SIAM Journal on Computing
An efficient approximation scheme for variable-sized bin packing
SIAM Journal on Computing
Bin packing with divisible item sizes
Journal of Complexity
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
An improved lower bound for the bin packing problem
Discrete Applied Mathematics
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
Solving the variable size bin packing problem with discretized formulations
Computers and Operations Research
The two-dimensional bin packing problem with variable bin sizes and costs
Discrete Optimization
Worst-case analysis of the subset sum algorithm for bin packing
Operations Research Letters
Heuristics for the variable sized bin-packing problem
Computers and Operations Research
Hybrid algorithms for the variable sized bin packing problem
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
Variable neighbourhood search for the variable sized bin packing problem
Computers and Operations Research
Efficient algorithms for real-life instances of the variable size bin packing problem
Computers and Operations Research
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We address a generalization of the classical one-dimensional bin packing problem with unequal bin sizes and costs. We investigate lower bounds for this problem as well as exact algorithms. The main contribution of this paper is to show that embedding a tight network flow-based lower bound, dominance rules, as well as an effective knapsack-based heuristic in a branch-and-bound algorithm yields very good performance. In addition, we show that the particular case with all weight items larger than a third the largest bin capacity can be restated and solved in polynomial-time as a maximum-weight matching problem in a nonbipartite graph. We report the results of extensive computational experiments that provide evidence that large randomly generated instances are optimally solved within moderate CPU times.