New Lower Bounds for the Three-dimensional Orthogonal Bin Packing Problem

In this paper, we consider the three-dimensional orthogonal bin packing problem, which is a generalization of the well-known bin packing problem. We present new lower bounds for the problem from a combinatorial point of view and demonstrate that they theoretically dominate all previous results from the literature. The comparison is also done concerning asymptotic worst-case performance ratios. The new lower bounds can be more efficiently computed in polynomial time. In addition, we study the non-oriented model, which allows items to be rotated.

[1]  Jean-Marie Bourjolly,et al.  An analysis of lower bound procedures for the bin packing problem , 2005, Comput. Oper. Res..

[2]  Paolo Toth,et al.  Lower bounds and reduction procedures for the bin packing problem , 1990, Discret. Appl. Math..

[3]  Gilbert Laporte,et al.  Capacitated Vehicle Routing on Trees , 1991, Oper. Res..

[4]  Bassem Jarboui,et al.  A new destructive bounding scheme for the bin packing problem , 2010, Ann. Oper. Res..

[5]  Jacques Carlier,et al.  New data-dependent dual-feasible functions and lower bounds for a two-dimensional bin-packing problem , 2009 .

[6]  Sándor P. Fekete,et al.  A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems , 2004, Math. Methods Oper. Res..

[7]  Teodor Gabriel Crainic,et al.  Computing the asymptotic worst-case of bin packing lower bounds , 2007, Eur. J. Oper. Res..

[8]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[9]  Daniele Vigo,et al.  The Three-Dimensional Bin Packing Problem , 2000, Oper. Res..

[10]  Jacques Carlier,et al.  Computing redundant resources for the resource constrained project scheduling problem , 2007, Eur. J. Oper. Res..

[11]  Andrea Lodi,et al.  Two-dimensional packing problems: A survey , 2002, Eur. J. Oper. Res..

[12]  Antoine Jouglet,et al.  A new lower bound for the non-oriented two-dimensional bin-packing problem , 2007, Oper. Res. Lett..

[13]  S. Martello,et al.  Exact Solution of the Two-Dimensional Finite Bon Packing Problem , 1998 .

[14]  Jacques Carlier,et al.  New reduction procedures and lower bounds for the two-dimensional bin packing problem with fixed orientation , 2007, Comput. Oper. Res..

[15]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[16]  Sándor P. Fekete,et al.  New classes of fast lower bounds for bin packing problems , 2001, Math. Program..

[17]  Marco A. Boschetti.  New lower bounds for the three-dimensional finite bin packing problem , 2004, Discret. Appl. Math..

[18]  Cláudio Alves,et al.  A survey of dual-feasible and superadditive functions , 2010, Ann. Oper. Res..

[19]  David S. Johnson,et al.  Near-optimal bin packing algorithms , 1973 .

[20]  El-Ghazali Talbi,et al.  New lower bounds for bin packing problems with conflicts , 2010, Eur. J. Oper. Res..

[21]  Alberto Caprara,et al.  Bidimensional packing by bilinear programming , 2005, Math. Program..

[22]  Teodor Gabriel Crainic,et al.  Efficient lower bounds and heuristics for the variable cost and size bin packing problem , 2011, Comput. Oper. Res..

[23]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[24]  Daniele Vigo,et al.  A lower bound for the non-oriented two-dimensional bin packing problem , 2002, Discret. Appl. Math..

[25]  Rob van Stee,et al.  New Bounds for Multidimensional Packing , 2003, Algorithmica.

[26]  George S. Lueker,et al.  Bin packing with items uniformly distributed over intervals [a,b] , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[27]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[28]  Richard M. Karp,et al.  An efficient approximation scheme for the one-dimensional bin-packing problem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[29]  Jens Vygen,et al.  The Book Review Column1 , 2020, SIGACT News.

[30]  G. S. Lueker,et al.  Bin packing can be solved within 1 + ε in linear time , 1981 .

[31]  Cláudio Alves,et al.  Theoretical investigations on maximal dual feasible functions , 2010, Oper. Res. Lett..

[32]  Armin Scholl,et al.  Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem , 1997, Comput. Oper. Res..

[33]  David Pisinger,et al.  Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem , 2007, INFORMS J. Comput..