{"paper":{"title":"Approximation algorithms for the three-machine proportionate mixed shop scheduling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"An Zhang, Bing Su, Guanqun Ni, Guohui Lin, Jianming Dong, Longcheng Liu, Randy Goebel, Yong Chen, Yue Luo","submitted_at":"2018-09-15T17:16:26Z","abstract_excerpt":"A mixed shop is a manufacturing infrastructure designed to process a mixture of a set of flow-shop jobs and a set of open-shop jobs. Mixed shops are in general much more complex to schedule than flow-shops and open-shops, and have been studied since the 1980's. We consider the three machine proportionate mixed shop problem denoted as $M3 \\mid prpt \\mid C_{\\max}$, in which each job has equal processing times on all three machines. Koulamas and Kyparisis [{\\it European Journal of Operational Research}, 243:70--74,2015] showed that the problem is solvable in polynomial time in some very special c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05745","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":""},"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"}