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The system comprises two sequential machines with a transition period between them and a setup time after completion of each job on the second machine. We first construct an exact algorithm that maximizes the profit. Since this problem is NP-hard, we construct a fully polynomial time approximation scheme (FPTAS) to address it and evaluate its computational complexity.<\/jats:p>","DOI":"10.1051\/ro\/2020006","type":"journal-article","created":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T09:47:16Z","timestamp":1580291236000},"page":"S727-S740","source":"Crossref","is-referenced-by-count":3,"special_numbering":"Supplement","title":["An FPTAS for just-in-time scheduling of a flow shop manufacturing process with different service quality levels"],"prefix":"10.1051","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7950-0785","authenticated-orcid":false,"given":"Amir","family":"Elalouf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s10951-007-0030-z","volume":"10","author":"Choi","year":"2007","journal-title":"J. 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