{"paper":{"title":"An open, reproducible branch-and-cut for the capacitated profitable tour problem: a component study","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.MS"],"primary_cat":"math.OC","authors_text":"Simon Spoorendonk","submitted_at":"2026-07-05T20:47:08Z","abstract_excerpt":"We present an open, reproducible branch-and-cut (B&C) algorithm for the capacitated profitable tour problem (CPTP) and its open s-t path variant, the capacity-constrained elementary shortest-path problem. The solver re-implements the formulation and cut families of Jepsen et al. (2014) on a fully open mixed-integer programming stack (HiGHS; Huangfu and Hall, 2018), and adds bound-based preprocessing, domain propagation, and reduced-cost variable fixing. We claim no new method; the contribution is twofold. First, an open, reproducible artifact: to our knowledge the first branch-and-cut for this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04497","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04497/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}