Lower bounds and reduction procedures for the bin packing problem
Discrete Applied Mathematics - Combinatorial Optimization
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Management Science
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
New lower bounds for the three-dimensional finite bin packing problem
Discrete Applied Mathematics
An analysis of lower bound procedures for the bin packing problem
Computers and Operations Research
Bin packing with items uniformly distributed over intervals [a,b]
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Bidimensional packing by bilinear programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Fast lifting procedures for the bin packing problem
Discrete Optimization
A new constraint programming approach for the orthogonal packing problem
Computers and Operations Research
New resolution algorithm and pretreatments for the two-dimensional bin-packing problem
Computers and Operations Research
An Exact Algorithm for the Two-Dimensional Strip-Packing Problem
Operations Research
Computers and Operations Research
New Stabilization Procedures for the Cutting Stock Problem
INFORMS Journal on Computing
LP bounds in various constraint programming approaches for orthogonal packing
Computers and Operations Research
General properties of staircase and convex dual feasible functions
WSEAS Transactions on Information Science and Applications
MPQ-trees for the Orthogonal Packing Problem
Journal of Mathematical Modelling and Algorithms
A new exact method for the two-dimensional bin-packing problem with fixed orientation
Operations Research Letters
A new lower bound for the non-oriented two-dimensional bin-packing problem
Operations Research Letters
Theoretical investigations on maximal dual feasible functions
Operations Research Letters
Conservative scales in packing problems
OR Spectrum
A New Graph-Theoretical Model for the Guillotine-Cutting Problem
INFORMS Journal on Computing
Improved bounds for hybrid flow shop scheduling with multiprocessor tasks
Computers and Industrial Engineering
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The two-dimensional bin-packing problem (2BP) consists of minimizing the number of identical rectangles used to pack a set of smaller rectangles. In this paper, we propose new lower bounds for 2BP in the discrete case. They are based on the total area of the items after application of dual feasible functions (DFF). We also propose the new concept of data-dependent dual feasible functions (DDFF), which can also be applied to a 2BP instance. We propose two families of Discrete DFF and DDFF and show that they lead to bounds which strictly dominate those obtained previously. We also introduce two new reduction procedures and report computational experiments on our lower bounds. Our bounds improve on the previous best results and close 22 additional instances of a well-known established benchmark derived from literature.