New integer programming formulations and an exact algorithm for the ordered cutting stock problem

Journal of the Operational Research Society

Volumn 59, Issue 11, 2008, Pages 1520-1531

  Alves, C ^a,b   De Carvalho, J M Valério ^a  

^a UNIVERSITY OF MINHO   (Portugal)

^b UNIVERSITY OF MINHO   (Portugal)

Author keywords

Branch and bound; Column generation; Cutting planes; Cutting stock; Integer programming models; Pattern sequencing

Indexed keywords

BRANCH AND BOUND METHOD; LINEAR PROGRAMMING; MACHINERY;

COLUMN GENERATION; CUTTING PLANES; CUTTING STOCK; INTEGER PROGRAMMING MODELS; PATTERN SEQUENCING;

INTEGER PROGRAMMING;

EID: 53349098136     PISSN: 01605682     EISSN: 14769360     Source Type: Journal    
DOI: 10.1057/palgrave.jors.2602494     Document Type: Article

References (25)

1. Alves C (2005). Cutting and packing: Problems, models and exact algorithms. PhD thesis, University of Minho.
2. Alves C and Valério de Carvalho JM (2006). A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem. Comput Opl Res, doi: 10.1016/j.cor.2006.08.014.
3. Alves C and Valério de Carvalho JM (2007). Accelerating column generation for variable sized bin-packing problems. Eur J Opl Res 183: 1333-1352.
4. Becceneri J, Yanasse H and Soma N (2004). A method for solving the minimization of the maximum number of open stacks problem within a cutting process. Comput Opl Res 31: 2315-2332.
5. Belov G (2003). Problems, models and algorithms in one- and two-dimensional cutting. PhD thesis, University of Dresden.
6. Chen C, Hart S and Tham W (1996). A simulated annealing heuristic for the one-dimensional cutting stock problem. Eur J Opl Res 93: 522-535.
7. Farley A (1990). A note on bounding a class of linear programming problems, including cutting stock problems. Opns Res 38: 922-923.
8. Fink A and Voß S (1999). Applications of modem heuristic search methods to pattern sequencing problems. Comput Opl Res 26: 17-34.
9. Foerster H and Waescher G (2000). Pattern reduction in one-dimensional cutting stock problems. Int J Prod Res 38: 1657-1676.
10. Gilmore P and Gomory R (1961). A linear programming approach to the cutting stock problem. Opns Res 9: 849-859.
11. Gilmore P and Gomory R (1963). A linear programming approach to the cutting stock problem: Part II. Opns Res 11: 863-888.
12. Haessler R (1971). A heuristic programming solution to a nonlinear cutting stock problem. Mngt Sci 17: 793-802.
13. ILOG (1999). CPLEX 6.5 User's Manual. 9, rue de Verdun, BP85, F-92453, Gentilly, France.
14. Johnson M, Rennick C and Zak E (1999). One-dimensional cutting stock problem in just-in-time environment. Pesquisa Operacional 19: 145-158.
15. Linhares A and Yanasse H (2002). Connections between cutting-pattern sequencing, VLSI design, and flexible machines. Comput Opl Res 29: 1759-1772.
16. Luebbecke M and Desrosiers J (2005). Selected topics in column generation. Opns Res 53: 1007-1023.
17. Madsen O (1988). An application of travelling-salesman routines to solve pattern-allocation problems in the glass industry. J Opl Res Soc 39: 249-256.
18. Nemhauser G and Wolsey L (1988). Integer and Combinatorial Optimization. John Wiley & Sons: New York.
19. Ragsdale C and Zobel C (2004). The ordered cutting stock problem. Decis Sci 35: 83-100.
20. Schreck H (2002). A sequence problem in practical trim optimization. Proceedings of the 16th triennial conference of the International Federation of Operational Research Societies. IFORS: Edinburgh, p 121.
21. Umetani S, Yagiura M and Ibaraki T (2003). One-dimensional cutting stock problem to minimize the number of different patterns. Eur J Opl Res 146: 388-402.
22. Valério de Carvalho JM (1999). Exact solution of bin-packing problems using column generation and branch-and-bound. Ann Opns Res 86: 629-659.
23. Vanderbeck F (2000). Exact algorithm for minimising the number of setups in the one-dimensional cutting stock problem. Opns Res 48: 915-926.
24. Villeneuve D, Desrosiers J, Luebbecke M and Soumis F (2005). On compact formulations for integer programs solved by column generation. Ann Opns Res 139: 375-388.
25. Yanasse H (1997). On a pattern sequencing problem to minimize the maximum number of open stacks. Eur J Opl Res 100: 454-463.