SIAM Journal on Computing
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Branch-and-bound placement for building block layout
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Management Science
A lower bound for the non-oriented two-dimensional bin packing problem
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems
INFORMS Journal on Computing
The Three-Dimensional Bin Packing Problem
Operations Research
Recent advances on two-dimensional bin packing problems
Discrete Applied Mathematics
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
On the two-dimensional Knapsack Problem
Operations Research Letters
INFORMS Journal on Computing
A new heuristic algorithm for rectangle packing
Computers and Operations Research
Solving the variable size bin packing problem with discretized formulations
Computers and Operations Research
Heuristic approaches for the two- and three-dimensional knapsack packing problem
Computers and Operations Research
Heuristics for the variable sized bin-packing problem
Computers and Operations Research
Multi-dimensional bin packing problems with guillotine constraints
Computers and Operations Research
Efficient lower bounds and heuristics for the variable cost and size bin packing problem
Computers and Operations Research
Relaxations and exact solution of the variable sized bin packing problem
Computational Optimization and Applications
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Journal of Network and Computer Applications
Models for the two-dimensional two-stage cutting stock problem with multiple stock size
Computers and Operations Research
Computers and Operations Research
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The two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins. The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles. We present an integer-linear formulation of the 2DVSBPP and introduce several lower bounds for the problem. By using Dantzig-Wolfe decomposition we are able to obtain lower bounds of very good quality. The LP-relaxation of the decomposed problem is solved through delayed column generation, and an exact algorithm based on branch-and-price is developed. The paper is concluded with a computational study, comparing the tightness of the various lower bounds, as well as the performance of the exact algorithm for instances with up to 100 items.