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Res."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> In this paper, we investigate a scheduling problem with optional job rejection in a proportionate flow shop setting, where the job processing times are machine independent. A solution to our problem is characterized by (i) partitioning the set of jobs into a set of accepted jobs and a set of rejected jobs, and (ii) scheduling the accepted jobs in a proportionate flow shop setting. The aim is to find a solution to minimize the sum of total weighted late work of the accepted jobs and total rejection cost of the rejected jobs. When all jobs share a common due date, we show that the single-machine case is [Formula: see text]-hard by reduction from the Subset Sum problem. When the operations of all jobs have equal processing times, we solve the case in [Formula: see text] time by reducing it into a linear assignment problem. For the general problem, we first provide a pseudo-polynomial-time algorithm via the dynamic programming method, then we convert it into a fully polynomial time approximation scheme. As a byproduct, we also resolve an open question in the literature. <\/jats:p>","DOI":"10.1142\/s0217595923500239","type":"journal-article","created":{"date-parts":[[2023,6,10]],"date-time":"2023-06-10T05:24:06Z","timestamp":1686374646000},"source":"Crossref","is-referenced-by-count":6,"title":["Minimizing Total Weighted Late Work in a Proportionate Flow Shop with Job Rejection"],"prefix":"10.1142","volume":"41","author":[{"given":"Ren-Xia","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou 450007, People\u2019s Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shi-Sheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou 450007, People\u2019s Republic of 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