Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
New Bounds for Variable-Sized Online Bin Packing
SIAM Journal on Computing
The Three-Dimensional Bin Packing Problem
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
The generalized bin packing problem under uncertainty
ICACM'11 Proceedings of the 2011 international conference on Applied & computational mathematics
Variable neighbourhood search for the variable sized bin packing problem
Computers and Operations Research
Communication: The stochastic generalized bin packing problem
Discrete Applied Mathematics
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We consider the variable cost and size bin packing problem, a generalization of the well-known bin packing problem, where a set of items must be packed into a set of heterogeneous bins characterized by possibly different volumes and fixed selection costs. The objective of the problem is to select bins to pack all items at minimum total bin-selection cost. The paper introduces lower bounds and heuristics for the problem, the latter integrating lower and upper bound techniques. Extensive numerical tests conducted on instances with up to 1000 items show the effectiveness of these methods in terms of computational effort and solution quality. We also provide a systematic numerical analysis of the impact on solution quality of the bin selection costs and the correlations between these and the bin volumes. The results show that these correlations matter and that solution methods that are un-biased toward particular correlation values perform better.