The two-dimensional bin packing problem with variable bin sizes and costs

Barnhart, 1998, Branch-and-price: column generation for solving huge integer programs, Oper. Res., 46, 316, 10.1287/opre.46.3.316 J.E. Beasley, OR-library, 2004, http://mscmga.ms.ic.ac.uk/info.html. G. Belov, Problems, models and algorithms in one- and two-dimensional cutting, Ph.D. Thesis, Technischen Universität Dresden, 2003, http://www.math.tu-dresden.de/∼belov/publ/text030908_SUBMIT.pdf. Belov, 2002, A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths, European J. Oper. Res., 141, 274, 10.1016/S0377-2217(02)00125-X Berkey, 1987, Two dimensional finite bin packing algorithms, J. Oper. Res. Soc., 38, 423, 10.1057/jors.1987.70 Boschetti, 2003, The two-dimensional finite bin packing problem, Part I: new lower bounds for the oriented case, 4OR, 1, 27 Boschetti, 2003, The two-dimensional finite bin packing problem, Part II: new lower and upper bounds, 4OR, 2, 135 Caprara, 2004, On the two-dimensional knapsack problem, Oper. Res. Lett., 32, 5, 10.1016/S0167-6377(03)00057-9 Chen, 1995, An analytical model for the container loading problem, European J. Oper. Res., 80, 68, 10.1016/0377-2217(94)00002-T Coffmann, 1997, Approximation algorithms for bin packing: a survey, 46 Csirik, 1998, On-line packing and covering problems, 147 Dell’Amico, 2002, A lower bound for the non-oriented two-dimensional bin packing problem, Discrete Appl. Math., 118, 13, 10.1016/S0166-218X(01)00253-0 Fekete, 2001, New classes of lower bounds for the bin packing problem, Math. Programming, 91, 11, 10.1007/s101070100243 S.P. Fekete, J. Schepers, An exact algorithm for higher-dimensional orthogonal packing. Oper. Res., to appear. Friesen, 1986, Variable sized bin packing, SIAM J. Comput., 15, 222, 10.1137/0215016 Gilmore, 1961, A linear programming approach to the cutting stock problem, Oper. Res., 9, 849, 10.1287/opre.9.6.849 Gilmore, 1963, A linear programming approach to the cutting stock problem—part II, Oper. Res., 13, 94, 10.1287/opre.13.1.94 Hopper, 2002, An empirical study of meta-heuristics applied to 2D rectangular packing problem, Studia Inform., 2 ILOG, CPLEX 7.0, Reference Manual, ILOG, S.A., France, 2000. Kupke, 1998 Lodi, 1999, Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems, INFORMS J. Comput., 11, 345, 10.1287/ijoc.11.4.345 Lodi, 2002, Recent advances on two-dimensional bin packing problems, Discrete Appl. Math., 123, 379, 10.1016/S0166-218X(01)00347-X Martello, 2000, The three-dimensional bin packing problem, Oper. Res., 48, 256, 10.1287/opre.48.2.256.12386 Martello, 1990 Martello, 1998, Exact solution of the two-dimensional finite bin packing problem, Management Sci., 44, 388, 10.1287/mnsc.44.3.388 M. Monaci, Algorithms for packing and scheduling problems, Ph.D. Thesis, University of Bologna, 2002. Mukhacheva, 1993, Linear programming for cutting problems, Internat. J. Software Eng. Knowledge Eng., 3, 463, 10.1142/S0218194093000240 H. Onodera, Y. Taniguchi, K. Tmaru, Branch-and-bound placement for building block layout, 28th ACM/IEEE Design Automation Conference, 1991, pp. 433–439. Pisinger, 1995, An expanding-core algorithm for the exact 0-1 knapsack problem, European J. Oper. Res., 87, 175, 10.1016/0377-2217(94)00013-3 D. Pisinger, M.M. Sigurd, Using decomposition techniques and constraint programming for solving the two-dimensional bin packing problem, Technical Report DIKU-03/01, Department of Computer Science, University of Copenhagen, Denmark, 2002. S. Thienel, ABACUS—A Branch-And-CUt System, Ph.D. Thesis, Universität zu Köln, 1995. Williams, 1999