A note on linear models for two-group and three-group two-dimensional guillotine cutting problems

International Journal of Production Research

Volumn 46, Issue 21, 2008, Pages 6189-6206

  Yanasse, H H ^a   Morabito, R ^b  

^a INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS   (Brazil)

^b FEDERAL UNIVERSITY OF SÃO CARLOS   (Brazil)

Author keywords

2 Group and 3 group guillotine cutting; Cutting and packing problems; Furniture industry; Integer linear models

Indexed keywords

CUTTING; FURNITURE MANUFACTURE; MACHINERY; MATHEMATICAL MODELS; TWO DIMENSIONAL;

2-GROUP AND 3-GROUP GUILLOTINE CUTTING; CUTTING AND PACKING PROBLEMS; FURNITURE INDUSTRY; INTEGER LINEAR MODELS;

PROBLEM SOLVING;

EID: 53349119021     PISSN: 00207543     EISSN: 1366588X     Source Type: Journal    
DOI: 10.1080/00207540601011543     Document Type: Article

References (41)

1. Arenales, M., Morabito, R., Yanasse, H. (Eds), Special issue: cutting and packing problems. Pesquisa Oper., 1999, 19, 107-299.
2. Beasley, J., Algorithms for unconstrained two-dimensional guillotine cutting. J. Oper. Res. Soc., 1985, 36, 297-306.
3. Bischoff, E. and Waescher, G. (Eds), Special issue: cutting and packing. Euro. J. Oper. Res., 1995, 84, 503-715.
4. Brooke, A., Kendrick, D., Meeraus, A. and Rosenthal, R.E., GAMS: a User's Guide, Release 2.25, 1992 (The Scientific Press: San Franciso).
5. Carnieri, C., Guillermo, A. and Gavinho, L., Solution procedures for cutting lumber into furniture parts. Euro. J. Oper. Res., 1994, 73, 495-501.
6. Christofides, N. and Hadjiconstantinou, E., An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts. Euro. J. Oper. Res., 1995, 83, 21-38.
7. Cui, Y., An exact algorithm for generating homogeneous T-shape cutting patterns. Comput. Oper. Res., 2005, 32, 143-152.
8. Dowsland, K. and Dowsland, W., Packing problems. Euro. J. Oper. Res., 1992, 56, 2-14.
9. Dyckhoff, H. and Finke, U., Cutting and Packing in Production and Distribution: Typology and Bibliography, 1992 (Heidelberg: Springler-Verlag Co).
10. Dyckhoff, H., Scheithauer, G. and Terno, J., Cutting and packing. In Annotated Bibliographies in Combinatorial Optimisation, edited by M. Amico, F. Maffioli and F. Martello, pp. 393-414, 1997 (John Wiley & Sons: New York, NY).
11. Dyckhoff, H. and Waescher, G. (Eds), Special issue: cutting and packing. Euro. J. Oper. Res., 1990, 44, 133-306.
12. ESICUP, Euro Special Interest Group on Cutting and Packing, 2006. Available at: http://www.apdio.pt/esicup/ (accessed June 2006).
13. Foronda, S. and Carino, H., A heuristic approach to the lumber allocation and manufacturing in hardwood dimension and furniture manufacturing. Euro. J. Oper. Res., 1991, 54, 151-162.
14. Gilmore, P. and Gomory, R., Multistage cutting stock problems of two and more dimensions. Oper. Res., 1965, 14, 94-120.
15. Gramani, M.C. and Franccedil;a, P.M., The combined cutting stock and lot-sizing problem in industrial processes. Euro. J. Oper. Res., in press.
16. Harjunkoski, I., Pörn, R., Westerlund, T. and Skifvars, H., Different strategies for solving bilinear integer non-linear programming problems with convex transformations. Comput. Chem. Eng., 1997, 21, 487-492.
17. Hifi, M., The DH/KD algorithm: A hybrid approach for unconstrained two-dimensional cutting problems. Euro. J. Oper. Res., 1997, 97, 41-52.
18. Hifi, M. (Ed.), Special issue on cutting and packing. Studia Informatica Universalis, 2002, 2, 1-161.
19. Hifi, M. and Roucairol, C., Approximate and exact algorithms for constrained (un)weighted two-dimensional two-staged cutting stock problems. J. Combin. Optim., 2001, 5, 465-494.
20. Hinxman, A., The trim-loss and assortment problems: a survey. Euro. J. Oper. Res., 1980, 5, 8-18.
21. Johnston, R.E. and Sadinlija, E., A new model for complete solutions to one-dimensional cutting stock problems. Euro. J. Oper. Res., 2004, 153, 176-183.
22. Lirov, Y. (Ed.), Special issue: cutting stock: geometric resource allocation, Math. Comput. Model., 1992, 16.
23. Lodi, A., Martello, S. and Monaci, M., Two-dimensional packing problems: a survey. Euro. J. Oper. Res., 2002, 141, 241-252.
24. Lodi, A. and Monaci, M., Integer programming models for 2-staged two-dimensional knapsack problems. Math. Program., 2003, 94, 257-278.
25. Martello, S. (Ed.), Special issue: knapsack, packing and cutting, Part I: one-dimensional knapsack problems. INFOR, 1994a, 32, 124-214.
26. Martello, S. (Ed.), Special issue: knapsack, packing and cutting, Part II: multidimensional knapsack and cutting stock problems. INFOR, 1994b, 32, 219-309.
27. Morabito, R. and Arenales, M., Staged and constrained two-dimensional guillotine cutting problems: an and/or-graph approach. Euro. J. Oper. Res., 1996, 94, 548-560.
28. Morabito, R. and Arenales, M., Optimizing the cutting of stock plates in a furniture company. Int. J. Prod. Res., 2000, 38, 2725-2742.
29. Morabito, R. and Belluzzo, L., Optimising the cutting of wood fibre plates in the hardboard industry. Euro. J. Oper. Res., 2007, 183, 1405-1420.
30. Morabito, R. and Garcia, V., The cutting stock problem in a hardboard industry: a case study. Comput. Oper. Res., 1998, 25, 469-485.
31. Mukhacheva, E.A. (Ed.), Decision Making Under Conditions of Uncertainty: Cutting -Packing Problems, 1997 (The International Scientific Collection: Ufa, Russia).
32. Riehme, J., Scheithauer, G. and Terno, J., The solution of two-stage guillotine cutting stock problems having extremely varying order demands. Euro. J. Oper. Res., 1996, 91, 543-552.
33. Scheithauer, G., On a two-dimensional guillotine cutting problem. Presented at IFORS 2002, Edinburgh, UK, 2002.
34. Sweeney, P. and Paternoster, E., Cutting and packing problems: a categorised, application-oriented research bibliography. J. Oper. Res. Soc., 1992, 43, 691-706.
35. Vianna, A.C., Arenales, M. and Gramani, M.C., Two-stage and constrained two-dimensional guillotine cutting problems. Working Paper, Universidade de São Paulo, Brazil, 2002.
36. Yanasse, H.H. and Katsurayama, D.M., Checkerboard patterns: proposals for its generation. Inter. Trans. Oper. Res., 2005, 12, 21-45.
37. Yanasse, H.H. and Morabito, R., Linear models for one-group two-dimensional guillotine cutting problems. Int. J. Prod. Res., in press.
38. Yanasse, H.H., Zinober, A. and Harris, R., Two-dimensional cutting stock with multiple stock sizes. J. Oper. Res. Soc., 1991, 42, 673-683.
39. Waescher, G. and Gau, T., Heuristics for the integer one-dimensional cutting stock problem: a computational study. OR Spectrum, 1996, 18, 131-144.
40. Waescher G., Haussner H. and Schumann H., An improved typology of cutting and packing problems. Euro. J. Oper. Res., in press.
41. Wang, P. and Waescher, G. (Eds), Special issue on cutting and packing problems. Euro. J. Oper. Res., 2002, 141, 239-469.