{"ID":2823698,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24785","arxiv_id":"2512.24785","title":"A first approximation algorithm for the Bin Packing Problem with Setups","abstract":"We study constant-factor approximation algorithms for the Bin Packing Problem with Setups (BPPS). First, we show that adaptations of classical BPP heuristics can have arbitrarily poor worst-case performance on BPPS instances. Then, we propose a two-phase heuristic for the BPPS that applies an α-approximation algorithm for the BPP to the items of each class and then performs a merging phase on the open bins. We prove that this heuristic is a 2 α-approximation algorithm for the BPPS.","short_abstract":"We study constant-factor approximation algorithms for the Bin Packing Problem with Setups (BPPS). First, we show that adaptations of classical BPP heuristics can have arbitrarily poor worst-case performance on BPPS instances. Then, we propose a two-phase heuristic for the BPPS that applies an α-approximation algorithm...","url_abs":"https://arxiv.org/abs/2512.24785","url_pdf":"https://arxiv.org/pdf/2512.24785v1","authors":"[\"Roberto Baldacci\",\"Fabio Ciccarelli\",\"Stefano Coniglio\",\"Valerio Dose\",\"Fabio Furini\"]","published":"2025-12-31T11:10:24Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}