An exact algorithm for constrained two-dimensional two-staged cutting problems

Operations Research

Volumn 53, Issue 1, 2005, Pages 140-150

  Hifi, Mhand ^a,b,c   M'Hallah, Rym ^d  

^a LaRIA   (France)

^b UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

^c PSL RESEARCH UNIVERSITY   (France)

^d KUWAIT UNIVERSITY   (Kuwait)

Author keywords

Dynamic programming; Industries; Programming: algorithms Branch and bound; Simulation: applications, efficiency

Indexed keywords

ALGORITHMS; COMPUTER PROGRAMMING; COMPUTER SIMULATION; CONSTRAINT THEORY; CUTTING; DYNAMIC PROGRAMMING; OPTIMIZATION;

ALGORITHMS-BRANCH-AND-BOUND; CONSTRAINED TWO DIMENSIONAL CUTTING (C-TDC); TWO-DIMENSIONAL CUTTING; TWO-STAGED CUTTING;

OPERATIONS RESEARCH;

EID: 14644390239     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1040.0154     Document Type: Article

References (18)

1. Beasley, J. E. 1985. Algorithms for unconstrained two-dimensional guillotine cutting. J. Oper. Res. Soc. 36 297-306.
2. Dyckhoff, H. 1990. A typology of cutting and packing problems. Eur. J. Oper. Res. 44 145-159.
3. Dyckhoff, H., G. Scheithauer, J. Terno. 1997. Cutting and packing (C&P). M. Dell'Amico, F. Maffioli, S. Martello, eds. Annotated Bibliographies in Combinatorial Optimization. John Wiley and Sons, Chichester, U.K.
4. Garey, M. R., D. S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco, CA.
5. Gilmore, P. C., R. E. Gomory. 1961. A linear programming approach to the cutting stock problem. Oper. Res. 9 849-859.
6. Gilmore, P. C., R. E. Gomory. 1965. Multistage cutting problems of two and more dimensions. Oper. Res. 13 94-119.
7. Hifi, M. 1999. Contribution à la résolution de quelques problèmes difficiles de l'optimisation combinatoire. [A contribution to the solution of some difficult problems of combinatorial optimization] Habilitation thesis, PRiSM, Université de Versailles, Saint-Quentin-en-Yvelines, France.
8. Hifi, M. 2001. Exact algorithms for large-scale unconstrained two and three staged cutting problems. Comput. Optim. Appl. 18 63-88.
9. Hifi, M., R. M'Hallah. 2001. Strip generation algorithms for constrained two-dimensional two-staged cutting stock problems. Technical report 2001-Cahiers Bleu, Maison des Sciences Economiques, Université Paris 1 Panthéon-Sorbonne, France.
10. Hifi, M., C. Roucairol. 2001. Approximate and exact algorithms for constrained (un)weighted two-dimensional two-staged cutting stock problems. J. Combin. Optim. 5 465-494.
11. Kantorovich, L. V. 1960. Mathematical methods of organizing and planning production. Management Sci. 6 363-422.
12. Lodi, A., M. Monaci. 2003. Integer linear programming models for 2-staged two-dimensional knapsack problems. Math. Programming 94 257-278.
13. Martello, S., P. Toth. 1990. An exact algorithm for large unbounded knapsack problems. Oper. Res. Lett. 9 15-20.
14. Martello, S., P. Toth. 1997. Upper bounds and algorithms for hard 0-1 knapsack problems. Oper. Res. 45 768-778.
15. Morabito, R., M. Arenales. 1996. Staged and constrained two-dimensional guillotine cutting problems: An and-or-graph approach. Eur. J. Oper. Res. 94/3 548-560.
16. Morabito, R., V. Garcia. 1998. The cutting stock problem in hardboard industry: A case study. Comput. Oper. Res. 25 469-485.
17. Pisinger, D. 1997. A minimal algorithm for the 0-1 knapsack problem. Oper. Res. 45 758-767.
18. Vanderbeck, F. 2001. A nested decomposition approach to a 3-stage 2-dimensional cutting stock problem. Management Sci. 47 864-879.