of Mathematics B, Technical University Graz, 2003.
4. Degraeve Z. and Schrage L.: Optimal integer solutions to industrial cutting stock problems, INFORMS Journal on Computing 11 (1999), 406-419.
5. Degraeve Z. and Peeters M.: Optimal integer solutions to industrial cutting-stock problems: Part2, benchmark results, INFORMS Journal on Computing 15 (2003), 58-81.
6. Dongarra J. J.: Performance of various computers using standard linear equations software, Technical Report No. CS-89-85, Computer Since Department, University of Tennessee, 2005 (available as http://www.netlib.org/benchmark/ performance.ps).
7. Foerster H. and Wäscher G.: Pattern reduction in one-dimensional cutting stock problems, International Journal of Production Research 38 (2000), 1657-1676.
8. Garey M. R. and Johnson D. S.: Computers and Intractability - A Guide to the Theory of NP-Completeness -, W.H. Freeman and Company, 1979.
9. Gau T. and Wäscher G., CUTGEN1: A problem generator for the standard one-dimensional cutting stock problem, European Journal of Operational Research 84 (1995), 572-579.
10. Gilmore P. C. and Gomory R. E.: A linear programming approach to the cutting-stock problem, Operations Research 9 (1961), 849-859.
11. Gilmore P. C. and Gomory R.E.: A linear programming approach to the cutting-stock problem - part II, Operations Research 11 (1963), 863-888.
12. Haessler R. E.: A heuristic programming solution to a nonlinear cutting stock problem, Management Science 17 (1971), 793-802.
13. Haessler R. E.: Controlling cutting pattern changes in one-dimensional trim problems, Operations Research 23 (1975), 483-493.
14. Lourenço H. R., Martin O. C. and Stützte T.: Iterated local search F. Glover and G. A. Kochenberger eds. Handbook of Metaheuristics, Kluwer Academic Publishers (2003), 321-353.
15. Umetani S., Yagiura M. and Ibaraki T.: An LP-based local search to the one dimensional cutting stock problem using a given number of cutting patterns, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E86-A (2003), 1093-1102.
16. Vance P. H.: Branch-and-price algorithms for the one-dimensional cutting stock problem, Computational Optimization and Applications 9 (1998), 211-228.
17. Vanderbeck F.: Computational study of a column generation algorithm for bin packing and cutting stock problems, Mathematical Programming A86 (1999), 565-594.
18. Vanderbeck F.: Exact algorithm for minimizing the number of setups in the one-dimensional cutting stock problem, Operations Research 48 (2000), 915-926.
19. Zionts S.: The criss-cross method for solving linear programming problems, Management Science 15 (1969), 426-445.