Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems
| Autor: | Maxence Delorme, Manuel Iori |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
050210 logistics & transportation
021103 operations research Bin packing problem Variable size 05 social sciences 0211 other engineering and technologies General Engineering 02 engineering and technology Pseudo-polynomial time 0502 economics and business Applied mathematics Equivalence relation Stock (geology) Mathematics |
| Zdroj: | INFORMS Journal on Computing. 32:101-119 |
| ISSN: | 1526-5528 1091-9856 |
| Popis: | We study pseudo-polynomial formulations for the classical bin packing and cutting stock problems. We first propose an overview of dominance and equivalence relations among the main pattern-based and pseudo-polynomial formulations from the literature. We then introduce reflect, a new formulation that uses just half of the bin capacity to model an instance and needs significantly fewer constraints and variables than the classical models. We propose upper- and lower-bounding techniques that make use of column generation and dual information to compensate reflect weaknesses when bin capacity is too high. We also present nontrivial adaptations of our techniques that solve two interesting problem variants, namely the variable-sized bin packing problem and the bin packing problem with item fragmentation. Extensive computational tests on benchmark instances show that our algorithms achieve state of the art results on all problems, improving on previous algorithms and finding several new proven optimal solutions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|