New lower bounds based on column generation and constraint programming for the pattern minimization problem

Computers and Operations Research

Volumn 36, Issue 11, 2009, Pages 2944-2954

  Alves, Cláudio ^a   Macedo, Rita ^a   Valério de Carvalho, José ^a  

^a UNIVERSITY OF MINHO   (Portugal)

Author keywords

Constraint programming; Cutting and packing problems; Integer programming; Lower bounds; Pattern minimization problem

Indexed keywords

COLUMN GENERATIONS; COMPUTATIONAL EXPERIMENTS; CONSTRAINT PROGRAMMING; CONSTRAINT-PROGRAMMING MODELS; CUTTING AND PACKING PROBLEMS; CUTTING MACHINES; CUTTING STOCK PROBLEMS; EXACT SOLUTIONS; INTEGER PROGRAMMING MODELS; LOWER BOUNDS; NEW RESULTS; PATTERN MINIMIZATION PROBLEM; RANDOM INSTANCES; SET-UP COSTS; VALID INEQUALITIES;

COMPUTER PROGRAMMING; CONSTRAINT THEORY; CONTROL THEORY; CUTTING; DYNAMIC PROGRAMMING; MACHINERY; OPTIMIZATION;

INTEGER PROGRAMMING;

EID: 64549140086     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2009.01.008     Document Type: Article

References (26)

1. Aloisio A, Arbib C, Marinelli F. On LP relaxations for 1-dimensional cutting stock with setup costs. Technical Report, Dipartimento di Informatica, Università degli Studi dell'Aquila, via Vetoio, Coppito, L'Aquila, Italy; 2006.
2. Aloisio A, Arbib C, Marinelli F. Cutting stock with no three parts per pattern: work-in-process and pattern minimization. Technical Report, Dipartimento di Informatica, Università degli Studi dell'Aquila, via Vetoio, Coppito, L'Aquila, Italy; 2008.
3. Alves C., and Valério de Carvalho J.M. A branch-and-price-and-cut algorithm for the pattern minimization problem. RAIRO Operations Research 42 (2008) 435-453
4. Belov G. Problems, models and algorithms in one- and two-dimensional cutting. PhD thesis, Dresden University; 2003.
5. Chen C., Hart S., and Tham W. A simulated annealing heuristic for the one-dimensional cutting stock problem. European Journal of Operational Research 93 (1996) 522-535
6. Clautiaux F, Alves C, Valério de Carvalho JM. A survey of dual-feasible and superadditive functions. Annals of Operations Research 2008, doi:10.1007/S10479-008-0453-8.
7. Cui Y., Zhao X., Yang Y., and Yu P. A heuristic for the one dimensional cutting stock problem with pattern reduction. Proceedings of the Institution of Mechanical Engineers, Part B, Journal of Engineering Manufacture 222 6 (2008) 677-685
8. Valério de Carvalho J.M. Exact solution of bin-packing problems using column generation and branch-and-bound. Annals of Operations Research 86 (1999) 629-659
9. Diegel A, Chetty M, Van Schalkwyck S, Naidoo S. Setup combining in the trim loss problem-3-to-2 & 2-to-1. Working paper, Business Administration, University of Natal, Durban, First Draft, 1993.
10. Fekete S., and Schepers J. New classes of fast lower bounds for bin packing problems. Mathematical Programming 91 (2001) 11-31
11. Foerster H., and Wäscher G. Pattern reduction in one-dimensional cutting stock problems. International Journal of Production Research 38 7 (2000) 1657-1676
12. Gau T., and Waescher G. CUTGEN1: a problem generator for the standard one-dimensional cutting stock problem. European Journal of Operational Research 84 (1995) 572-579
13. Gilmore P., and Gomory R. A linear programming approach to the cutting stock problem. Operations Research 9 (1961) 849-859
14. Haessler R. Controlling cutting pattern changes in one-dimensional trim problems. Operations Research 23 3 (1975) 483-493
15. Ilog. Ilog CPLEX 10.0 reference manual, Gentilly, France; 2006.
16. Ilog. Ilog CP optimizer reference manual, Gentilly, France; 2007.
17. Jain V., and Grossmann I. Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing 13 4 (2001) 258-276
18. Martello S., and Toth P. Knapsack problems-algorithms and computer implementation (1990), Wiley, Chichester
19. McDiarmid C. Pattern minimisation in cutting stock problems. Discrete Applied Mathematics 98 (1999) 121-130
20. Milano M. Constraint and integer programming: toward a unified methodology (2004), Kluwer Academic Publishers, Dordrecht
21. Teghem J., Pirlot M., and Antoniadis C. Embedding of linear programming in a simulated annealing algorithm for solving a mixed integer production planning problem. Journal of Computational and Applied Mathematics 64 (1995) 91-102
22. Umetani S., Yagiura M., and Ibaraki T. One-dimensional cutting stock problem to minimize the number of different patterns. European Journal of Operational Research 146 (2003) 388-402
23. Umetani S., Yagiura M., and Ibaraki T. 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 5 (2006) 43-64
24. Vanderbeck F. Exact algorithm for minimising the number of setups in the one-dimensional cutting stock problem. Operations Research 48 6 (2000) 915-926
25. Wäscher G., Haußner H., and Schumann H. An improved typology of cutting and packing problems. European Journal of Operational Research 183 (2007) 1109-1130
26. Yanasse H., and Limeira M. A hybrid heuristic to reduce the number of different patterns in cutting stock problems. Computers and Operations Research 33 (2006) 2744-2756