Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem

Published Online:https://doi.org/10.1287/ijoc.1060.0181

References

  • Apt K. R.Principles of Constraint Programming (2003) (Cambridge University Press, Cambridge, UK) CrossrefGoogle Scholar
  • Belov G. Problems, models and algorithms in one- and two-dimensional cutting. (2003) . Ph.D. thesis, Institute of Numerical Mathematics, Technischen Universität Dresden, Dresden, GermanyGoogle Scholar
  • Bengtsson B. E. Packing rectangular pieces—A heuristic approach. Comput. J. (1982) 25:353–357CrossrefGoogle Scholar
  • Berkey J. O., Wang P. Y. Two dimensional finite bin packing algorithms. J. Oper. Res. Soc. (1987) 38:423–429CrossrefGoogle Scholar
  • Bockmayr A., Kasper T. Branch-and-infer: A unifying framework for integer and finite domain constraint programming. INFORMS J. Comput. (1998) 10:287–300LinkGoogle Scholar
  • Boschetti M. A., Mingozzi A. The two-dimensional finite bin packing problem. Part I: New lower bounds for the oriented case. 4OR (2003a) 1:27–42CrossrefGoogle Scholar
  • Boschetti M. A., Mingozzi A. The two-dimensional finite bin packing problem. Part II: New lower and upper bounds. 4OR (2003b) 2:135–148Google Scholar
  • Caprara A., Monaci M. On the two-dimensional knapsack problem. Oper. Res. Lett. (2004) 32:5–14CrossrefGoogle Scholar
  • Chen C. S., Lee S. M., Shen Q. S. An analytical model for the container loading problem. Eur. J. Oper. Res. (1995) 80:68–76CrossrefGoogle Scholar
  • Dell’Amico M., Martello S., Vigo D. A lower bound for the non-oriented two-dimensional bin packing problem. Discrete Appl. Math. (2002) 118:13–24CrossrefGoogle Scholar
  • Dowsland K. Some experiments with simulated annealing techniques for packing problems. Eur. J. Oper. Res. (1993) 68:389–399CrossrefGoogle Scholar
  • Eremin A., Wallace M., Walsh T. Hybrid Benders decomposition algorithms in constraint logic programming. CP 2001, Lecture Notes in Computer Science (2001) 2239(Springer, Berlin, Germany) 1–15CrossrefGoogle Scholar
  • Faroe O., Pisinger D., Zachariasen M. Guided local search for the three-dimensional bin packing problem. INFORMS J. Comput. (2003) 15:267–283LinkGoogle Scholar
  • Fekete Sandor P., Schepers Joerg. New classes of lower bounds for the bin packing problem. Math. Programming (2001) 91:11–31CrossrefGoogle Scholar
  • Fekete Sandor P., Schepers Joerg, van der Veen Jan C. An exact algorithm for higher-dimensional orthogonal packing. Oper. Res. (2007) . ForthcomingLinkGoogle Scholar
  • Gilmore P. C., Gomory R. E. A linear programming approach to the cutting stock problem. Oper. Res. (1961) 9:849–859LinkGoogle Scholar
  • Gilmore P. C., Gomory R. E. A linear programming approach to the cutting stock problem—Part II. Oper. Res. (1963) 13:94–119LinkGoogle Scholar
  • Gilmore P. C., Gomory R. E. Multistage cutting stock problems of two and more dimensions. Oper. Res. (1965) 13:94–120LinkGoogle Scholar
  • Hadjiconstantinou E., Christofides N. An exact algorithm for general, orthogonal, two-dimensional knapsack problems. Eur. J. Oper. Res. (1995) 83:39–56CrossrefGoogle Scholar
  • Hifi M. Exact algorithms for large-scale unconstrained two and three staged unconstrained cutting problems. Comput. Optim. Appl. (2001) 18:63–88CrossrefGoogle Scholar
  • ILOGILOG CPLEX 7.0, Reference Manual (2000) . ILOG SA, Gentilly, FranceGoogle Scholar
  • Junger Michael, Thienel Stafan. The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization. Software Practice Experience (2000) 30(11):1325–1352CrossrefGoogle Scholar
  • Junker U., Karisch S. E., Kohl N., Vaaben B., Fahle T., Sellmann M., Jaffar J. Constraint programming based column generation for crew assignment. Proc. CP’99, Lecture Notes in Computer Science (1999) 1713(Springer, Berlin, Germany) 261–274Google Scholar
  • Kellerer H., Pferschy U., Pisinger D.Knapsack Problems (2004) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Lasdon L. S.Optimization Theory for Large Systems (1970) (Macmillan, London, UK) Google Scholar
  • Lodi A., Martello S., Vigo D. Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS J. Comput. (1999) 11:345–357LinkGoogle Scholar
  • Lodi A., Martello S., Vigo D. Recent advances on two-dimensional bin packing problems. Discrete Appl. Math. (2002) 123:379–396CrossrefGoogle Scholar
  • Martello S., Vigo D. Exact solution of the two-dimensional finite bin packing problem. Management Sci. (1998) 44:388–399LinkGoogle Scholar
  • Martello S., Pisinger D., Vigo D., den Boef Edgar, Korst Jan. Algorithms for general and robot-packable variants of the three-dimensional bin packing problem. ACM Trans. Math. Software (2007) 33(1CrossrefGoogle Scholar
  • Monaci M., Toth P. A set-covering based heuristic approach for bin-packing problems. INFORMS J. Comput. (2006) 18(1):71–85LinkGoogle Scholar
  • Onodera H., Taniguchi Y., Tamaru K. Branch-and-bound placement for building block layout. Proc. 28th ACM/IEEE Design Automation Conf. (1991) (ACM Press, New York) 433–439CrossrefGoogle Scholar
  • Padberg M. Packing small boxes into a big box. Math. Methods Oper. Res. (2000) 52:1–21CrossrefGoogle Scholar
  • Parada V., Palma R., Sales D., Gómes A. A comparative numerical analysis for the guillotine two-dimensional cutting problem. Ann. Oper. Res. (2000) 96:245–254CrossrefGoogle Scholar
  • Pisinger D., Sigurd M. M. The two-dimensional bin packing problem with variable bin sizes and costs. Discrete Optim. (2005) 2:154–167CrossrefGoogle Scholar
  • Ryan D. M., Foster B. A., Wren A. An integer programming approach to scheduling. Computer Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling (1981) (North-Holland, Amsterdam, The Netherlands) 269–280Google Scholar
  • Voudouris C. Guided local search for combinatorial optimisation problems. (1997) . Ph.D. thesis, Department of Computer Science, University of Essex, Colchester, UKGoogle Scholar
  • Voudouris C., Tsang E. Guided local search and its application to the traveling salesman problem. Eur. J. Oper. Res. (1999) 113:469–499CrossrefGoogle Scholar
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