{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/branch-and-price-for-submodular-bin-packing","title":"Branch and Price for Submodular Bin Packing","arxiv_id":"2204.00320","date":"2022-04-01","proceeding":null,"authors":["Liding Xu","Claudia D'Ambrosio","Sonia Haddad Vanier","Emiliano Traversi"],"abstract":"The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques.","url_abs":"https://arxiv.org/abs/2204.00320v2","url_pdf":"https://arxiv.org/pdf/2204.00320v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"branch-and-price-for-submodular-bin-packing","repo_url":"https://github.com/lidingxu/cbp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}