Pseudo-polynomial formulations for the bin packing problem with minimum color fragmentation
Barkel,Mathijs Delorme,Maxence Malaguti,Enrico Monaci,Michele
Barkel,Mathijs
Delorme,Maxence
Malaguti,Enrico
Monaci,Michele
Abstract
We study the bin packing problem with minimum color fragmentation (BPPMCF), an extension of the well-known bin packing problem (BPP) in which a given set of weighted colored items has to be packed into a set of identical capacitated bins. Differently from the BPP, in this problem, the number of available bins is fixed and the objective is to minimize the total number of times that colors appear in the bins. After reviewing the integer linear programming models proposed in the literature, we show that one of these models, a flow formulation, shares several features with existing BPP flow formulations. We then exploit these ideas to develop three new flow formulations for the BPPMCF and demonstrate their effectiveness on a set of benchmark instances. We also outline theoretical and empirical dominance relations between the studied flow models. Finally, we empirically show how the number of color fragmentations varies when the number of available bins changes.
Description
Date
2025-08
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Publisher
Research Projects
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Keywords
bin packing, color fragnentation, integer programming, arcflow formulation
Citation
Barkel, M, Delorme, M, Malaguti, E & Monaci, M 2025, 'Pseudo-polynomial formulations for the bin packing problem with minimum color fragmentation', INFORMS Journal on Computing. https://doi.org/10.1287/ijoc.2024.0972